Abstracts of the 50th DDA Meeting (Boulder, CO)

American Astronomical Society

June, 2019

100 — Dynamics on Asteroids

100.01 — Simulations of a Synthetic EurybatesCollisional Family

Timothy Holt1; David Nesvorny2; Jonathan Horner1;Rachel King1; Brad Carter1; Leigh Brookshaw1

1 Centre for Astrophysics, University of Southern Queensland(Longmont, Colorado, United States)

2 Southwest Research Institute (Boulder, Connecticut, UnitedStates)

Of the six recognized collisional families in the Jo-vian Trojan swarms, the Eurybates family is thelargest, with over 200 recognized members. Locatedaround the Jovian L4 Lagrange point, librations ofthe members make this family an interesting studyin orbital dynamics. The Jovian Trojans are thoughtto have been captured during an early period of in-stability in the Solar system. The parent body of thefamily, 3548 Eurybates is one of the targets for theLUCY spacecraft, and our work will provide a dy-namical context for the mission. Recent modelinghas suggested that some members of the family haveescaped the swarm on a time scale comparable to theage of the Solar system. The aim of the present workis to provide a dynamical simulation of the early his-tory of the Eurybates family to explain its origins.Our modeling involved the creation of a 1000 mem-ber synthetic fragment cloud, centered on 3548 Eury-bates as the parent body. The synthetic family wascreated using the Gauss equations, with a 100m/sescape velocity and random ejection angles. The dy-namical evolution of the synthetic cloud was mod-eled using high precision n-body simulations withthe REBOUND code on a variety of time scales. Fromthese simulations, we find that the synthetic familystabilizes into the modern observed libration patternwithin a relatively short time span. By using statisti-cal comparisons with the observed family members,our results provide the first estimate of the minimumage of the Eurybates family. The Eurybates colli-sional family also provides a unique opportunity toexamine the dynamical evolution of the fragments of

break-up event around a Lagrange point.

100.02 — High-Fidelity Testing of Binary AsteroidFormation with Applications to 1999 KW4

Alex B. Davis1; Daniel Scheeres11 Aerospace Engineering Sciences, University of Colorado Boulder

(Boulder, Colorado, United States)

The commonly accepted formation process for asym-metric binary asteroids is the spin up and eventualfission of rubble pile asteroids as proposed by Walsh,Richardson and Michel (Walsh et al., Nature 2008)and Scheeres (Scheeres, Icarus 2007). In this theorya rubble pile asteroid is spun up by YORP until itreaches a critical spin rate and experiences a massshedding event forming a close, low-eccentricitysatellite. Further work by Jacobson and Scheeresused a planar, two-ellipsoid model to analyze theevolutionary pathways of such a formation eventfrom the moment the bodies initially fission (Jacob-son and Scheeres, Icarus 2011). They provide statis-tical analysis on the conditions for the bodies to en-ter a stable orbit, reimpact, escape, or fission further,forming a triple system. The planar, two-ellipsoidmodel used in this study ignores higher order massparameters which have been shown to have signif-icant influence on the dynamics of bodies in closeproximity. To understand the effect of these terms,we apply recently developed high-fidelity, computa-tionally efficient full two-body problem (F2BP) mod-elling tools, which allow us to represent each body asan arbitrary mass distribution in three-dimensionalspace. With this tool we perform a Monte Carlo anal-ysis for the evolution of an asymmetric binary sys-tem from the point of fission until the system set-tles into a stable state or evolves further. Duringthe dynamical simulations standard analytic meth-ods for assessing asteroid breakup are used to assessthe spin rate of the system; the simulation is haltedin the case of fission, reimpact, or escape. We select1999 KW4 as a test case because the shape, geome-try, and dynamics of the system have been well char-acterized and provide the knowledge necessary for

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such a high-fidelity analysis. At the end of this pro-cess we perform statistical analysis of the conditionsfor binary evolutionary pathway and contrast our re-sults with those of Jacobson and Scheeres.

100.03 — The Dynamical Surface Environment ofTumbling Asteroids

Daniel Brack1; Jay McMahon11 University of Colorado Boulder (Boulder, Colorado, United States)

Non-principal axis rotating asteroids, or tumblingasteroids, are a small subset of known asteroids, ob-served both in the main asteroid belt and in near-Earth orbit. In non-principal axis rotation a body’sangular velocity vector is not aligned with any of itsprincipal axes, causing fluctuations in the evolutionof the angular velocity direction and magnitude ofthe body. For tumbling asteroids such fluctuationslead to a dynamic environment on their surfaces.These dynamics manifest in an ever-changing geopo-tential, with surface accelerations and surface slopeschanging magnitudes and directions. Research hasshown that tumbling is not a stable state for an aster-oid and that it tends to dissipate throughout the as-teroid’s lifetime. However, the existence of tumblingasteroids does point to some de-stabilizing mecha-nisms such as planetary flybys and the Yarkovsky–O’Keefe–Radzievskii–Paddack effect. The former be-ing an immediate impulsive mechanism and the lat-ter perturbing an asteroid’s rotation over millennia.We investigate the surface environment of several as-teroids, both observed and hypothetical, combiningtheir angular velocity vectors and the shape modelsto examine the fluctuations in surface accelerationsand surface slopes. In addition, we examine motiontrends on the surfaces of such bodies, seeking to un-derstand what would happen to particles placed onthe surface as the asteroid tumbles and as the tum-bling state suddenly changes. The sudden change intumbling state of asteroid (99942) Apophis is exam-ined in particular due to its expected flyby of Earthin 2029 and possibility of mass shedding after to theencounter.

100.04 — Disassociation Energies for Rubble PileAsteroids

Daniel Scheeres11 Smead Aerospace Engineering Sciences, University of Colorado

Boulder (Boulder, Colorado, United States)

We study the disassociation of rubble pile asteroidsunder rapid spin rates and the resultant asteroidpairs and clusters that can arise as a function of

the system angular momentum and energy. To dothis rigorous results from Celestial Mechanics areapplied to determine the Hill Stability of a rubblepile asteroid spun fast enough to disassociate into itscomponent pieces. Depending on the overall energyand angular momentum in the system, the numberof components that can escape will be limited. Ifthe rubble pile consists of N components, the en-ergy required for different combinations of compo-nents to escape can be related to the integer partitionsof the number N. If the rubble pile is modeled as asize distribution with a given porosity, the energyrequired to disrupt the system into different clusterscan be reduced to a power series summation. Thistalk reviews the application of Hill Stability theoryto this problem and presents the overall conclusionsand their implications for forming asteroid pairs andclusters.

100.05 — The Dynamics of Surface LaunchedParticles around Bennu

Jay McMahon1; Daniel Scheeres1; Steven R. Chesley2;Andrew S. French1; Daniel Brack1; Davide Farnocchia2;Yu Takahashi2; Pasquale Tricarico3; Erwan Mazarico4;Dante S. Lauretta5

1 Smead Aerospace Engineering Sciences, University of ColoradoBoulder (Boulder, Colorado, United States)

2 JPL (Pasadena, California, United States)3 PSI (Tucson, Arizona, United States)4 NASA Goddard Space Flight Center (Greenbelt, Maryland,

United States)5 University of Arizona (Tucson, Arizona, United States)

The OSIRIS-REx spacecraft has recently discoveredsmall particles being ejected from the surface of thenear-Earth asteroid Bennu. Observations to datehave shown that a number of particles have survivedin orbit for multiple days after leaving the asteroidsurface, while others escape or quickly return to thesurface. This behavior is governed by the complexdynamical environment near the surface of smallasteroids, as well as the constraints on the launch-ing conditions provided by the spacecraft observa-tions. This talk will explore the effects of the differ-ent forces that influence these trajectories, and willdemonstrate the surprising variety of orbits that canbe produced in this environment.

100.06 — Earth’s missing Trojans: Lessons fromMars and the role of radiation forces

Apostolos Christou11 Armagh Observatory and Planetarium (Armagh, Northern Ire-

land, United Kingdom)

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There is renewed interest in the possibility of stableTrojan asteroids of the Earth and observational con-straints from the recent search by the OSIRIS-RExspacecraft allow a population of at least several tensof few-hundred-m-sized such asteroids (Cambioni etal, 2018). These objects may represent leftover ma-terial from the formation and early evolution of theterrestrial planets (Malhotra, 2019).

If primordial terrestrial Trojans do exist, the clos-est analogue population within our solar system isprobably the small retinue of Trojans hosted by Marsat moderate (15-30 deg) inclination, compared to the<10 deg inclination region where long-lived EarthTrojans should exist. Though limited in number,the population of Mars Trojans hints at an intrigu-ing evolutionary history. Their orbits are stronglyclustered, indicating a genetic association to one ofthe largest Trojans, (5261) Eureka. The bulk physi-cal properties and orbit distribution of these aster-oids as well as the existence of relatively large but or-bitally isolated Trojans, is most readily explained bythe long-term action of solar-radiation-driven forcesoperating at 1.5 au from the Sun. In this scenario,YORP is primarily responsible for creating new as-teroids while Yarkovsky determines their orbit dis-tribution, stability and rate of escape from the Trojanclouds (Cuk et al, 2015; Christou et al, 2019). Inter-estingly, Trojan longevity depends as much in the di-rection of the Yarkovsky acceleration as in the mag-nitude.

To better understand how the example of Marsmight apply to an extant population of Earth Trojans,I carry out test particle simulations over timescalesof a few Gyr, relevant to Yarkovsky-driven evolu-tion. In the process, I confirm and extend the ear-lier result by Cuk et al (2012) that horseshoe orbitsare as likely to survive as tadpoles under planetaryperturbations. In this presentation I will show howthe inclusion of Yarkovsky affects the residence timeof Earth trojan and horseshoe asteroids compared topoint-mass forces alone. I will then discuss whetheran old population of Earth coorbitals can be accom-modated under the new dynamical constraints andhow they might affect the NEA population in thevicinity of Earth’s orbit.

100.07 — Radar Astrometry of Near-EarthAsteroids from the Arecibo Observatory:2018-2019

Flaviane Venditti1,2; Sean Marshall1,2; AnneVirkki1,2; Patrick Taylor3; Jon Giorgini4; LuisaZambrano-Marin1,2; Edgard Rivera-Valentin3; SriramBhiravarasu3; Betzaida Aponte3

1 Arecibo Observatory (Arecibo, USA, Puerto Rico)2 University of Central Florida (Orlando, Florida, United States)3 Lunar and Planetary Institute (Houston, Texas, United States)4 Jet Propulsion Laboratory (Pasadena, California, United States)

Arecibo Observatory has the world’s most power-ful planetary radar system, which provides ground-based observations whose quality could only be ex-ceeded with a spacecraft flyby. It allows one to char-acterize near-Earth objects (NEOs) in terms of size,shape, spin, and surface properties, and to discovernatural satellites that form binary and triple asteroidsystems. In addition, radar astrometry is a valuabletool for orbit refinement, providing precise measure-ments that can significantly improve the accuracy oforbit determination.

We present an overview of radar astrometric ob-servations obtained using the Arecibo planetaryradar system since January 2018. Especially fornewly discovered objects, that usually have large or-bit uncertainties, Doppler and/or range measure-ments can prevent the object from being lost and re-quiring re-discovery in the future. We’ll present alist of targets that had their orbits secured after radarobservations, and an evaluation of how much radarhelped to reduce their orbital uncertainties.

Every year about 40-60 recently discovered NEOsare observed at Arecibo. From January 1, 2018 toMarch 31, 2019, 90 NEOs were observed at Arecibo,including a comet. A total of 44 were newly discov-ered objects, almost half of the observed targets, and33 are designated as potentially hazardous asteroids(PHAs). At least one Doppler measurement was ob-tained for each target, plus at least one range mea-surement for 55 of them.

Radar offers the great advantage of controlling theproperties of the transmitted signal. The changes inthe received echo compared to the transmitted signalprovides clues about the characteristics of the object.The time delay gives information about the distanceto a target with precision as fine as meters, and theDoppler-shifted frequency of the echo provides theradial velocity with precision as fine as mm/s, mak-ing it possible to detect even small changes in theorbit due to perturbations, such as the nongravita-tional acceleration generated by the Yarkovsky effect.Radar astrometry can also quickly eliminate impactfalse alarms with the improvement of estimates of anasteroid’s orbital elements. Therefore, radar astrom-etry is crucial for planetary defense.

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100.08 — On the Anomalous Acceleration of1I/2017 U1 ‘Oumuamua

Darryl Seligman1; Gregory Laughlin1; KonstantinBatygin2

1 Astronomy, Yale University (New Haven, Connecticut, UnitedStates)

2 Caltech (Pasadena, California, United States)

We show that the P ∼ 8 h photometric period andthe astrometrically measured Ang ∼ 2.5 × 10−4 cms−2 non-gravitational acceleration (at r ∼ 1.4 AU)of the interstellar object 1I/2017 (‘Oumuamua) canbe explained by a nozzle-like venting of volatileswhose activity migrated to track the sub-solar loca-tion on the object’s surface. Adopting the assump-tion that ‘Oumuamua was an elongated a×b×c ellip-soid, this model produces a pendulum-like rotationof the body and implies a long semi-axis a ∼ 5 AngP2 / 4π2 ∼ 260 m. This scale agrees with the in-dependent estimates of ‘Oumuamua’s size that stemfrom its measured brightness, assuming an albedoof p ∼ 0.1, appropriate to ices that have undergonelong-duration exposure to the interstellar cosmic rayflux. Using ray-tracing, we generate light curves forellipsoidal bodies that are subject to both physicallyconsistent sub-solar torques and to the time-varyinggeometry of the Sun-Earth-‘Oumuamua configura-tion. Our synthetic light curves display variationsfrom chaotic tumbling and changing cross-sectionalillumination that are consistent with the observa-tions, while avoiding significant secular changes inthe photometric periodicity. If our model is cor-rect, ‘Oumuamua experienced mass loss that wasted∼10% of its total mass during the ∼100 d span ofits encounter with the inner Solar System and hadan icy composition with a very low [C/O] ≲ 0.003.Our interpretation of ‘Oumuamua’s behavior is con-sistent with the hypothesis that it was ejected fromeither the outer regions of a planetesimal disk afteran encounter with an embedded Mp ∼ MNep planetor from an exo-Oort cloud.

101 — Formation, DynamicalEvolution, and Detection ofCircumbinary Planets

101.01 — Circumbinary disks: Planet formation ina dynamically complex environment

Rebecca Martin1; Stephen Lubow2; Jeremy Smallwood1;Alessia Franchini1; Cheng Chen1

1 Department of Physics and Astronomy, University of Nevada, LasVegas (Las Vegas, Nevada, United States)

2 Space Telescope Science Institute (Baltimore, Maryland, UnitedStates)

Circumbinary disks around young stars have beenobserved to be misaligned to the binary orbital plane.A misaligned circumbinary disk evolves towards oneof two states: alignment with the binary orbital planeor polar alignment where the disk is approximatelyperpendicular to the binary orbital plane. With ana-lytic and numerical methods we explore how the bi-nary and the disk properties affect the process. Thedisk evolution has important implications for planetformation around binary star systems.

101.02 — Multi-planet disc interactions in binarysystems

Alessia Franchini1; Rebecca Martin1; Stephen Lubow21 University of Nevada Las Vegas (Las Vegas, Nevada, United

States)2 Space Telescope Science Institute (Baltimore, Maryland, United

States)

Understanding the evolution of multi-planet systemsin binary stars is crucial to explaining observed exo-planet orbital properties. In particular, most massiveextrasolar planets have significantly eccentric orbitsand misalignments of planets very close to their hoststar are quite common. We examine the evolutionof a misaligned multi-planet-disc system around onecomponent of a binary star. We find that planets thatopen gaps in a tilted disk become misaligned withrespect to the disc and to each other. In addition,the planet orbits can become eccentric due to to theKozai-Lidov effect. We find also that the innermostplanet inclination can reach very high values and itsmotion can switch from prograde to retrograde.

101.03 — Using orbital dynamics to detectcircumbinary planets: A novel approach

Veselin Kostov1; William Welsh2; Nader Haghighipour31 NASA GSFC and SETI Institute (Greenbelt, Maryland, United

States)2 San Diego State University (San Diego, California, United States)3 University of Hawaii (Honolulu, Hawaii, United States)

One of Kepler’s most exciting breakthroughs was thediscovery of circumbinary planets. Only about adozen were found, however, leaving a vast gap in ourunderstanding — similar to the state of exoplanet sci-ence when only hot Jupiters were known. TESS, and

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only TESS, will allow us to detect an order of magni-tude more circumbinary planets using a novel tech-nique we have developed and tested: the occurrenceof multiple transits during one conjunction. In ad-dition to enchanting individual-case discoveries andtheir intriguing dynamics, our sample will enablestatistical studies of occurrence rates, formation, andhabitability.

101.04 — Planet migration in circumbinary disksand the boundary of stability

Nader Haghighipour1; Frederic Masset21 Institute for Astronomy, University of Hawaii (Honolulu, Hawaii,

United States)2 Univ. Nacional Autonoma de Mexico (UNAM) (Cuernavaca,

Mexico)

It is widely accepted that circumbinary planets format large distances from their host binaries and un-dergo (substantial) radial migration. It is also wellunderstood that in a circumbinary disk, planets stopmigration at the edge of the disk cavity due to thetidal effect of the binary on the gaseous disk. It hasbeen argued that the latter also corresponds to theboundary of orbital stability, promoting the idea thatcircumbinary planets stop migration at the edge ofthe stability region. To examine this idea, we haveinitiated a large program on understanding planetmigration in circumbinary disk, focusing specificallyon the stopping locations of planet in term of thedisk’s physical properties. We considered the cen-tral binary to be Kepler 38 and planet to be 10 and15 Earth-masses, and carried out a large number ofplanet migration simulations for different values ofthe viscosity and scale height of the disk. In orderfor simulations to be self-consistent, we allowed theplanet interact with the disk and migrate as the diskevolves. As expected, in the majority of cases, planetmigrated inward and stopped at the same locationon the edge of the cavity. This is consistent with thefact that planet migration is independent of the dy-namical history of the system and is solely driven bythe physical properties of the gas. Our simulationsdid not indicate any logical and causal connectionbetween the stopping location of the planet and theboundary of orbital stability around the binary. Wewill present the results of our simulations and dis-cuss their implications in more detail.

102 — Dynamics of Satellites

102.01 — The Gravity Field of the SaturnianSystem and the Orbits of Saturn’s Satellites

Robert Jacobson11 Jet Propulsion Laboratory (Pasadena, California, United States)

Since the end of the Cassini mission we have beenworking on a comprehensive reconstruction of thepath of the Cassini spacecraft from the time of itsinsertion into orbit about Saturn to the time of itsplunge into Saturn’s atmosphere. The reconstruc-tion relies upon a common set of planet and satel-lite ephemerides and gravity parameters. The dataset used to determine the Cassini trajectory, theSaturn orbit, the satellite orbits, and the gravityfield contains: Cassini Doppler tracking, radiomet-ric range, optical navigation and Imaging Scienceobservations, and very-long baseline interferomet-ric (VLBI) observations; Pioneer 11 Doppler tracking;Voyager Doppler tracking, radiometric range, and op-tical navigation observations; Earth-based and Hub-ble Space Telescope satellite astrometry; satellite mu-tual events (occultations and eclipses); Earth-basedplanet and satellite transits; Saturn ring stellar occul-tations observed from the Earth, with the Voyager 2Photopolarimeter (PPS), and the Cassini Visual andInfrared Mapping Spectrometer (VIMS) and Ultra-violet Imaging Spectrograph (UVIS); Saturn ring oc-cultations measured with the Voyager 1 and CassiniRadio Science Subsystem (RSS).

In this paper we discuss our findings concern-ing the masses of the satellites, Saturn, and Saturn’srings, and the gravity fields of Enceladus, Dione,Rhea, Titan, and Saturn. We compare our resultswith those published by the Cassini Gravity ScienceTeam. We also summarize our results concerning thesatellite orbits.

102.02 — And Then There Was One

Thomas Rimlinger1; Douglas P. Hamilton11 Astronomy, University of MD, College Park (Reston, Virginia,

United States)

Titan, Saturn’s lonely giant, is an anomaly, as de-scribed by Rimlinger & Hamilton at the 2018 DDAmeeting. Then, we argued that Titan could haveformed after an initially stable resonant chain ofsatellites underwent dynamical instability. For sim-plicity, we simulated a worst-case scenario withpowerful eccentricity damping forces. We found thatthree-body resonances could be disrupted, but orbitsdid not cross and the bodies did not merge due to the

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stabilizing effects of the damping forces. Now, wesimulate three satellites orbiting Saturn for 160 Myrusing twenty five unique mass configurations withmore realistic eccentricity damping assumptions toexplore instabilities that lead to mergers. We initial-ize the bodies in the 1:2:4 mean motion resonanceand simulate tidal migration of the innermost bodyonly. We augment the migration rate by a factorof ∼10-100, but it remains well within the adiabaticlimit for the resonances of interest. In one of our sce-narios, we damp only the inner body’s eccentricity.We observe instabilities in seven cases, all of whichoccur when the outer body is more massive thanone or both of the inner two; this feature may be anecessary (but insufficient, as per, e.g., the Galileanmoons) condition for instability. In most cases, in-stabilities happen when the radial center of mass q ofthe moons lies well beyond Titan’s current semima-jor axis (∼21 RS). However, in one case, the systemgoes unstable quite early, when q = 19.4 RS. This sim-ulation is promising because it not only verifies thatdynamical instabilities are possible but also suggeststhat they can yield Titan analogues. We are now ex-ploring more realistic eccentricity damping rates thatscale like msr−6, where ms is the mass of the satelliteand r is the distance from Saturn. Although eccen-tricity damping tends to stabilize systems, our ad-ditional damping terms will in general be small, sothey may not cause dramatic differences in our re-sults. We will report on our findings, emphasizingany divergence from our earlier results along withany additional instabilities, especially those that gounstable with q ∼ 21 RS.

102.03 — Evolution of Saturn’s mid-sized moons

Marc Neveu1,2; Alyssa Rhoden31 University of Maryland (College Park, Maryland, United States)2 NASA Goddard Space Flight Center (Greenbelt, Maryland,

United States)3 Southwest Research Institute (Boulder, Colorado, United States)

The orbits of Saturn’s inner mid-sized moons (Mi-mas, Enceladus, Tethys, Dione and Rhea) have beennotably difficult to reconcile with their geology.Here we present recently published numerical sim-ulations (Neveu & Rhoden 2019) coupling thermal,geophysical and simplified orbital evolution for 4.5billion years that reproduce the observed character-istics of their orbits and interiors, provided that theouter four moons are old. Tidal dissipation withinSaturn expands the moons’ orbits over time. Dissipa-tion within the moons decreases their eccentricities,which are episodically increased by moon−moon in-teractions, causing past or present oceans to exist

in the interiors of Enceladus, Dione and Tethys. Incontrast, Mimas’s proximity to Saturn’s rings gener-ates interactions that cause such rapid orbital expan-sion that Mimas must have formed only 0.1−1 billionyears ago if it postdates (or forms together with) therings. The resulting lack of radionuclides keeps itgeologically inactive. These simulations explain theMimas−Enceladus dichotomy, reconcile the moons’orbital properties and geological diversity, and self-consistently produce a recent ocean on Enceladus.These results are sensitive to unknown initial con-ditions, such as the initial orbits and time of forma-tion of the moons. They cover a small fraction ofan immense parameter space, especially regardingthe time and frequency dependence of tidal dissi-pation inside Saturn, the rings’ mass through time,and the number of moons through time (a balancebetween accretion/capture and collisions/ejections).The simplifications in the orbital modeling remain tobe checked with N-body simulations. Despite theselimitations, coupled modeling of interior and orbitalevolution holds the key to unlocking questions suchas the age of Enceladus’ ocean, the properties of Sat-urn’s interior, and the age of its rings.

Reference: Neveu, M. and Rhoden, A.R. (2019)Evolution of Saturn’s mid-sized moons. Nature As-tronomy, doi: 10.1038/s41550-019-0726-y

The code used to carry out these simulations isfreely available at https://github.com/MarcNeveu/IcyDwarf.

102.04 — The Orbital Connection between Mimasand Enceladus

Maryame El Moutamid1; Matija Ćuk2; MatthewTiscareno2

1 Cornell University (Ithaca, New York, United States)2 SETI Institute (Mountain View, California, United States)

The observed internal heating of Saturn’s moonEnceladus is driven by its 2:1 Mean Motion Reso-nance (MMR) with the moon Dione that excites Ence-ladus’ eccentricity. In light of the measurements ofa high dissipation rate of Saturn (Lainey et al., 2012,2017), it is likely that this resonance is currently in(or near) an equilibrium. However, an explanationis still needed for the fact that Enceladus is currentlyin the e-Enceladus sub-resonance of the 2:1 MMR,as other sub-resonances should have been encoun-tered earlier, and would have had a very high prob-ability of resonant capture. In this work, we attemptto explain the capture into the current Enceladus-Dione 2:1 MMR via the hypothesis of a ”handoff”scenario between the Mimas-Enceladus 3:2 MMRand the Mimas-Dione 3:1 MMR. We find that Mimas

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would affect the Enceladus-Dione MMR by i) creat-ing orbital overlap of resonances, during which theeccentricity of Mimas is excited to its current value,ii) pushing Enceladus outward faster and thus con-tributing to its capture into the present MMR. Ourmodel can explain the time scale of less than 100 Myrfor capture of Enceladus into MMR with Dione, de-spite their slow orbital convergence.

102.05 — Dynamical History of the UranianSatellites

Matija Cuk1; Maryame El Moutamid2; MatthewTiscareno1

1 SETI Institute (Mountain View, California, United States)2 Cornell University (Ithaca, New York, United States)

The five Uranian major satellites are not currentlyin any mean motion resonance. Large orbital incli-nation of Miranda, and geological evidence of pasttidal heating of Miranda and Ariel both suggest thatthe system did experience dynamical excitation inthe past, likely due to mutual resonances. In theliterature the favored mechanism for exciting Mi-randa’s inclination is the past 3:1 mean-motion res-onance (MMR) between Miranda and Umbriel (Tit-temore and Wisdom, 1989; Malhotra and Dermott,1990). However, much of the work on Uranian satel-lite dynamics has been done semi-analytically us-ing averaged Hamiltonians, with only specific res-onant terms taken into account. Here we use asymplectic integrator to revisit the last likely reso-nance between Uranus’s major moons, the 5:3 Ariel-Umbriel MMR, previously studied by Tittemore andWisdom (1988). We find that this resonance tendsto be highly chaotic as its sub-resonances are notseparated. Therefore, the Ariel-Umbriel 5:3 MMRshould excite both eccentricities and inclinations ofAriel and Umbriel. Furthermore, we find that Ariel-Miranda secular coupling communicates the reso-nant effects to Miranda, exciting Miranda’s eccentric-ity and inclination. Current low inclinations of Arieland Umbriel imply a period of string tidal damping(probably by Ariel) while these moons were still inthe resonance. Breaking of the resonance is easy inthe absence of such tidal dissipation within Ariel, butappears to be much harder if Ariel is dissipative andkeeps the moons’ eccentricities low. We are currentlyexploring whether interactions with Miranda couldbreak the Ariel-Umbriel resonance and help repro-duce the current system, and we will present the re-sults at the meeting.

102.06 — Orbits and resonances of the regularmoons of Neptune

Marina Brozovic1; Mark Showalter2; Robert Jacobson1;Robert French2; Jack Lissauer3; Imke de Pater4

1 Jet Propulsion Laboratory/California Institute of Technology(Pasadena, California, United States)

2 SETI Institute (Mountain View, California, United States)3 NASA Ames (Moffett Field, California, United States)4 University of California Berkley (Berkley, California, United

States)

The Neptune system consists of seven regular in-ner moons, Triton, Nereid, and five irregular outermoons. Naiad, Thalassa, Despina, Larissa, Galatea,and Proteus are the regular moons discovered bythe Voyager 2 spacecraft during the 1989 flyby ofNeptune. The seventh regular moon – Hippocampwas discovered in 2013 by the Hubble Space Tele-scope (HST). We report integrated orbital fits forthese moons based on the most complete astromet-ric data set to date, with position measurements fromEarth-based telescopes, Voyager 2, and the HST ob-servations covering 1981-2016. Our orbital model ac-counts for the equatorial bulge of Neptune, pertur-bations from the Sun and the planets, and perturba-tions from Triton. We summarize the fits in termsof state vectors, mean orbital elements, and plane-of-sky uncertainties. The orbital uncertainties showthat the positions of the satellites are known withinseveral hundred kilometers until at least 2030. Wefound that the inner-most moons, Naiad and Tha-lassa, are in 73:69 mean motion resonance that alsoinvolves the node of Naiad. This fourth-order reso-nance is unique among the planetary satellites. Weestimated GMs of Naiad and Thalassa of GMNaiad=0.0080±0.0043 km3 s−2 and GMThalassa=0.0236±0.0064km3 s−2. More high precision astrometry is neededto better constrain their masses. We also found thatthe newly discovered Hippocamp is in a 13:11 near-resonance with Proteus and the future astrometry ofHippocamp could reveal the mass of Proteus. TheGMs of Despina, Galatea, and Larissa are more dif-ficult to measure because they are not in any directresonances and their masses are small.

103 — Dirk Brouwer AwardLecture

103.01 — Numerical Methods for AstrophysicalFluid Dynamics

James Stone1

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1 Astrophysical Sciences, Princeton University (Princeton, NJ, NewJersey, United States)

I will discuss recent advances in the developmentof numerical methods for astrophysical fluid dy-namics, especially magnetohydrodynamics (MHD).A variety of different methods are now in commonuse, including structured mesh codes with adap-tive mesh refinement, moving-mesh methods, andparticle-based discretizations. Some comparisonsbetween these methods on astrophysical problems ofinterest, such as MHD instabilities and turbulence,will be described. Extensions of these methods tomore complex physics, such as radiative transfer,chemical and nuclear reaction networks, and gen-eral relativity will be presented. Results from ap-plication of these methods to study problems in ac-cretion physics, turbulence and star formation in theinterstellar medium, and planet formation will bediscussed. The continuing rapid advance in per-formance of modern computer systems (with exas-cale systems planned in the next 2 years) will onlyincrease the range of future discoveries enabled bycomputational fluid dynamics in astrophysics.

104 — Vera Rubin Prize Lecture

104.01 — The LMC vs. the Milky Way

Gurtina Besla11 Astronomy, University of Arizona (Tucson, Arizona, United

States)

Recent advancements in astrometry and in cosmo-logical models of dark matter halo growth have sig-nificantly changed our understanding of the dynam-ics of the Local Group. The most dramatic changesowe to a new picture of the structure and dynam-ics of the Milky Way’s most massive satellite galaxy,the Large Magellanic Cloud (LMC), which is mostlikely on its first passage about the Milky Way andten times larger in mass than previously assumed. Iwill discuss the implications of the LMC’s passage onthe dynamics of the Milky Way and its satellites andprovide a look forward to the era of high precisionastrometry in the Andromeda system.

200 — In Honor of theContributions of Andrea Milani

200.01 — The Dynamical Evolution of AsteroidFamilies

William Bottke1; David Vokrouhlicky2

1 Southwest Research Institite (Boulder, Colorado, United States)2 Charles University (Prague, Czechia)

One of Andrea Milani’s great interests involved theorigin, evolution, and age of asteroid families. In mytalk, we will discuss recent advances in this topic,how well our current family evolution models com-pare to observations/constraints, how certain fam-ilies may be linked to asteroids observed by space-craft, and the prospects for specific families to pro-duce asteroid showers.

A key example in this talk will be the Flora fam-ily. It was formed from the catastrophic disruptionof a diameter D > 150 km parent body, and it dom-inates the innermost main belt region. Flora familymembers, when pushed onto planet-crossing orbits,also have relatively high probabilities of striking theEarth, Moon, and Mars. To quantify what happened,we used collisional and dynamical models to trackthe evolution of Flora family members immediate af-ter the family-forming event. We created an initialFlora family and followed test asteroids using a nu-merical code that accounted for planetary perturba-tions and non-gravitational effects (e.g., Yarkovskyand YORP thermal forces). We found that our testFlora family members can reproduce the observedsemimajor axis, eccentricity, and inclination distri-butions of the real family after 1.4 ± 0.3 Ga. Thisage not only reproduces the crater retention age ofFlora-family member (951) Gaspra, but also sampleages returned by Hayabusa from Itokawa, a likely es-caped Flora family member. Additional work showsthat an “asteroid shower” by Flora family memberswas a major source of impactors to both the mid-Proterozoic Earth and Amazonian-era Mars, withpotentially interesting implications for each world interms of the evolution of their biospheres.

We have also done comparable work on the Eu-lalia and New Polana families, likely sources for sam-ple return targets Bennu and Ryugu. Intriguingly,like Itokawa, the largest craters on these small worldsyield crater retention ages consistent with the esti-mated dynamical ages of the source families. Col-lectively, these results imply that many small bod-ies are less susceptible to resurfacing processes viaYORP spin-up mechanisms than previous thought,with ”stochastic YORP” a possible means to havemany asterioids avoid mass shedding events.

200.02 — New advances on chaotic orbitdetermination

Federica Spoto1; Daniele Serra21 Observatoire de la Côte d’Azur (Nice, France)2 University of Pisa (Pisa, Italy)

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Chaotic orbit determination intervenes in many prac-tical problems, such as the chaotic rotation state of acelestial body, the chaotic orbit of a planet-crossingasteroid experiencing many close approaches, or thechaotic orbit of a spacecraft orbiting a giant planetsystem undergoing many close encounters with itssatellites. Chaotic dynamical systems are character-ized by the existence of a predictability horizon, con-nected to its Lyapounov time, beyond which the pre-diction of the state starting from the initial state of thesystem loses its meaning. Spoto and Milani (2016)apply the differential corrections algorithm for thedetermination of an orbit and of a dynamical param-eter of a simple discrete system, the standard map.They define a computability horizon, a time limit be-yond which numerical calculations are affected bynumerical instability, and gives a formula for ap-proximating its value.

We test, in the same case of the standard map,the constrained multi-arc method with the goal ofpushing forward the computability horizon inher-ent in the least squares orbit determination (Serra,Spoto and Milani 2018). This method entails the de-termination of an orbit of a dynamical system whenobservations are grouped in separate observed arcs.For each arc a set of initial conditions is determinedand during the orbit determination process all sub-sequent arcs are constrained to belong to the sametrajectory. We show that the use of these techniquesin place of the standard least-squares method hassignificant advantages: not only can we perform ac-curate numerical calculations well beyond the com-putability horizon, in particular, the constrainedmulti-arc strategy improves considerably the deter-mination of the dynamical parameter.

200.03 — Planetary close encounters: an analyticalapproach

Giovanni Valsecchi1,21 IAPS-INAF (Roma, Italy)2 IFAC-CNR (Sesto Fiorentino, Italy)

Close encounters with the planets play an impor-tant role in the dynamical evolution of objects inplanet-crossing orbits. This subject has been most of-ten dealt with using massive numerical integrations;however, some useful insight can be obtained usingan analytic approach, at the price of having to treatthe problem in a simplified version of the restricted3-body problem. This presentation addresses someissues related to the motion of strongly scatteredsmall bodies in the outer planetary region.

200.04 — The tale of three small impactingasteroids

Davide Farnocchia1; Steven R. Chesley1; Paul W.Chodas1; Eric Christensen2; Richard A. Kowalski2; Pe-ter G. Brown3; Peter Jenniskens4

1 Jet Propulsion Laboratory, California Institute of Technology(Pasadena, California, United States)

2 University of Arizona (Tucson, Arizona, United States)3 University of Western Ontario (London, Ontario, Canada)4 SETI Institute (Moffett Field, California, United States)

The asteroid community has been engaged in the ef-fort of characterizing and mitigating the near-Earthobject impact hazard for over two decades. The pri-ority was initially on objects larger than a kilome-ter that could cause global devastation, and this fo-cus was later extended to objects larger than 140 mthat could cause substantial regional damage if theyreached the Earth, which happens with a mean in-terval of approximately 10,000 years. On the otherhand, smaller objects reach the Earth more fre-quently. In particular, objects of several meters insize reach the Earth every few years and since 2008three of them were indeed discovered by the CatalinaSky Survey within a day prior to impact: 2008 TC3,2014 AA, and 2018 LA. Though these three aster-oids caused no damage, they represented good testcases for how the near-Earth object tracking and haz-ard assessment systems can cope with short-termimpactors. We discuss the processes of discovery,tracking, orbit characterization, and impact locationestimation for these three objects, outlining com-monalities and differences between them. While2014 AA impacted above the Atlantic Ocean, frag-ments of 2008 TC3 and 2018 LA landed in Sudanand Botswana, respectively. Our impact location es-timates allowed the recovery of the correspondingmeteorites.

200.05 — Orbit determination for space missionsin Pisa: results and simulations from Juno andBepiColombo

Daniele Serra1; Giacomo Lari1; Giulia Schettino2,1; Gia-como Tommei1

1 Department of Mathematics, University of Pisa (Pisa, Italy)2 IFAC-CNR (Sesto Fiorentino, Florence, Italy)

The gravitational field of a planet is the main sourceof information about its interior structure, provid-ing, e.g., constraints on the core size or the state ofrotation. The most effective way to map a planet’sgravity is by means of an orbiter which is endowedwith a radio communication system. The radio link

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allows measurements of the spacecraft’s range andrange-rate, which can be used to reconstruct its or-bit and ultimately to determine a number of physicalparameters relative to the planet, including the coef-ficients of its gravitational field’s spherical harmonicexpansion. The same data can be used to undertakefundamental physics experiments, like the determi-nation of the parameters relative to the ParametrizedPost-Newtonian formulation of the metric theoriesof gravity. The aim of this presentation is to sum-marize the main results about the Radio Science Ex-periments of the NASA’s Juno mission, now orbit-ing Jupiter, and the ESA/JAXA’s BepiColombo mis-sion, launched in October 2018 to reach Mercury in2025, obtained at the University of Pisa using theself-developed ORBIT14 orbit determination code.As regards the Juno mission, we show a solutionof Jupiter’s gravity field obtained by analysis of realdata from the first two Juno gravity orbits, and com-pare it to the one obtained with the JPL’s operativesoftware MONTE ([1]). As far as the BepiColombomission is concerned, we present numerical simula-tions of the Superior Conjunction Experiment for thedetermination of the PPN parameter γ, related to thespace-time curvature.

[1] Iess et al., Nature 555, 220-222 (2018)

200.06 — Trajectory estimation for Bennu’sparticles

Steven R. Chesley1; Coralie Adam4; Peter Antreasian4;Brent J. Bos3; William V. Boynton5; Marina Brozović1;Brian T. Carcich4; Alex B. Davis2; Joshua P. Emery7;Davide Farnocchia1; Andrew S. French2; CarlHergenrother5; Robert A. Jacobson1; Dante S. Lauretta5;Jason Leonard4; Erik Lessac-Chenen4; Andrew J.Liounis3; Jay McMahon2; Michael C. Moreau3; MichaelC. Nolan5; William M. Owen1; John Pelgrift4; Ben-jamin Rozitis6; Daniel Scheeres2; Sanford Selznick5; YuTakahashi1

1 Jet Propulsion Laboratory, California Institute of Technology(Pasadena, California, United States)

2 University of Colorado (Boulder, Colorado, United States)3 Goddard Space Flight Center (Greenbelt, Maryland, United

States)4 KinetX Aerospace (Simi Valley, California, United States)5 University of Arizona (Tucson, Arizona, United States)6 The Open University (Milton Keynes, United Kingdom)7 University of Tennessee (Knoxville, Tennessee, United States)

On Dec. 31, 2018 the OSIRIS-REx spacecraft enteredorbit around its sample return target, near-Earth as-teroid (101955) Bennu. Optical navigation imagestaken less than a week after orbit insertion revealed

that the asteroid was emitting centimeter to decime-ter sized particles, many of which immediately es-caped from Bennu. The mission team quickly be-gan to tailor observations in order to better monitorthe Bennu environment for additional ejection eventsand particle tracking. This monitoring effort re-vealed that, in addition to those ejected directly ontohyperbolic orbits, some ejected particles returned tothe surface on sub-orbital trajectories, while othersentered relatively long-lived orbits, up to five daysand over a dozen revolutions. This talk will de-scribe the process of linking particle detections intodatasets sufficient for orbit estimation, as well as thetechnical approaches and dynamical models used inthe orbit estimation process.

201 — Dynamics of the OuterSolar System

201.01 — Computationally and ObservationallyConstraining the Outer Solar System PerihelionGap to Help Find Planet X

William Jared Oldroyd1; Chad Trujillo11 Physics and Astronomy, Northern Arizona University (Flagstaff,

Arizona, United States)

In recent years, there have been several studies show-ing evidence for an undiscovered giant planet in theouter solar system (sometimes referred to as PlanetX or Planet 9). Efforts to constrain the on-sky loca-tion of this planet have been made, but, thus far, theplanet has escaped detection. The most distant ob-jects in our solar system have elongated and inclinedorbits and the orientation of their orbits is one of theprimary evidences for the undiscovered giant planet.Intriguingly, no solar system objects have periheliabetween ∼50-65 au, yet bodies are known with peri-helia less than and greater than this range. This per-ihelion gap has the potential to provide additionalconstraints for the undiscovered planet, which will,in turn, aid in the search for this mysterious world.We constrain the observed perihelion gap utilizingcomputational N-body simulations where suites oftest particles, seeded in and around the gap, are ex-posed to gravitational interactions of the Sun, the gi-ant planets, and the undiscovered planet. These sim-ulations are carried out for the age of the solar system(4.5 Gyr) using REBOUND. A wide range of planetand test particle parameters are explored and will bepresented.

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201.02 — Resilience of the Self-Gravity Instabilityto Precession

Alexander Zderic1; Ann-Marie Madigan1; Jacob Fleisig11 University of Colorado Boulder (Boulder, Colorado, United States)

Disks of eccentric orbits have a self-gravity insta-bility that can explain Neptune detachment and ar-gument of perihelion clustering observed in the ex-treme trans-Neptunian objects (Madigan & McCourt2016 and Madigan et al. 2018). However, previouswork on the instability has focused on a simplifiedsystem lacking the influences of the giant planets, anomission that could affect the instability. Here weemulate the presence of the giant planets by addinga quadrupole moment (J2) to the potential in systemsotherwise susceptible to the self-gravity instability.We find that for a sufficiently large J2 the self-gravityinstability is suppressed, and we derive how this crit-ical J2 scales with disk mass, particle number, andinitial orbital configuration to extrapolate our resultsto the solar system.

201.03 — Positions of the secular resonances in theprimordial Kuiper Belt disk

Daniel Baguet1; Alessandro Morbidelli2; Jean-MarcPetit3

1 Université de Franche-Comté - Institut UTINAM - OSU Theta(Besançon, France)

2 CNRS - Observatoire de la Côte d’Azur - Laboratoire Lagrange(Nice, France)

3 CNRS - Institut UTINAM - Université Bourgogne-Franche-Comté - OSU Theta (Besançon, France)

In current dynamical evolution models aiming at re-producing the orbital structure of the Kuiper Belt, thegiant planets start from a compact multiresonant or-bital configuration and migrate to their current posi-tions by interacting with a planetesimal disk extend-ing beyond the orbit of Neptune. In order to stopthe migration of Neptune at 30 AU and to reproducethe distinction between the dynamically cold and hotpopulations, it is often assumed that the primordialplanetesimal disk was divided into two parts: a mas-sive disk extending from Neptune to 30 AU and a lowmass extension of the disk extending beyond 30 AU,the outer limit of which is quite uncertain. Beforethe dynamical instability between the giant planets,which strongly depletes the mass of the planetesimaldisk, the massive part of the disk can have a signifi-cant influence on the apsidal and nodal precessionsof the giant planets and of the planetesimals, leadingto the shift of the positions of the secular resonances.In particular, the presence of the massive disk re-moves the degenaracy of the f5 nodal frequency and

allows for a new secular resonance. We investigatethese effects in the linear secular theory of Lagrange-Laplace and find the locations of the secular reso-nances for different orbital configurations. We showthat during the pre-instability period, for some or-bital configurations the f5 nodal secular resonance islocated in the region where the primordial cold clas-sical Kuiper belt formed. If the inclination betweenthe plane orthogonal to the total angular momen-tum of the giant planets and the mean plane of themassive disk is high enough, this nodal secular res-onance is efficient at rising the inclinations of objectslocated in it. Thus, this could be a potential solutionfor the problem of the low density of the cold objectsin the region near 45-47 AU.

201.04 — Origin and Evolution of Long-PeriodComets

Luke Dones1; David Vokrouhlicky2; David Nesvorny11 Southwest Research Institute (Boulder, Colorado, United States)2 Institute of Astronomy, Charles University (Prague, Czechia)

Nesvorny et al. (2017) performed the first end-to-end, 4.5 billion year simulations of the formation andevolution of the cometary reservoirs, focusing pri-marily on short-period (Jupiter-family and Halley-type) comets. Here we report the results of oursimulations of long-period comets (Vokrouhlicky etal. 2019). The calculations begin with 1 milliontest particles in a massive disk beyond Neptune,with Uranus and Neptune migrating in a ”jump-ing Jupiter” model of the early dynamical instabil-ity (Brasser et al. 2009, Nesvorny and Morbidelli2012, Nesvorny and Vokrouhlicky 2016). The sim-ulations include the effects of the four giant plan-ets, galactic tides, and passing stars. Some 5% of theparticles survive for 4.5 Gyr, with 90% of those inthe Oort Cloud. The populations of the inner andouter Oort Cloud are roughly equal. Francis (2005)inferred from LINEAR data that there were 11 long-period comets/year with perihelia < 4 AU and abso-lute magnitude 10.9. Our simulations, which are cal-ibrated to the Jupiter Trojan implantation efficiencyfrom the original planetesimal disk, predicts about 4such comets/year. If we assume the magnitude-sizerelationship from Sosa and Fernandez (2011), theseare cometary nuclei with diameters > 0.6 km. Be-yond perihelion distances of 15 au, the number ofcomets increases rapidly, and the inner Oort Cloudis the dominant source beyond 20 au. Surveys suchas LSST should soon reveal the true structure of theOort Cloud (Silsbee and Tremaine 2016).

This research was supported by the Czech ScienceFoundation (DV) and by NASA Emerging Worlds

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program (DN).References: Brasser R, Morbidelli A, Gomes R, Tsi-

ganis K, Levison HF (2009). A&A 507, 1053; Fran-cis PJ (2005). ApJ 635, 1348; Nesvorny D, MorbidelliA (2012). AJ 144, 117; Nesvorny D, Vokrouhlicky D(2016). ApJ 825, 94; Nesvorny D, Vokrouhlicky D,Dones L, Levison HF, Kaib N, Morbidelli A (2017).ApJ 845, 27; Silsbee K, Tremaine S (2016). AJ 152,103; Sosa A, Fernandez JA (2011). MNRAS 416,767; Vokrouhlicky D, Nesvorny D, Dones L (2019).arXiv:1904.00728

201.05 — Not a simple relationship betweenNeptune’s migration speed and Kuiper beltinclination excitation

Kathryn Volk1; Renu Malhotra11 Lunar & Planetary Laboratory, The University of Arizona (Tuc-

son, Arizona, United States)

We examine the inclination excitation mechanismsfor Kuiper belt objects captured into Neptune’s 3:2mean motion resonance and the hot classical beltduring Neptune’s outward migration. The widelydispersed present day inclination distributions inthese populations have been interpreted as strongevidence that Neptune must have migrated slowlybecause slow migration allows for multiple scatter-ing events to raise the inclinations of Kuiper belt ob-jects. However, in our numerical simulations we findcounter-examples that show that the degree of incli-nation excitation is not necessarily correlated withmigration timescale. A deep analysis of the simu-lations finds that secular excitation of inclinationscan play an important role in shaping the final in-clination distributions, especially for Neptune’s 3:2resonance which is located very near a strong in-clination secular resonance in the Kuiper belt. Inthe simulations, the relative importance of scatter-ing versus secular excitation depends on the selec-tion of pre-migration initial conditions for the plan-ets and how their eccentricities and inclinations are(made to) evolve during migration; these choices af-fect the secular architecture of the giant planets asthey migrate. The degree of inclination excitationin the post-migration 3:2 and hot classical popula-tions can be very sensitive to the planets’ initial con-ditions and to the simplifications adopted in the nu-merical model to make the simulations computation-ally tractable. We suggest that the inclination distri-bution of the Kuiper belt is not conclusive evidencefor a slow migration speed of Neptune and that otherlines of evidence are required to constrain migrationspeed.

201.06 — Candidate Resonant Family Members ofthe Dwarf Planet Haumea

Benjamin C. N. Proudfoot1; Darin A. Ragozzine11 Brigham Young University (Highland, Utah, United States)

The dwarf planet Haumea in the outer solar systempresents a challenge for collisional modeling withits near-breakup spin, two regular satellites, and asurprisingly compact collisional family. In our re-cent detailed analysis of the distribution of colli-sional family members, no self-consistent formationhypothesis was able to match all we know about thefamily (Proudfoot & Ragozzine 2019). Further clas-sification and identification of Haumea family mem-bers (“Haumeans”) will improve our understandingthe formation of the Haumea family. We will presentour search for and study of candidate Haumeans thatwere and/or are influenced by mean motion reso-nances with Neptune. Though harder to identify dy-namically, these resonant Haumeans could providecrucial constraints on the Haumea family formationevent. For example, resonant Haumeans could shedlight on proper element distribution of the Haumeafamily. They could also provide insights on the ageof the family and/or its possible interaction withNeptune’s orbital migration.

202 — Dynamics of Stars

202.01 — Vertical Mass Segregation in EccentricNuclear Disks

Hayden Foote1; Ann-Marie Madigan1; AlekseyGenerozov1

1 Astrophysical and Planetary Sciences, University of ColoradoBoulder (Boulder, Colorado, United States)

Eccentric nuclear disks are a type of nuclear star clus-ter in which the stars lie on apsidally-aligned orbitsin a disk around the central supermassive black hole.These disks can produce a high rate of tidal disrup-tion events (TDEs) via secular gravitational torques.Here, we show that eccentric nuclear disks exhibitstrong vertical mass segregation, in which massivestars sink to low inclinations through dynamical fric-tion with a more numerous population of lighterstars. This results in a much higher TDE rate perstar among the heavy stars (∼0.10) than the light stars(∼0.06).

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202.02 — The Fate of Binaries in the GalacticCenter: The Mundane and the Exotic

Alexander Patrick Stephan1,6; Smadar Naoz1,6; AndreaM. Ghez1; Mark R. Morris1; Anna Ciurlo1; Tuan Do1;Katelyn Breivik2; Scott Coughlin3,4; Carl L. Rodriguez5

1 Physics and Astronomy, UCLA (Los Angeles, California, UnitedStates)

2 CITA, University of Toronto (Toronto, Ontario, Canada)3 Cardiff University (Cardiff, Wales, United Kingdom)4 CIERA, Northwestern University (Evanston, Illinois, United

States)5 MIT (Cambridge, Massachusetts, United States)6 Bhaumik Institute, UCLA (Los Angeles, California, United

States)

The Galactic Center (GC) is dominated by the grav-ity of a super-massive black hole (SMBH), Sagittar-ius A*, and is suspected to contain a sizable popula-tion of binary stars. Such binaries form hierarchicaltriples with the SMBH, undergoing Eccentric Kozai-Lidov (EKL) evolution, which can lead to high ec-centricity excitations for the binary companions’ mu-tual orbit. This effect can lead to stellar collisionsor Roche-lobe crossings, as well as orbital shrinkingdue to tidal dissipation. In this work, we investi-gate the dynamical and stellar evolution of such bi-nary systems, especially with regards to the bina-ries’ post-main-sequence evolution. We conduct alarge Monte-Carlo simulation including the effectsof EKL, tides, general relativity, and stellar evolu-tion. We use the dynamical break-up of binaries byscattering interactions with passing stars as a timelimit for our simulations. We find that the majorityof binaries (∼75%) is eventually separated into singlestars, joining the large population of singles in theGC, while the remaining binaries (∼25%) undergophases of common-envelope evolution and/or stel-lar mergers. These mergers or common-envelope bi-naries can produce a number of different exotic out-comes, including rejuvenated stars, extended dustygas cloud-like infrared-excess objects, stripped giantstars, Type Ia supernovae (SNs), cataclysmic vari-ables (CVs), symbiotic binaries (SBs), or compact ob-ject binaries. In particular, we estimate that, within asphere of 250 Mpc radius, about 7.5 to 15 Type Ia SNs,on average, per year should occur in galactic nucleidue to this mechanism, potentially detectable by ZTFand ASAS-SN. Likewise we estimate that, within asphere of 1 Gpc3 volume, about 10 to 20 compact ob-ject binaries form per year that could become grav-itational wave sources. This compact object binaryformation rate translates to about 15 to 30 events peryear detectable by Advanced LIGO.

202.03 — Detecting Black Hole Dynamics in theHeart of Galaxies with LISA

Bao-Minh Hoang1; Smadar Naoz1; Bence Kocsis2; WillFarr3; Jess McIver4

1 University of California, Los Angeles (Los Angeles, California,United States)

2 Eotvos University (Budapest, Hungary)3 Stony Brook University (Stony Brook, New York, United States)4 California Institute of Technology (Pasadena, California, United

States)

Stellar-mass black hole binaries (BHBs) near su-permassive black holes (SMBH) in galactic nucleiundergo dynamical eccentricity oscillations due togravitational perturbations from the SMBH. Previ-ous works have shown that this channel can con-tribute to the overall BHB merger rate detected bythe Laser Interferometer Gravitational-Wave Obser-vatory (LIGO) and Virgo Interferometer. Signifi-cantly, the SMBH gravitational perturbations on thebinary’s orbit may produce eccentric BHBs whichare expected to be visible using the upcoming LaserInterferometer Space Antenna (LISA) for a largefraction of their lifetime before they merge in theLIGO/Virgo band. As a proof-of-concept, we showthat the eccentricity oscillations of these binaries canbe detected with LISA for BHBs in the local universeup to a few Mpcs, with observation periods shorterthan the mission lifetime, thereby disentangling thisdynamical merger channel from others.

202.04 — Rotation Period Evolution in Low-MassBinary Stars: The Impact of Tidal Torques andMagnetic Braking

David Fleming1,2; Rory Barnes1,2; James R. A.Davenport1; Rodrigo Luger3

1 Astronomy, University of Washington (Seattle, Washington,United States)

2 Virtual Planetary Laboratory (Seattle, Washington, United States)3 Center for Computational Astrophysics, Flatiron Institute (New

York, New York, United States)

The long-term angular momentum evolution of iso-lated low-mass (M < 1 MSun) stars is controlled bymagnetic braking, the torque exerted on stars dueto the coupling of stellar winds to the surface mag-netic field (e.g. Dunn 1961, Mestel 1968). In stellarbinaries, however, tidal torques can dominate the an-gular momentum evolution for short orbital periods(Porb). We examine how tides, stellar evolution, andmagnetic braking combine to shape the rotation pe-riod (Prot) evolution of low-mass stellar binaries with

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Porb < 100 d. We test a wide range of tidal dissi-pation parameters and two commonly-used equilib-rium tidal models and find that many binaries withPorb < 20 d tidally-lock, and nearly all with Porb <4 d tidally-lock into synchronous rotation on circu-larized orbits. At short Porb, tidal torques produce apopulation of fast rotators that single-star only mod-els of magnetic braking fail to produce, but are nat-urally created when tidal effects are included. Fur-thermore, we show that the competition betweenmagnetic braking and tides can generate a popu-lation of subsynchronous rotators that persists forGyrs, even in short Porb binaries, a population thathas been observed in the Kepler field by Lurie et al.(2017). Both equilibrium tidal models predict that bi-naries can tidally-interact out to Porb ∼ 80 d, and onemodel predicts that binaries can tidally-lock out toPorb ∼ 100 d. Tidal torques often force the Prot evolu-tion of stellar binaries to depart from the long-termmagnetic braking-driven spin down experienced bysingle stars, revealing that Prot is not be a valid proxyfor age in all cases, i.e. gyrochronology methods canfail unless one accounts for binarity. We suggest thataccurate determinations of orbital eccentricities andProt, especially for Porb > 20 d, can be used to discrim-inate between which equilibrium tidal models bestdescribes tidal interactions in low-mass binary stars.

202.05 — Companion-driven evolution of massivestellar binaries

Sanaea Cooper Rose1; Smadar Naoz1; Aaron Geller21 Physics & Astronomy, University of California, Los Angeles (Los

Angeles, California, United States)2 Northwestern University (Evanston, Illinois, United States)

The majority of massive (OBA-type) stars reside inbinary or higher-order systems. We consider the dy-namical evolution of massive binary stars in the pres-ence of a faraway companion. For dynamical stabil-ity, these triple systems must have a hierarchical con-figuration. We explore the effects of a distant thirdcompanion’s gravitational perturbations on a mas-sive binary’s orbital configuration before significantstellar evolution has taken place (< 10 Myr). We in-clude tides and general relativistic precession. Werun large Monte-Carlo realizations of massive hier-archical triples and find signatures of the birth con-ditions on the final orbital distributions. Specifically,we find that the final eccentricity distribution is anexcellent indicator of its birth distribution. Further-more, we find that the period distributions have asimilar mapping for wide orbits. Finally, we demon-strate that the observed period distribution for ap-proximately 10 Myr-old massive stars is consistent

with triple-body evolution. The dynamical evolutionof these systems can lend insight into the origins ofextreme phenomena such as X-ray binaries and grav-itational wave sources.

202.06 — Eccentricity and the Hills Mechanism

Aleksey Generozov1; Ann-Marie Madigan11 CU Boulder (Boulder, Colorado, United States)

Binary stars in a galactic nucleus can be tidally sep-arated by a central supermassive black hole (SMBH)via the Hills mechanism. One of the stars in the bi-nary is ejected as a hypervelocity star, while the otheris left in a bound orbit around the SMBH. This mech-anism likely produced the S-stars in our own GalacticCenter, and may have produced a similar populationin M31. In this talk I will review the physics of theHill’s mechanism and discuss the underappreciatedrole of the initial binary eccentricity in the process.I will also discuss the subsequent evolution of thebound stars.

202.07 — From Ultra-wide Binaries to InteractingBinaries in the Field

Erez Michaely11 Astronomy, University of Maryland (Rockville, Maryland, United

States)

The galactic field is regularly considered as a colli-sionless environment. However, for ultra-wide bi-naries ( >1000AU) that the field is not collisionless.These binaries experience perturbations from ran-dom stellar fly-bys which can excite their orbital ec-centricities. Once the eccentricity is sufficiently highthe binary component interact and can produce ex-otic binaries. In this talk I present the theoreticalmodel that describes the binary-single interaction, inthe impulsive regime, in the field of a galaxy. Fur-thermore, two examples of these kind of interactionwill be discussed: 1. The production rates of low-mass X-ray binaries from wide binaries in the field 2.A novel GW merger channel for binary black-holes(BBH) from wide BBHs. The merger rate is compa-rable to the lower value of the observed BBH mergerrate. For both examples specific observational signa-tures are discussed.

202.08 — Distribution of Planetesimals DuringStellar Encounters

Nathaniel Wyatt Hotchkiss Moore1; Gongjie Li1; FredAdams2

1 Georgia Institute of Technology (Atlanta, Georgia, United States)2 University of Michigan (Ann Arbor, Michigan, United States)

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Most stars form in clusters where close encounterswith other stars are common. Such encounters leavearchitectural imprints on the orbits of planetesimals.Here, we investigate the dependence of these fea-tures on incoming stellar orbital parameters. We ex-plore the parameter space of stellar encounters usingN-body simulations and find that stellar encounterscan leave unique signatures in the inclination dis-tribution of a debris disk (the analog of the KuiperBelt). Analytical expressions have been obtained todescribe the distribution of possible inclination exci-tations. We can apply these results to constrain theconditions in our Solar System Birth Cluster usingongoing and future observational surveys for objectsin the outer Solar System (including DES, LSST).

203 — Dynamics of Galaxies

203.01 — Dyanmics of Local Group SatelliteGalaxies in the Era of High Precision Astrometry

Ekta Patel11 University of Arizona (Tucson, Arizona, United States)

High-precision astrometric data from space obser-vatories, such as the Hubble Space Telescope (HST)and Gaia, are revolutionizing our ability to studythe Local Group. In this talk, I will describe howcombining this 6D phase space information (derivedfrom proper motions) with high-resolution state-of-the-art simulations allows us to revisit models ofthe Local Group’s dynamical history and its futurefate. In particular, Andromeda (M31) are a recentbreakthrough that have yielded a revised orbital his-tory for M31’s HST proper motion measurementsfor most massive satellite galaxy, M33, shifting theparadigm away from morphologically motivated or-bital models (Patel et al. 2017a). I will show that con-straining the orbit of a massive satellite galaxy likeM33 is crucial for reconstructing the assembly his-tory of the M31 satellite system, refining estimatesfor the total mass of M31, and for testing LCDM pre-dictions at small scales through searches for “satel-lites of satellites” around M33 (Patel et al. 2017b,2018a, 2018b). Additionally, I will discuss how wehave used Gaia DR2 to independently measure theproper motions of M33 and M31. These measure-ments show good agreement with M33’s new orbitalhistory and allow us to revisit the parameters of thefuture collision between the Milky Way and M31. Asthe next decade will yield even more high precisiondata for the M31 system, I will conclude by outlininghow we can use M31 as a benchmark for next gener-ation studies of galaxies beyond the Local Group in

the era of WFIRST, JWST, and LSST.

203.02 — Hot and Cold Exponential Galaxy Disksfrom Star and Gas Scattering

Curtis Struck1; Bruce G. Elmegreen21 Department of Physics & Astronomy, Iowa State University

(Ames, Iowa, United States)2 IBM T. J. Watson Research Center (Yorktown Heights, New York,

United States)

The near universality of exponential (or double expo-nential) surface brightness profiles in galaxy disks,over a wide range of masses and Hubble types, hasbeen well documented observationally. Stellar scat-tering off bars and spirals, as well as secular radialmigration induced by such waves, can contribute toevolving the surface profile, but the former does notexplain exponential profiles in spiral-free dwarf ir-regular galaxies, while the latter does not seem ef-ficient enough to modify whole profiles. We previ-ously showed, using scattering simulations and an-alytical arguments that massive young disk clumps,or massive clouds and holes in dwarf galaxies, canscatter stars into an exponential profile. These diskstend to be thick, with fairly high velocity dispersions.More recent work shows that widespread fountainflows from young star-forming regions can producean exponential profile in the dense interstellar gas.Stars subsequently formed from this gas inherit theexponential profile in a low dispersion thin disk.

203.03 — Using Kinematics to Discover an AGNTurning Off and On

Julia Comerford11 University of Colorado, Boulder (Boulder, Colorado, United

States)

We present the discovery of an active galacticnucleus (AGN) that is turning off and then onagain. The AGN resides in the z=0.06 galaxy SDSSJ1354+1327 and the episodic nuclear activity is theresult of discrete accretion events, which could havebeen triggered by a past interaction with the com-panion galaxy that is currently located 12.5 kpcaway. We originally targeted SDSS J1354+1327 be-cause its Sloan Digital Sky Survey spectrum has nar-row AGN emission lines that exhibit a kinematic ve-locity offset of 69 km/s relative to systemic. To deter-mine the nature of the galaxy and its velocity-offsetemission lines, we observed SDSS J1354+1327 withChandra/ACIS, Hubble Space Telescope/Wide FieldCamera 3, Apache Point Observatory optical longslit

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spectroscopy, and Keck/OSIRIS integral-field spec-troscopy. We find a ∼10 kpc cone of photoionizedgas south of the galaxy center and a ∼1 kpc semi-spherical front of shocked gas, which is responsiblefor the velocity offset in the emission lines, north ofthe galaxy center. By modeling the kinematics of thegas, we interpret these two outflows as the result oftwo separate AGN accretion events; the first AGNoutburst created the southern outflow, and then <105

yrs later the second AGN outburst launched thenorthern shock front. The AGN in SDSS J1354+1327fits into the broader context of AGN flickering thatincludes observations of AGN light echoes.

203.04 — Accurate Identification of GalaxyMergers with Imaging and Kinematics

Rebecca Nevin1; Laura Blecha2; Julia Comerford11 University of Colorado Boulder (Boulder, Colorado, United States)2 University of Florida (Gainesville, Florida, United States)

Merging galaxies play a key role in galaxy evolu-tion, and progress in our understanding of galaxyevolution is slowed by the difficulty of making ac-curate galaxy merger identifications. Mergers aretypically identified using individual imaging tech-niques, each of which has its own limitations andbiases. The stellar kinematics more directly tracethe dynamics of galaxies (independent of their vi-sual morphologies) and can be powerful probes oftheir assembly histories. With the growing popular-ity of integral field spectroscopy (IFS), it is now pos-sible to introduce kinematic signatures to improvegalaxy merger identifications. I use GADGET-3 N-body/hydrodynamics simulations of merging galax-ies coupled with SUNRISE dust radiative transfersimulations to create mockup stellar kinematic mapsand images to match the specifications of the Map-ping Nearby Galaxies at Apache Point (MaNGA) sur-vey, which is the largest IFS survey of galaxies todate. From the mockup galaxies, I have developedthe first merging galaxy classification scheme that isbased on kinematics and imaging. I will discuss thestrengths and limitations of the classification tech-nique and my plans to apply the classification to the>10,000 observed galaxies in the MaNGA survey. Iwill then discuss my plans to utilize these large sam-ples of merging galaxies (of different stages and massratios) to advance our understanding of open ques-tions related to galaxy evolution, such as how starformation and AGN triggering change for differentstages and types of mergers.

300 — Dynamics of Rings

300.01 — Are moonlets hidden among the clumpsin Saturn’s innermost ring?

Joseph A’Hearn1; Matthew Hedman1; Douglas P.Hamilton2

1 University of Idaho (Moscow, Idaho, United States)2 University of Maryland (College Park, Maryland, United States)

Saturn’s D68 ringlet is the rings’ innermost narrowfeature. Four clumps that appeared in D68 in 2014-15remained evenly spaced about 30 degrees apart andmoved very slowly relative to each other (Hedman2019, Icarus), which is reminiscent of the stationaryconfigurations of co-orbital nearly equal-mass satel-lites (Salo & Yoder 1988, A&A). We therefore explorethe possibility that the source bodies for these fourclumps are in such a co-orbital configuration. Thespacing between the clumps is somewhat smallerthan one would expect for a configuration of fourmoons, and changing the mass ratios is unable to fixthis. We therefore consider whether an unseen fifthobject could account for the discrepancies in the an-gular separations and allow the system to reach sta-tionarity (Renner & Sicardy 2004, CMDA). We find arange of possible longitudes where a fifth co-orbitalobject could be, as well as the mass ratios between thefive objects for any specified longitude within theseranges.

300.02 — The shape of Saturn’s outer B ring

Philip David Nicholson1; Matthew M. Hedman2;Richard G. French3

1 Astronomy, Cornell University (Ithaca, New York, United States)2 University of Idaho (Moscow, Idaho, United States)3 Wellesley College (Wellesley, Massachusetts, United States)

It has long been known that the outer edge of Sat-urn’s B ring is strongly perturbed by the 2:1 innerLindblad resonance with Mimas (Porco et al. 1984),and suspected that this resonance is responsible forconfining the outer edge of this ring (Goldreich &Tremaine 1978, Tajeddine et al. 2017). Cassini imag-ing and occultation data revealed a more complexpicture, wherein the resonantly-forced m = 2 pertur-bation exhibits a large-amplitude libration with a pe-riod of ∼5.4 yr and a radial amplitude of as much as70 km (Hedman et al. 2010, Spitale & Porco 2010,Nicholson et al. 2014). In addition, there are freemodes with m = 1, 3, 4 and 5 (Spitale & Porco 2010,Nicholson et al. 2014) and amplitudes of 7–22 km.We have used the last seven years of Cassini occulta-tion data to update our previous fits, extending our

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coverage to span ∼2.5 libration periods. The new re-sults are consistent with our previous fits, while alsosuggesting an additional normal mode with m = 6.Furthermore, optical depth profiles and Csssini im-ages reveal that these radial distortions extend for atleast 500 km inward from the B ring’s outer edge.Using a large set of stellar occultations obtained bythe Cassini VIMS instrument, we have searched forwavelike structures in this region. In addition to in-dications of periodic perturbations with m = 1 and aradial wavelength of ∼110 km reported previously,we find evidence for what appears to be an axisym-metric (i.e., m = 0) wave propagating inwards fromthe ring’s outer edge (Hedman & Nicholson 2019).Supporting evidence for such a wave is found inmosaics assembled from several Cassini imaging se-quences. We suggest that this wave, along with simi-lar ones seen at two other locations in Saturn’s rings,are driven by non-linear interactions between multi-ple edge modes.

300.03 — Changes in Saturnian Ring Particle-SizeDistribution after Satellite Passage

Rebecca Harbison11 Physics & Astronomy, University of Nebraska – Lincoln (Lincoln,

Nebraska, United States)

The behavior of ring material near the satellite-bearing gaps in the A Ring is shaped by several grav-itational processes. Like the rest of the A Ring, self-gravity pulls material together into larger, tempo-rary aggregates called ’self-gravity wakes’. How-ever, regular passage of Pan and Daphnis in their re-spective gaps stirs up adjacent material in the ringinto ’satellite wakes’. Theoretical work by Bordrovaet al. (2011) show that the particle-size distributionis shaped by the velocity dispersion (such as causedby satellite wakes) determining which collisions be-tween ring particles cause adhesion of small particlesto larger ones, and numerical simulations by Lewisand Stweart (2005) show that ’satellite wakes’ candisrupt ’self-gravity wakes’ and the region a few tensof kilometers from the gap edge changes in time aftera satellite passage.

During stellar occultations of Saturn’s rings ob-served by Cassini, we have observed ’gap overshoots’or ’horns’: places near a sharp edge of the rings, suchas the gaps of A Ring, where the transmission ofstarlight appears to exceed unity. This excess lightis due to starlight forward-scattered from the nearbyring into the detector and is dependent on the par-ticle size distribution. Work by Becker et al. (2016)with UVIS occultations detected a possible change inthe observed particle-size distribution in data taken

shortly after a Pan encounter but limited to a fewdata points. I will present particle size distributionmodels from dozens of VIMS occultations, confirm-ing Becker’s work at the Encke Gap, and explore thenarrower Keeler Gap. This will allow us to test hy-potheses of the time-variability of self-gravity wakes(and the particle-size distribution itself) near the gapedges, and to look for observational differences be-tween the behavior of the distribution near each gap.

300.04 — Simulating Saturn’s A ring edge with asingle chain of gravitationally-interacting particles

Yuxi Lu1; Douglas P. Hamilton1; Thomas Rimlinger1;Joseph Hahn2

1 University of Maryland (College Park, Maryland, United States)2 Space Science Institute (Austin, Texas, United States)

The edge of the A ring, located 136,769 km fromSaturn, has a 7-lobed pattern that appears and dis-appears every 4 years as the nearby satellites Janusand Epimetheus swap their orbital positions. WhileJanus is in the inner position, its 7:6 resonance fromJanus is located only ∼4 km inside the ring. This ex-cites the 7-lobed normal mode on the ring edge, andthe feature disappears as Janus moves from the innerposition to the outer. We wish to model this satellite-ring system and have, accordingly, developed a newcode to do so. We modified the N-body code, hn-body, to simulate narrow rings and ring edges us-ing a single chain of gravitationally-interacting parti-cles. We have tested our code on isolated resonancesand can reproduce normal mode patterns includ-ing the 7-lobed feature in the A ring. However, theouter portion of the real A ring is perturbed by sev-eral resonances. The four most important resonancesare The Lindblad Eccentric Resonances from Janusand Epimetheus that affect the eccentricities and theCorotation Eccentric resonances from each satellitethat primarily affect the semi-major axes. Moreover,these four resonances move rapidly as the satellitesswap orbital positions. We apply our new code tosimulate the A ring edge with both satellites presentand we are able to study the global patterns on thering due to the action of multiple resonances. Inthis talk, we will describe how the outer parts of Aring change over a Janus-Epimetheus orbital periodin our simulations and we will compare our resultsto observations.

300.05 — Stability of One Dimensional Rings ofGravitationally Interacting Masses

Douglas P. Hamilton2; Yuxi Lu1; Thomas Rimlinger1;Joseph Hahn3

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1 Astronomy, University of Maryland (College Park, Maryland,United States)

2 University of Maryland (College Park, Maryland, United States)3 SSI (Austin, Texas, United States)

The narrow rings of Saturn, Uranus, and Neptune or-bit at distances of ∼100,000 km and have widths ofjust a few km, suggesting that they might profitablybe modeled as one-dimensional chains of masses.We investigate the promise and the limitations ofthese models by exploring the effects of particle-particle gravity. One dimensional models can bemade extremely efficient by neglecting all but thedominant forces arising between the nearest dozenor so neighbors in a chain. We routinely run simu-lations with thousands of masses, with increases inspeed of factors of tens to hundreds over a direct N2

calculation of interparticle forces. Conversely, utiliz-ing a single chain of particles suppresses all of the im-portant effects that depend on interactions betweenneighboring streamlines, and so applications for asingle chain of particles are limited.

In our first set of experiments, we initialize ringscomposed of N equally-spaced low masses with un-inclined circular orbits and follow their subsequentevolution as the masses are adiabatically raised. Wefind that instability invariably sets in when massesincrease to the point that particle Hill radii reach∼25% of the azimuthal particle spacing. This effectlimits the total ring mass that may be modeled by asingle chain of N particles and it also limits the num-ber of individual particle that may comprise a givenring.

We also initialized our particle chains with differ-ent normal modes and studied the self precession ofthe resulting structures. While each configurationhas given nodal and apsidal precession rates that wecan calculate analytically, we find that splicing thering mass into smaller and smaller bits does not leadto convergence of the precession rate to fixed valuesas might initially be expected. Since splicing a givenring mass ever more finely inevitably leads to full in-stability, however, it is not surprising that ring pre-cession rates do not converge during this process.

300.06 — A Variational Principle for Self-GravityWakes and Spiral Density Waves

Glen Robert Stewart11 Laboratory for Atmospheric and Space Physics, University of

Colorado (Boulder, Colorado, United States)

An important limitation of the Streamline Model fordensity waves in planetary rings is the complete ne-glect of local gravitational instabilities which lead to

the formation of self-gravity wakes in the A and Brings of Saturn as well as the formation of straw-like textures in the troughs of strong density wavesand super-sized self-gravity wakes near the edges ofsatellite-perturbed ring edges, such as the Encke gapedge and the outer B ring edge. These local struc-tures have significant pitch angles relative to the az-imuthal direction, so they can be much more effi-cient at transporting angular momentum comparedto binary particle collisions. I will present a varia-tional principle for density waves that can describethe formation of local gravitational instabilities inthe wave train. This has been achieved by modify-ing a variational principle derived by Alain Brizardfor gyrokinetic plasma physics problems. The objec-tive of gyrokinetic theory is to obtain a reduced de-scription of the plasma where the fast gyro-motionof charged particles about the background mag-netic field has been transformed away by using Lie-transform based Hamiltonian perturbation theory.My planetary rings version of the variational princi-ple uses the same Lie-transform method to transformaway the fast orbital motion of the ring particles inorder to obtain a reduced description of the dynam-ics that is similar, but more general than the tradi-tional Streamline Model. In particular, local gravi-tational instabilities are not thrown away as in theStreamline Model, but rather are transformed intoterms in the variational principle that are analogousto the ponderomotive potential in plasma physics.In the absence of resonant forcing by a satellite, thevariational principle recovers the integral equationfor self-gravity wakes in the form presented by Fuchs(2001), which is equivalent to the original Julian andToomre (1966) theory. The variational principle alsofacilitates an easy derivation of the angular momen-tum flux caused by the self-gravity wakes and the as-sociated enhanced “viscosity” described by Daisakaet al. (2001).

300.07 — Rings around irregular bodies: a rich zooof resonances

Bruno Sicardy11 LESIA, Sorbonne Université and Paris Observatory (Meudon,

France)

Dense and narrow rings have been discovered in2013 around the small Centaur object Chariklo(Braga-Ribas et al., Nature 508, 72, 2014), and aroundthe dwarf planet Haumea in 2017 (Ortiz et al. Nature550, 219, 2017). This came as a surprise as rings hadbeen only known the around giant planets until then.

Due to their irregularities, small bodies exertstrong resonances on a surrounding collisional disk.

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In particular, non-axisymmetric terms in the poten-tial of the body create sectoral resonances of the formj κ = m (n-Ω), where κ and n are the epicyclic fre-quency and the mean motion of the particle, respec-tively, Ω is the rotation rate of the body, and j and mare integers (j being non-negative). In those circum-stances n/Ω ∼ m/(m-j), which is referred to as a m:m-jresonance.

Because non-axisymmetric terms for small bod-ies are relatively much larger than for giant plan-ets, higher order resonances must be considered.Also, retrograde resonances are relevant becauserings around small bodies may have been created af-ter an impact, with no preference for prograde overretrograde motions.

Here we present various results related to the na-ture and dynamics of the sectoral resonances: (1) Ingeneral, j is the order of the resonance, i.e. the orderof the leading term in eccentricity of the correspond-ing perturbing term. However, this requires somecare when labeling the resonances. (2) A resonantorbit crosses itself |m|(j-1) times if m and j are rel-atively prime. This has important consequences onthe structure of the streamlines near a resonance andthe physics of a collisional ring. (3) Simple rules tocalculate the strength of a m:m-j resonance are pro-vided. (4) Prograde and retrograde resonances canactually be described in a unique frame. For instancethe 1:3 and -1:1 (retrograde co-orbital) resonanceshave the same dynamical structure. (5) Examplesof phase portraits of first, second, third and fourthorder resonances are given. Their topology and im-plications for Chariklo and Haumea’s rings are dis-cussed.

The work leading to these results has receivedfunding from the European Research Council underthe European Community’s H2020 2014-2020 ERCGrant Agreement n°669416 ”Lucky Star”.

301 — Dynamics of Lunar Probes

301.01 — The dynamical demise of Luna-3

Davide Amato1,2; Aaron Jay Rosengren1; RenuMalhotra1; Vladislav Sidorenko4; Giulio Baù3

1 Aerospace and Mechanical Engineering, The University of Ari-zona (Tucson, Arizona, United States)

2 University of Colorado Boulder (Boulder, Colorado, United States)3 Università di Pisa (Pisa, Italy)4 Keldysh Institute of Applied Mathematics (Moscow, Russian

Federation)

Luna-3 was a Soviet spacecraft launched in October1959 on a nearly polar, highly elliptical orbit with

a semi-major axis of 0.7 lunar distance. After per-forming a lunar flyby, it collided with the Earth inlate March 1960. Such a short dynamical lifetimehas been ascribed in the literature to the increasein eccentricity due to Lidov-Kozai dynamics. How-ever, considering that the Lidov-Kozai solutions arestrictly valid for orbits close to the primary in the cir-cular, restricted three-body problem, whereas Luna-3’s orbit is far from the primary and it also inter-sects the orbit of the perturber, we find that the or-bit of Luna-3 is better understood in the context ofthe Earth-Sun-Moon-spacecraft four-body problem.In light of this, we carried out a dynamical inves-tigation about the main factors affecting the evolu-tion of its trajectory and its demise. We numericallyintegrate the osculating trajectory of the spacecraftfrom published ephemerides with a high-fidelity or-bit propagation tool, and find excellent agreementwith previous solutions. Additionally, a sensitiv-ity analysis shows the dynamics to be regular un-der small variations in the initial conditions and arewell described by considering lunisolar perturba-tions only; higher gravity harmonics and other phys-ical perturbations have negligible effects. We com-pare the numerically propagated osculating trajec-tory to single- and double-averaged solutions. Wefind that the osculating evolution is heavily influ-enced by close encounters that cannot be reproducedwith averaged approaches, and induce large impul-sive changes in the semi-major axis, eccentricity andinclination. Under lunar perturbations alone, Luna-3’s trajectory collides with the Earth after 200 daysin the single- or double-averaged propagations butsurvives for more than 100 years in the non-averagedsolution. All of these phenomena result in the trajec-tory diverging from the level curves of the double-averaged quadrupolar Hamiltonian in Lidov-Kozaidiagrams. We deduce that the Lidov-Kozai ansatz isnot sufficient to capture the complexity of translunartrajectories, whose evolution is dictated by an inter-play of lunisolar perturbations of both low and highfrequencies and close lunar encounters.

302 — Dynamics of PlanetarySystems

302.01 — Mean motion resonance widths at lowand high eccentricity

Renu Malhotra11 Lunar and Planetary Laboratory, The University of Arizona (Tuc-

son, Arizona, United States)

Orbital resonances play an important role in the dy-

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namics of planetary systems. Classical theoreticalanalyses found in textbooks report that the widthsof first order mean motion resonances diverge fornearly circular orbits; and numerical analyses basedon averaging of the disturbing potential report diver-gence of resonance widths at planet-grazing eccen-tricity. We examined the nature of these divergenceswith non-perturbative analyses using Poincare sec-tions based on the circular planar restricted threebody problem. At low eccentricity, we show that theapparent divergence of first order resonance widthsis an artifact of the leading order perturbation the-ory; the true resonance width has an asymmetry anda discontinuity around the nominal resonance loca-tion and a non-trivial transition to neighboring res-onances. At planet-grazing eccentricity the diver-gence of resonance widths is shown to be an artifactof the single resonance approximation; the true res-onance width is finite and, for first order resonance,scales as ∼μ𝛽 where μ is the perturber’s mass andβ is ≤ 0.5. Furthermore, for orbits of planet-crossingeccentricity there exists a second resonance librationzone whose libration center is displaced from theclassical one at low eccentricity known from pertur-bation theory. We will illustrate these insights withapplications to the asteroid belt and the Kuiper belt.

We acknowledge research funding fromNSF (grant AST-1824869) and NASA (grantNNX14AG93G and 80NSSC18K0397).

302.02 — Collision rates of planetesimals nearmean-motion resonances

Spencer Clark Wallace1; Aaron C. Boley2; ThomasQuinn1

1 Astronomy, University of Washington (Seattle, Washington,United States)

2 University of British Columbia (Vancouver, British Columbia,Canada)

In circumstellar disks, collisional grinding of plan-etesimals produces second-generation dust, whichcan be observed through its thermal emission. Whileit remains unclear when second-generation dust firstbecomes a major component of the total dust con-tent, the presence of such dust and potentially thesubstructure within it can be used to explore a disk’sphysical conditions. For example, a perturbingplanet has been shown to produce nonaxisymmetricstructures, as well as gaps in disks, regardless of theorigin of the dust. However, small grains will havevery different dynamics compared with planetesi-mals when in the presence of gas, and as such, thecollisional evolution of planetesimals could createdusty disk structures that would not exist otherwise.

In particular, mean motion resonances (MMRs) areextremely nonlinear and could drive disk morpholo-gies. We use a direct N-body model to track colli-sion rates in a planetesimal disk under the gravita-tional influence of an external Jupiter-sized planet.The combined excitation and inward migration ofplanetesimals near MMRs tends to enhance the colli-sion rate interior to the nominal resonance locations.This should produce observable variations in the ra-dial structure of the dust, which could be used to in-fer the orbital parameters and mass of the perturbingplanet. Because these simulations are very compu-tationally expensive, we also compare with a modelin which only a narrow annulus of material centeredaround the resonance is considered.

302.03 — The Solar wind as a sculptor ofterrestrial planet formation

Christopher Spalding11 Astronomy, Yale University (New Haven, Connecticut, United

States)

The Kepler mission revealed that a substantial frac-tion of stars in the Galaxy possess planets residing onorbits that lie significantly closer to their host starsthan Mercury does to the Sun. Furthermore, theseclose-in worlds typically exceed the Earth in size.Owing to the large amount of gas these bodies re-tain, they must have formed within the disk-hostingstage, lasting 1-10 million years. Our inner Solarsystem, on the other hand, is peculiarly deficient inmass, with absolutely no material detected interior toMercury. The cause of the Solar system’s hollowed-out architecture remains mysterious. Moreover, theEarth likely formed in 10s of millions of years, whichis after the disk-hosting phase. In this talk, I willpropose and test the hypothesis that the primordialwind emanating from the young Sun was sufficientlystrong to remove planetary building blocks from in-terior to Mercury’s orbit, with this material insteadenriching the Earth’s orbital viscinity with materialfrom the high-temperature inner reaches of the So-lar system. In this way, the mass deficit close toplanet-hosting stars like our Sun arises as a natu-ral consequence when planet formation occurs sub-sequent to the disk-hosting stage, as occured in theSolar system. This wind-induced, outward migra-tion of planetary building blocks predicts numerouscompositional anomalies within the terrestrial plan-ets and the asteroid belt that warrant further study. Itfurther predicts relationships between exoplanetarysizes and orbital architectures that may be comparedto forthcoming planetary detections.

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302.04 — Dynamical Evidence for TerrestrialPlanet Debris in the Asteroid Belt

Claudia Maria Sandine1; Seth Andrew Jacobson11 Earth and Planetary Sciences, Northwestern University

(Evanston, Illinois, United States)

The history of the solar system is dominated by colli-sions among large planetary embryos. Large plane-tary bodies form due to mass-gaining collisions thatbuild up planets from small planetesimals to largerplanet-sized objects, but these collisions also ejectplanetary material into orbit around the Sun. In thepast, collisions between large planetary bodies wereassumed to be perfectly accretionary. We have bro-ken this assumption and incorporated a full colli-sion model from Stewart & Leinhardt (2012) into ourterrestrial planet formation simulations. Before thisproject, numerical simulations determined that left-over primitive planetesimals were emplaced in theasteroid belt. However, here we show that about3% of the impact debris generated by collisions be-tween planetary embryos during this early epochwas also emplaced in the asteroid belt. Furthermore,we tracked the transport history of planetary debrisfrom its generation amongst the inner planets to sta-ble orbits in the asteroid belt discovering that mostdebris is emplaced by a series of interactions with theoutermost planetary embryo during periods whenthe embryo’s aphelion entered the asteroid belt. Thedebris is emplaced on stable orbits throughout theasteroid belt across all relevant semi-major axes andinclinations; however, there is a paucity of very low(e < 0.1) eccentricity debris objects. While these re-sults utilized a suite of 52 simulations within theGrand Tack scenario, this result should be genericto all terrestrial planet formation scenarios that haveplanetary debris generating impacts and embryoswhose eccentricity excursions bring the body into theasteroid belt to lift the perihelions of debris objects.While a small fraction of the debris is emplaced onstable orbits in the asteroid belt, most debris fromplanetary collisions in the inner solar system ends upin either the Sun (33%) or a planet (64%); also, abouta quarter of the debris is re-accreted by the planetfrom which it was blasted off. From this work, weconclude that there must be pieces of planets in theasteroid belt.

302.05 — Losing moons: The gravitationalinfluence of close encounters on satellite orbits

Jeremy Brooks1; Seth Andrew Jacobson11 Northwestern University (Evanston, Illinois, United States)

The early solar system was a period of ubiquitouscollisions and close encounters between protoplane-tary masses, all coalescing to form our current fourterrestrial planets. Earth and Mars have satelliteslikely formed by giant collisions, but Venus and Mer-cury do not despite forming in the same environ-ment and possessing similar collisional histories asEarth and Mars. Large collisions routinely producedisks from which moons will accrete (Rufu et al.2017). In particular, it is curious given the similar-ities between Earth and Venus in mass and orbitalcharacteristics that Venus does not possess a moonwhile Earth possesses one. One possible reason forthis discrepancy is that moons formed from giant im-pacts are later lost due to extended exposure to grav-itational perturbations from close encounters withother protoplanetary masses. Analogously, theseperturbations are thought to be responsible for theMoon’s five-degree orbital inclination, in contrast tothe physically-expected alignment with the equato-rial plane (Pahlevan & Morbidelli, 2015). Further ex-posure to close encounters may alter inclination andeccentricity enough to liberate moons from their or-bits. Here, we model the chaotic period of terres-trial accretion and moon formation to analyze thefrequency and orbital influence of close encounters.We find that close encounters are plausible mecha-nisms for altering moon orbital characteristics. If theexposure to close encounters is long enough (i.e., ifthe moon was early-forming), the moon may be com-pletely removed from its orbit. We apply these re-sults to Venus’ early history and to generalized ter-restrial planetary formation histories. These resultsdemonstrate that the timing of the moon-forming gi-ant impact helps explain the retention and orbitalcharacteristics moons.

303 — Dynamics of Exoplanets

303.01 — Excitation of Planetary ObliquitiesThrough Planet-Disk Interactions

Sarah Millholland1; Konstantin Batygin21 Astronomy, Yale University (New Haven, Connecticut, United

States)2 California Institute of Technology (Pasadena, California, United

States)

The tilt of a planet’s spin axis off its orbital axis(“obliquity”) is a basic physical characteristic thatplays a central role in determining the planet’s globalcirculation and energy redistribution. Moreover, re-cent studies have also highlighted the importance ofobliquities in sculpting not only the physical features

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of exoplanets but also their orbital architectures. It istherefore of key importance to identify and charac-terize the dominant processes of excitation of non-zero axial tilts. Here we highlight a simple mecha-nism that operates early on and is likely fundamen-tal for many extrasolar planets and perhaps even So-lar System planets. While planets are still formingin the protoplanetary disk, the gravitational poten-tial of the disk induces nodal recession of the orbits.The frequency of this recession decreases as the diskdissipates, and when it crosses the frequency of aplanet’s spin axis precession, large planetary obliq-uities may be excited through capture into a secularspin-orbit resonance. We study the conditions for en-countering this resonance and calculate the resultingobliquity excitation over a wide range of parameterspace. Planets with semi-major axes in the range 0.3AU < a < 2 AU are the most readily affected, but large-a planets can also be impacted. We present a casestudy of Uranus and Neptune and examine whetherthis mechanism can help explain their high obliqui-ties.

303.02 — Obliquity Evolution of Earthlike planetsin α Centauri AB

Billy Quarles1; Gongjie Li1; Jack Lissauer21 Georgia Institute of Technology (Marietta, Georgia, United States)2 NASA Ames Research Center (Moffett Field, California, United

States)

Changes in planetary obliquity, or axial tilt, influ-ence the climatic conditions on a potentially habit-able planet, where orbital perturbations from a bi-nary star companion can drive these changes to ex-tremes. We study the evolution of planetary obliq-uity for an Earthlike planet in the habitable zones ofα Centauri AB, our nearest stellar neighbor, throughnumerical simulations. Additionally, we explore theeffects on the spin precession due to terrestrial neigh-bors and the presence of a moon. From our simu-lations, we uncover low variability regions of phasespace that depend on the secular orbital precessionas well as starting values for the mutual inclina-tion relative to the binary planet, the spin longitude,and the initial obliquity. Moreover, we find thatthe added precession from a large moon typicallydestabilizes the host planet’s obliquity allowing upto ∼40° of variation. The consequences for climateon such worlds will be influenced by orbital, flux,and obliquity variations, where we will discuss andcompare the variations on an Earthlike planet in αCentauri AB with those in the solar system.

303.03 — Modeling the Architectures ofExoplanetary Systems using Clusters of SimilarPlanets

Darin A. Ragozzine1; Matthias Y. He2; Eric B. Ford21 Physics and Astronomy, Brigham Young University (Provo, Utah,

United States)2 Pennsylvania State University (University Park, Pennsylvania,

United States)

With over 700 systems of multiple transiting exo-planets, the Kepler Space Telescope has providedpowerful observational constraints on the orbital andphysical properties of planetary systems. As planetsin these systems often have mulitple planets and con-centrate at semi-major axes of ∼0.1 AU, we refer tothem as Systems with Tightly-spaced Inner Planets(STIPs). A full understanding of the true underlyingarchitectures of STIPs is challenging because of theobservational selection effects of the transit method.We compensate for these selection effects by propos-ing a model for the architectures systems, implementa forward model to produce a population of STIPs,using Kepler DR25 data products to model Kepler’sdetection efficiency and to produce a synthetic cata-log of simulated observations, compare these to Ke-pler’s observed catalog to produce a figure-of-merit,and infer the model parameters (including uncer-tainties) that best match the Kepler data. We inves-tigate a model where STIPs are composed of clus-ters of planets where the overall cluster parametersare drawn from power-laws, but the planets withina cluster have similar periods and radii. Using ad-vanced statistical techniques to incorporate a vari-ety of observational constraints, we show that thisclustered model performs much better than a non-clustered model, particularly in matching the ob-served period ratio and depth ratio distributions. Weconfirm previous results that most STIP planets arenot near resonances and that the observed excess ofsingle transiting planets implies that matching theKepler data requires at least two types of planetarysystems, with the higher-multiplicity system charac-terized by low eccentricities (∼0.01) and mutual in-clinations (∼1 degree). We will present our model,the results of our fitting procedure, and the implica-tions for STIP architectures.

303.04 — Dynamical Constraints on PlanetarySystems: Multi-Planet Systems Observed withSingle Transits

Fred Adams1; Juliette Becker11 Physics Department, University of Michigan (Ann Arbor, Michi-

gan, United States)

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Transit surveys are discovering enormous numbersof extrasolar planets, with a sizable fraction found inmulti-planet systems. Given the limitations on ob-servational resources, especially the available timebaselines, many planets are observed via single tran-sit events. This talk describes how dynamical sta-bility considerations can be used to constrain the al-lowed parameter space for such planetary systems inthe absence of complete data. In addition to planetsthat are detected, we can also constrain possibilitiesfor unseen planets that could exist in these systems.The orbital elements of these planets cannot be deter-mined exactly, but can be described in terms of prob-ability distributions, which in turn depend on thepriors used in the analysis. The nearby five-planetsystem HIP 41378, with its outer three planets firstdiscovered through single transit events, is used as atest case.

303.05 — Unseen companions of V Hya inferredfrom periodic ejections

Jesus Salas1; Smadar Naoz1; Mark R. Morris1; Alexan-der Patrick Stephan1

1 Physics and Astronomy, UCLA (Los Angeles, California, UnitedStates)

A recent study by Sahai et al (2016) found periodic,high-speed, collimated ejections (or ”bullets”) fromthe star V Hya, using data from the Hubble SpaceTelescope. The authors of that study proposed amodel associating these bullets with the periastronpassage of an unseen, substellar companion in an ec-centric orbit and with an orbital period of ∼8 yrs.Here we propose that V Hya is part of a triple system,with a substellar companion having an orbital pe-riod of ∼8 yrs, and a tertiary object on a much widerorbit. In this model, the more distant object causeshigh-eccentricity excitations on the substellar com-panion’s orbit via the Eccentric Kozai-Lidov mecha-nism. These eccentricities can reach such high val-ues, leading to Roche-lobe crossing, producing theobserved bullet ejections via a strongly enhanced ac-cretion episode. For example, we find that a bal-listic bullet ejection mechanism is consistent with abrown dwarf companion, while magnetically drivenoutows are consistent with a Jovian companion. Fi-nally, we suggest that the distant companion may re-side at few hundreds AUs on an eccentric orbit.

303.06 — Dynamical Scultiping of CompactPlanetary Systems

Alysa Obertas1,2; Norman Murray2; Daniel Tamayo3

1 Astronomy & Astrophysics, University of Toronto (Toronto, On-tario, Canada)

2 Canadian Institute for Theoretical Astrophysics (Toronto, Ontario,Canada)

3 Princeton University (Princeton, New Jersey, United States)

The Kepler mission found hundreds of multi-planetsystems, many of which have four or more planetsall with orbit periods under 150 days. These compactsystems have survived for 1011 to 1012 orbits. Thesesystems are not only dynamically old, but also dy-namically cold. Transit durations and transit timingvariations show that high multiplicity systems typi-cally have small orbital eccentricities and mutual in-clinations. Nbody integration suggest that observedsystems are packed close to their dynamical limits,but the mechanism ultimately driving the long-termevolution is still not well-understood. In a previousstudy, we investigated the long-term stability of a setof compact five-planet systems. In addition to re-covering the expected relationship between the sur-vival timescale and initial orbital spacing in mutualHill radii, we also saw survival vary by several or-ders of magnitude near period commensurabilities,suggesting that mean motion resonance (MMR) isdriving the dynamical evolution of the most com-pact planetary systems. It is not clear whether thischaos arises from resonance overlap of adjacent pairsof planets, or from overlap of subresonances for in-dividual pairs however. We will present our recentanalytical and numerical work to explore and under-stand subresonance overlap in compact multi-planetsystems.

303.07 — Low-Eccentricity Formation ofUltra-Short Period Planets in Multi-PlanetSystems

Bonan Pu11 Cornell University (Ithaca, New York, United States)

Recent studies suggest that ultra-short period plan-ets (USPs), Earth-sized planets with sub-day periods,constitute a statistically distinct sub-sample of Ke-pler planets: USPs have smaller radii (1–1.4 R⊕) andlarger mutual inclinations with neighboring planetsthan nominal Kepler planets, and their period dis-tribution is steeper than longer-period planets. Westudy a ”low-eccentricity” migration scenario for theformation of USPs, in which a low-mass planet withinitial period of a few days maintains a small but fi-nite eccentricity due to secular forcings from exte-rior companion planets, and experiences orbital de-cay due to tidal dissipation. USP formation in thisscenario requires that the initial multi-planet system

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have modest eccentricities (≳ 0.1) or angular momen-tum deficit. During the orbital decay of the inner-most planet, the system can encounter several ap-sidal and nodal precession resonances that signifi-cantly enhance eccentricity excitation and increasethe mutual inclination between the inner planets. Wedevelop an approximate method based on eccentric-ity and inclination eigenmodes to efficiently evolvea large number of multi-planet systems over Gyrtimescales in the presence of rapid (as short as ∼100years) secular planet-planet interactions and othershort-range forces. Through a population synthesiscalculation, we demonstrate that the ”low-e migra-tion” mechanism can naturally produce USPs fromthe large population of Kepler multis under a vari-ety of conditions, with little fine tuning of parame-ters. This mechanism favors smaller inner planetswith more massive and eccentric companion planets,and the resulting USPs have properties that are con-sistent with observations.

303.08 — The hot Jupiter period-mass distributionas a signature of in situ formation

Elizabeth Bailey11 Caltech (Pasadena, California, United States)

More than two decades after the widespread detec-tion of Jovian-class planets on short-period orbitsaround other stars, their dynamical origins remainimperfectly understood. In the traditional narrative,these highly irradiated giant planets, like Jupiter andSaturn, are envisioned to have formed at large stello-centric distances and to have subsequently under-gone large-scale orbital decay. Conversely, morerecent models propose that a large fraction of hotJupiters could have formed via rapid gas accretionin their current orbital neighborhood. In this study,we examine the period-mass distribution of close-ingiant planets, and demonstrate that the inner bound-ary of this population conforms to the expectationsof the in-situ formation scenario. Specifically, weshow that if conglomeration unfolds close to thedisk’s inner edge, the semi-major axis - mass relationof the emergent planets should follow a power law a∝ M−2/7 — a trend clearly reflected in the data. Wefurther discuss corrections to this relationship due totidal decay of planetary orbits. Although our find-ings do not discount orbital migration as an activephysical process, they suggest that the characteristicrange of orbital migration experienced by giant plan-ets is limited.

303.09 — Determining Stability Conditions forSubmoons Orbiting Exomoon Candidate: Kepler1625-b-I

Marialis Rosario-Franco1,2; Billy Quarles3; Zdzislaw E.Musielak2; Manfred Cuntz2

1 National Radio Astronomy Observatory (Socorro, Texas, UnitedStates)

2 University of Texas at Arlington (Arlington, Texas, United States)3 Georgia State University (Atlanta, Georgia, United States)

An intriguing question in the context of dynamicsarises: Could a moon possess a moon itself? Sucha configuration does not exist in the Solar System, al-though this may be possible in theory; Kollmeier &Raymond (2019) showed the critical size of a satel-lite necessary to host a long-lived sub-satellite, orsubmoon. However, the orbital constraints for thesesubmoons to exist are still undetermined, where acritical parameter is how far from the host satellitecan these submoons orbit. Previous studies (Domin-gos et al. 2006) indicate that moons should be sta-ble out to a fraction of the host planet’s Hill sphere,which in turn will depend on the eccentricity and in-clination of its orbit. Motivated by this, we have per-formed orbital integrations of the exomoon candi-date Kepler 1625-b-I, a Neptune-sized exomoon can-didate that orbits the Jovian planet Kepler 1625-b(Teachey & Kipping 2018). In our numerical study,we evaluate the orbital parameters where possiblesubmoons could be stable by varying the eccentricityand inclination of their orbits. Moreover, we providediscussion on the observational consequences of ob-serving these satellites through photometric or radialvelocity observations.

304 — Dynamics of the N(>=3)-Body Problem

304.01 — Three-body stability limit at infinite time

Mauri Valtonen1; Aleksandr Mylläri21 FINCA, University of Turku (Turku, Finland)2 2. St.George’s University (St. George’s, Grenada)

In the general three-body problem the initial phasespace may be divided in two parts: a chaotic regionwhere orbits can be described by statistical meansover the long term, and the stable region where defi-nite orbit behavior may be found e.g. by perturbationtechnique. The surface in phase space which sepa-rates the two regions is called the stability surface,and if measured in units of the closest encounter dis-tance between the binary and the pericenter of the

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initial third body orbit, it is called the stability limit.An expression for the stability limit Q, in units of thesemi-major axis of the binary, was derived by us: Q= 101/3 A [(f g)2/(1 - e3)]1/6 where A = 2.4, e3 is theeccentricity of the outer binary orbit and f and g arefunctions which at the limit of e = cos i = m = 0, ob-tain f = g = 1. Here e is the binary eccentricity, i theinclination between the inner and the outer orbits,and m is the mass of the third body with respect tothe binary mass (Mylläri et al. MNRAS, 476, 830,2018). The factor 101/3 comes from the number ofouter revolutions N = 10,000 used to define stability;for any other number of revolutions the coefficient isN1/12. This would imply that the stability limit goesto infinity at infinite time, i.e. when N becomes infi-nite. The question we address in this work is whetherthis is true. By extending orbit integrations to higherrevolution numbers, N up to 107, and by modifyingthe analytical theory, we show that the stability limitis always finite, at any N. When N goes toward in-finity, the factor 101/3 approaches 101/2 in the for-mula above which makes Q only about a factor of 1.5higher than at N = 10,000.

304.02 — Spatial Low-Energy Asteroid and CometTransit Analysis

Rodney Anderson1; Paul W. Chodas1; Robert W.Easton2; Martin W. Lo1

1 Jet Propulsion Laboratory/California Institute of Technology(Boulder, Colorado, United States)

2 University of Colorado at Boulder (Boulder, Colorado, UnitedStates)

The L1 and L2 gateways are well known to be keyto understanding the transit of natural bodies nearplanets in low-energy regimes. These types of tran-sit trajectories are particularly interesting for study-ing the temporary capture of objects near Earth andJupiter. Understanding their behavior is also impor-tant for exploring potential impacts of asteroid orcomets with these planets. Previous work by Ander-son, Chodas, Easton, and Lo (2016) analyzed thesetypes of trajectories using isolating block methods(Anderson, Easton, and Lo, 2017) within the con-text of the planar circular restricted three-body prob-lem (CRTBP) and found that many of the character-istics of transit trajectories observed in nature maybe captured using this model. Comparisons of thesource orbital elements of these types of trajectorieswith known bodies showed potential relationships tocomets and asteroids in the case of the Sun-Jupiterand Sun-Earth/Moon barycenter problems, respec-tively. Given that these initial results showed poten-tial relationships between the transit trajectories and

known bodies, further exploration has now been per-formed in the spatial CRTBP. For this analysis, theplanar isolating block methods for computing tran-sit through the region near the secondary (Jupiter orthe Earth/Moon barycenter) were extended to thespatial problem. These results produce topologi-cal disks, or portals, in configuration space throughwhich all transit trajectories must pass at a given en-ergy. These topological disks are computed both ex-terior to the L2 point and interior to the L1 point.Given these disks, analyses of the transit trajectoriesin the spatial problem are completed and comparedto the previous planar results. The source orbital ele-ments of the transit trajectories are also computed forcomparison with known bodies and to aid in guid-ing the search for these types of transit trajectories.In particular, trajectories that potentially loiter nearthe Earth for significant periods of time are identifiedand described.

304.03 — Operator splitting methods for numericalintegration of weakly perturbed N-body systems

Daniel Tamayo1; Hanno Rein2; David M. Hernandez31 Astrophysical Sciences, Princeton University (Princeton, New

Jersey, United States)2 University of Toronto at Scarborough (Toronto, Ontario, Canada)3 Harvard-Smithsonian CfA (Cambridge, Massachusetts, United

States)

Operator splitting methods have proven powerfultools for the numerical integration of N-body sys-tems. Symplectic splitting schemes in particular rev-olutionized celestial mechanics through their long-term conservation of the system’s Hamiltonian struc-ture. However, many astrophysically relevant per-turbations like tides and drag are dissipative, andthe numerical properties of splitting schemes thatinclude them are unclear. We argue that power se-ries expansions of splitting scheme errors applied tosymplectic algorithms generalize to dissipative sys-tems, and use these to analyze the numerical behav-ior of dissipative splitting schemes.

304.04 — Solving N-body problems

David M. Hernandez1,21 Astronomy, Harvard-Smithsonian Center for Astrophysics (San

Antonio, Texas, United States)2 RIKEN-CCS (Kobe, Japan)

The N-body problem describes a wide range of as-trophysical phenomena, ranging from planetary sys-tems to dark matter haloes. Perhaps the most pop-ular line of attack to solving the N-body ordinary

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differential equations is to use Hamiltonian, or sym-plectic, integrators to approximate their solutions.Examples of codes that do this include MERCURY,SyMBA, the Wisdom—Holman map, GADGET, orMERCURIUS. There is perhaps confusion as to whata symplectic integrator actually is, because codesconsidered symplectic in some works are not consid-ered symplectic in other works.

In this talk, I propose a new definition for symplec-tic integrators. In terms of differentiability class, theintegrator must be C1,1. I show an example wherenot satisfying this criteria makes a bound Kepler or-bit become hyperbolic in less than 10,000 periods. Inexperiments for several Hamiltonians, periodic or-bits did not exist when the criteria was not satisfied.Several popular codes do not satisfy this differen-tiability criteria. I show that, numerically, the codeMERCURY is not symplectic, and gives unphysicaldynamics in some cases. Our recent code, MER-CURIUS, is designed to overcome this limitation.

The N-body Hamiltonian has differentiabilityclass infinity and I argue symplectic integratorsshould also have this symmetry. I find that increas-ing the smoothness of a hybrid integrator from C0 toC4 improves the error of the Jacobi constant of a re-stricted three-body orbit by 105. While the differen-tiability class of popular codes can be increased withlittle effort, for other cases where the integrator hasnon-smooth changes, such as those using block time-stepping, the differentiability class may be difficult tochange.

References: arXiv:1903.04972, arXiv:1904.03364,and arXiv:1902.03684

400 — In Honor of theContributions of Bill Ward

400.01 — The Formation of Planetesimals

Andrew Youdin11 Steward Observatory, University of Arizona (Tucson, Arizona,

United States)

The quest to understand the origin of planetesimals,i.e. the gravitationally-bound, solid building blocksof planets, lies at the forefront of astrophysics andplanetary science. Work by Bill Ward has an on-going impact on the field, including (but not lim-ited to) the seminal Goldreich & Ward (1973) paper.The central hypothesis of these works is that plan-etesimals assembled by the gravitational collapse ofdense clumps of much smaller solids. Even withcurrent observational facilities, this hypothesis can-not be directly proved. However the hypothesis

is more popular than ever, having converted evensome ardent skeptics. More importantly, the hypoth-esis remains tremendously useful, as a way to de-velop physically consistent models of planet forma-tion which can explain salient features of Solar Sys-tem bodies and exoplanets. In this talk, I will presentan overview of state-of-the-art planetesimal forma-tion models, including those where the streaminginstability acts to seed the gravitational collapse ofplanetesimals. I will emphasize how Bill Ward’scontributions laid the foundation for recent develop-ments, and how some of his ideas — on the secularmode of gravitational collapse in particular — stillrequire further exploration.

400.02 — The Evection Resonance in theEarth-Moon system: Analytical analysis

Robin Canup1; William Ward1; Raluca Rufu11 Planetary Sciences Directorate, Southwest Research Institute

(Boulder, Colorado, United States)

As the initial Moon’s orbit expanded due to tidalinteraction with the Earth, it would have encoun-tered the evection resonance when the precessionfrequency of the Moon’s perigee equaled that of theEarth’s solar orbit (e.g., Brouwer & Clemence 1961;Kaula & Yoder 1976; Touma & Wisdom 1998). Cap-ture into evection excites the lunar eccentricity andcan drain angular momentum from the Earth-Moonsystem, transferring it to Earth’s heliocentric orbit.Touma and Wisdom (1998) modeled the capture ofthe Moon in evection for an Earth with an initial ro-tation period of 5 hr and the Mignard tidal model.In their simulations, the Moon’s residence in evec-tion is relatively brief, and results in only modestremoval of angular momentum, i.e., a few percentof LEM. In contrast, Ćuk and Stewart (2012) useda different tidal model and found that if the initialEarth-Moon angular momentum (L0) was substan-tially greater then LEM, capture into evection couldhave instead reduced L0 by up to a factor of twoor more. This would allow for a broader range ofMoon-forming impact scenarios, including high an-gular momentum impacts that can directly explainmany of the observed Earth-Moon isotopic similari-ties (Ćuk & Stewart 2012; Canup 2012).

We have developed an analytic model to track theevolution in evection using the Mignard tidal model.We show that as long as the resonance remains oc-cupied (i.e. librations are damped), the Earth-Moonwill approach a co-synchronous state, independentof the value of L0. This state has a substantially lowerangular momentum than LEM, and is ultimately un-stable, resulting in the eventual loss of the Moon due

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to slow-down of Earth’s spin by the Sun. The cur-rent Earth-Moon system implies either that captureinto evection did not occur, or that escape occurredprior to this point. Escape can occur if the librationamplitude becomes large. We examine how the libra-tion amplitude changes with time during evolutionin evection, and identify stages where escape may oc-cur as a function of the tidal parameters of the Earthand Moon.

400.03 — The Evection Resonance in theEarth-Moon system: Numerical analysis

Raluca Rufu1; Robin Canup11 Space Sciences, Southwest Research Institute (Boulder, Colorado,

United States)

Moon formation by a high-angular momentum im-pact may offer a compelling mechanism to create asatellite that is compositionally similar to the silicateEarth without requiring an Earth-like impactor (Ćuk& Stewart 2012, Canup 2012). In such impacts, theEarth-Moon system’s initially high angular momen-tum must be greatly reduced after the Moon forms.A possible angular momentum removal mechanismis the evection resonance with the Sun, which occurswhen the period of precession of the lunar perigeeequals one year (Touma and Wisdom 1998). Cap-ture into evection excites the lunar eccentricity andangular momentum is transferred from the Earth-Moon pair to Earth’s orbit around the Sun. However,previous studies have found contradicting outcomes(e.g., early vs. late resonance escape; Ćuk & Stewart2012, Wisdom & Tian 2015), and varied angular mo-mentum removal efficiency for different tidal mod-els. Understanding such behaviors is important forassessing the likelihood of high-angular momentumlunar origin scenarios. We study the system’s evolu-tion using a numerical model. Our results show thatboth early and late resonance escapes are possible indifferent parameter regimes. For early resonance es-capes we find that the system may enter a protractedquasi-resonance phase (reminiscent of the limit cy-cle found by Wisdom & Tian, 2015), in which theeccentricity oscillates about a value smaller than thestationary resonance eccentricity (Ward et. al 2019).We find that the final Earth-Moon system angularmomentum, set by the timing of resonance/quasi-resonance escape, is a function of both the ratio ofphysical and tidal parameters in the Earth and Moon(A), and the absolute rate of tidal dissipation in theEarth. Large rates are preferred for a fluid-like post-impact Earth (Zanhle et al. 2015) and for these valuesthe angular momentum removal is controlled purelyby evection (late resonance escape). Moreover, our

results do not show a preference for obtaining a fi-nal angular momentum similar to that in the currentEarth-Moon system.

400.04 — Bill Ward’s Contributions to PlanetFormation and Migration

John Papaloizou11 DAMTP, University of Cambridge (Cambridge, United Kingdom)

The fundamental theoretical developments in thefield of planet formation and orbital evolution thatwere pioneered by Bill Ward will be reviewed. Theareas covered range from how particles accumulateto form planetesimals to delineating how protoplan-etary cores migrate in the protoplanetary disk. In thelatter case he established the main forms of migra-tion that are driven by generation of density waves:type I for embedded protoplanets and type II forgap forming protoplanets. He was the first to clearlyshow that type I migration, applicable to embeddedprotoplanets was predominantly directed inwards.Perhaps not as well known was his original 1991 for-mulation of the non linear coorbital torque know asthe ’horse shoe drag’. This and elaborations of ithave proved significant for understanding how mi-gration may be halted in for example planet trapsand thus constitute an important ingredient of lowmass planet formation modelling.

400.05 — Tilting Ice Giants With CircumplanetaryDisks

Zeeve Rogoszinski1; Douglas Hamilton11 University of Maryland (College Park, Maryland, United States)

The leading hypothesis to the origin of Uranus’ andNeptune’s large obliquities, the angle between theplanet’s spin-axis and its orbital plane, is giant colli-sions, with impact masses ranging from Mars-sizedfor Neptune to Earth-sized for Uranus. Collisionsthis big, however, should also leave a strong imprinton planetary spin rates. While a Mars-sized impactorwould change spin rate at the 10% level, an Earth-mass strike could alter it by up to a factor of 3. Theice giants’ near identical spin rates are statistically in-consistent with such large impacts and instead sug-gest a shared origin with gas accretion dominatingthe final spin rate (Batygin, 2018); this, however,tends to drive obliquities towards 0°. Furthermore,tilting Uranus beyond 90° requires at least two im-pacts in order to explain the prograde motion of itssatellites (Morbidelli et al., 2012). Is there a way toreconcile the tension between ice giant spin rates andobliquities?

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Hamilton & Ward (2004) posit that Saturn’s 27°tilt is caused by a secular spin-orbit resonance: amatch between the precession frequencies of Sat-urn’s spin-axis and Neptune’s orbit. The advantageof this mechanism is that it preserves the spin-stateof the entire planetary system as the planet tilts over.Uranus’ and Neptune’s spin precession frequenciesare currently too slow for a similar resonance, butthat may not have always been the case. The spin pre-cession rate is enhanced by the circumplanetary diskwhich must have existed for Uranus and Neptune toacquire their H and He gas and inner satellites. Thelow gas content of the ice giants suggests that sizablecircumplanetary disks existed for just a few Myrs asthe solar nebula dissipated. We show that realisticdisk profiles can speed up the ice giants’ spin preces-sion rates to match their orbital precession rates. Thisresonance can be strong enough to tilt each planetby 30° - 50° on Myr timescales, providing an alterna-tive origin for Neptune’s tilt and perhaps also half ofUranus’. We are currently tuning parameters to pushUranus to an obliquity of 70°. If successful, Uranus’sfinal 98° tilt could be a product of a subsequent Mars-sized collision, with the associated change to its spinrate limited to ∼10%.

400.06 — Multi-Gyr obliquity history of Marsretrieved using the bombardment compass

Edwin Stephen Kite1; Samuel Holo1; Stuart Robbins21 Geophysical Sciences, University of Chicago (Chicago, Illinois,

United States)2 Southwest Research Institute (Boulder, Colorado, United States)

Because the Solar System is chaotic, planet orbitscannot be deterministically reverse-integrated be-yond ∼100 Mya. Many geologic methods have beenproposed to vault this fundamental barrier, but allare indirect. We present a direct method, whichwe term the bombardment compass, and apply itto Mars. Mars’ obliquity is currently ∼25° but haschanged dramatically over billions of years since so-lar system formation (e.g., Ward, 1973; Touma andWisdom, 1993; Laskar and Robutel, 1993; Laskaret al., 2004). The dynamics of Mars’ obliquity arebelieved to be chaotic, and the historical ∼3.5 Gyr(late-Hesperian onward) obliquity probability den-sity function (PDF) is highly uncertain and cannot beinferred from direct simulation alone. We developeda new technique using the orientations of ellipticalcraters to constrain the true late-Hesperian-onwardobliquity PDF. We developed a forward model ofthe effect of obliquity on elliptic crater orientationsusing ensembles of simulated Mars impactors and∼3.5 Gyr-long Mars obliquity simulations. In our

model (Holo et al. 2018), the inclinations and speedsof Mars crossing objects bias the preferred orienta-tion of elliptic craters which are formed by low-angleimpacts. Comparison of our simulation predictionswith a validated database of elliptic crater orienta-tions allowed us to invert for the best-fitting obliq-uity history. We found that since the onset of the lateHesperian, Mars’ mean obliquity was likely low, be-tween ∼10° and ∼30°, and the fraction of time spentat high obliquities >40° was likely <20%.

400.07 — Scanning Secular Resonance Theory andthe Epoch of Giant Planet Migration

Craig B. Agnor11 Queen Mary University of London (London, United Kingdom)

Ward (1981) introduced the concept of scanning sec-ular resonances and showed that the observed or-bital architecture of a system can be used to con-straints earlier epochs of evolution. This work estab-lished a generalised framework for tracing the linearsecular evolution of a planetary system through anepoch where the system’s gravitational potential ischanging. The central ideas of this work have beenbroadly applied to cosmogonical theories. For ex-ample, scanning secular resonances in the early so-lar system may explain the excitation of Mercury’sorbit, constrain the dispersal of the gaseous nebula,account for the obliquity of Saturn, drive the excita-tion and clearing of primitive body belts, and informthe orbital structure and history of exoplanetary sys-tems. In this presentation I will review key aspects ofthe scanning secular resonance framework of Ward(1981) and discuss how the fundamental ideas of thiswork can be used to gain insight into several aspectsof giant planet migration in the solar system.

401 — Spin-Orbit Dynamics

401.01 — Tidally-driven collapse of outer solarsystem binaries.

David A. Minton1; Andrew Hesselbrock11 EAPS, Purdue University (West Lafayette, Indiana, United

States)

Small body binary systems are common throughoutthe solar system and are typically comprised of twosimilar mass bodies orbiting their mutual barycen-ter. Binary systems are particularly common in sub-populations of Kuiper Belt Objects (KBOs), and theprevalence of binaries may correlate with the dy-namical excitation level of the sub-population, with

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the Cold Classical population having a higher preva-lence of observed binaries than the more excited pop-ulations. Recent observations by the New Horizonsspacecraft revealed that the Cold Classical KuiperBelt Object 2016 MU69 is composed of two flattenedlobes. Here we investigate the mechanisms by whichKBO binaries can be induced to undergo tidally-driven collapse and reconfiguration, forming contactbinaries. We also investigate how this collapse pro-cess may provide source material for the rings ob-served around some Centaurs.

401.02 — The Search for Spin-Orbit Resonances inthe Pluto System

Mark Robert Showalter1; Anne Verbiscer3; Marc Buie2;Paul Helfenstein4

1 Carl Sagan Center, SETI Institute (Mountain View, California,United States)

2 Southwest Research Institute (Boulder, Colorado, United States)3 U. Virginia (Charlottesville, Virginia, United States)4 Cornell University (Ithaca, New York, United States)

During the New Horizons flyby of Pluto, it was ob-served that the four small moons, Styx, Nix, Ker-beros and Hydra, have very unusual spin states.Whereas we might have expected the moons to betidally locked, they are in fact all spinning at ratesmarkedly faster than their mean motions. Also, all ofthe moons’ rotation poles are misaligned with theirorbital poles; several moons have obliquities near 90degrees. We explore the possibility that these moonsmay be trapped in an unusual type of spin-orbit res-onances driven by the influence of Pluto’s very large,inner moon, Charon. In this situation, a spin-orbitresonance is defined by three different periods: themoon’s rotation period, its polar precession period,and its synodic orbital period with Charon. The com-bination of high obliquity and nonnegligible polarprecession plays a very large role in this analysis,leading to resonant spin rates that are very differentfrom what one would have predicted if polar preces-sion is ignored.

We are currently in the second year of HubbleSpace Telescope observing program focused on thephotometry and dynamics of Pluto’s small moons.The recent data set, combined with earlier HST dataobtained during 2010-2015, provides a very longbaseline for determining each moon’s rotation pe-riod. In addition, we see direct evidence for po-lar precession in the year-by-year variations of eachmoon’s photometry, suggesting that several of thepoles precess over periods of a few years. With directmeasurements of all three relevant rates, we are now

able to test the hypothesis that these unusual reso-nances might be active. Although our observationalresults are not yet definitive, initial results are en-couraging. We note that the model of high-obliquitymoons that are both spinning and precessing ex-plains the photometry better than the earlier hypoth-esis by Showalter and Hamilton (Nature 522, 45-49,2015, doi:10.1038/nature14469) that these moons arein chaotic rotation.

401.03 — Constraints on the Masses of Nix andHydra

Simon Bernard Porter1; Robin Canup11 Southwest Research Institue (Boulder, Colorado, United States)

Pluto and its five satellites is the most complex cir-cumbinary system yet visited with a spacecraft. Thecentral binary of Pluto and the very large satelliteCharon is surrounded by four much smaller, almostcoplanar satellites. Here we will present initial re-sults of an effort to constrain the masses of Nix andHydra, the two larger small satellites, based on boththeir mutual perturbations and their perturbationson the two smaller small satellites, Styx and Ker-beros. These constraints use a reanalysis with GaiaDR2 of all available Hubble Space Telescope andNew Horizons observations of the small satellites toprovide extremely high precision absolute astrome-try. The range of mass+orbit solutions which bothfit this high-precision astrometry and which are dy-namically stable over long timescales allows us toplace constraints on the masses of Nix and Hydra.These masses can then be combined with the vol-ume estimates for Nix and Hydra from New Hori-zons resolved imaging in order to estimate the den-sities of those satellites. Since the small satelliteswere likely created in the same giant impact that cre-ated Charon, constraining their densities provides aunique insight in the giant impact process.

401.04 — Spin and orbit dynamics of uniqueKuiper belt trinary Lempo

Seth L. Pincook1; Darin A. Ragozzine1; Simon BernardPorter2

1 Physics and Astronomy, Brigham Young University (Provo, Utah,United States)

2 Southwest Research Institute (San Antonio, Texas, United States)

Many Kuiper belt objects orbiting beyond Neptuneare found in binaries with a variety of mass ratios,but the only objects with three or more componentsare Pluto, Haumea, and 47171 Lempo (1996 TC36).

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While Pluto and Haumea are large objects with mul-tiple small moons, the Lempo system is unique in theKuiper belt (and the solar system) as a true trinarysystem: a close binary (both bodies having nearlyidentical mass) and a single moon orbiting the bi-nary. Due to the unique configuration of the sys-tem, especially the similar masses of all three com-ponents, the orbits cannot be modeled using Ke-plerian dynamics, though an approximate double-Keplerian solution was presented in Benecchi et al.2010. We are studying the spin and orbit dynamics ofthe Lempo system using our new n-quadrupole inte-grator SPINNY (SPIN+N-bodY). SPINNY accountsfor the quadrupole gravitational components in thespin and orbital evolution of an arbitrary number ofbodies. Similar to Correia 2018, we use SPINNY toinvestigate the spin and orbit dynamics of this sys-tem, in coordination with a parallel effort to infer thephysical and orbital parameters of the three compo-nents using astrometric data. We will present thenew SPINNY integrator and insights into the spinand orbit dynamics of the Lempo system.

401.05 — νA 2-DOF triaxial model for theroto-orbital coupling in a binary system. The slowrotation regime

Sebastian Ferrer1; Antonio Cantero1; Francisco Crespo2;Jorge Zapata2

1 DITEC Matematica Aplicada, Universidad de Murcia (Espinardo,Murcia, Spain)

2 Universidad de Bio-Bio (Concepción, Chile)

The Full Gravitational 2-Body Problem is far from be-ing integrable and continues to be a challenge. Fromthe analytical point of view, several approximationsare studied ranging from fundamental astronomy tospace mission applications. A classical approach,that we assume from now on is to consider the roto-orbital dynamics of a triaxial body around a primaryhomogeneous sphere. In this regard, the gravita-tional potential is commonly assumed to be the Mac-Cullagh’s truncation, although several recent papersgo further than this approximation. We investigateanalytical approximations, integrable or not, thatcould drastically simplify the search for special fam-ilies of periodic or quasi-periodic orbit, where theinfluence of the roto-orbital coupling is considered.In this regard, we have presented recently some re-sults [2], [3]. Our formulation is in Hamiltonian formand the variables in which the model is expressedare crucial in order to get compact expressions andintuitive geometric insight. Our choice is variablesreferred to the total angular momentum [1], whichcarry out the elimination of the nodes. The model is

chosen from the MacCullagh’s approximation with-out averaging. More precisely we choose the terms ofthe potential with depends only on the orbital vari-able r and the angular variable ν. Thus the Hamil-tonian takes the form H = H(r,ν, R, N) is a 2-DOFsystem made of the Kepler and free rigid body to-gether with the mentioned simplified potential. Weexamine families of relative equilibria leading to con-stant and non-constant radius solutions. We focus onthe regime of slow rotations of the triaxial body, anassumption that brings different scenarios from theclassical free rigid body. These families of relativeequilibria include some of the classical ones, includ-ing ‘conic’ trajectories reported in the literature andsome new types showing the critical role played bythe triaxiality. The applicability of our model is as-sessed numerically.

[1] J.M. Ferrandiz and M.E. Sansaturio, Celest.Mech. Dyn. Astr. 46 (1989), 307-320; [2] F. Crespo,F.J. Molero, S. Ferrer and D. Scheeres, J. of the Astro.Sci 65, (2018), 1-28; [3] F. Crespo and S. Ferrer, Ad. inSpace Research 61 (2018), 2725-2739.

401.06 — Relevance of Solar System Dynamics forPresent-Day Studies of Planetary AtmosphericCirculations (and other Geophysical Phenomena)

James Shirley11 3226, Jet Propulsion Laboratory (Pasadena, California, United

States)

An expression describing a non-tidal coupling of theorbital and rotational motions of extended bodiesis derived in [Plan. Space Sci. 141, 1, 2017]. Theorbit-spin coupling torque (or, ‘coupling term accel-eration,’ CTA) is given by CTA = -c (dL/dt × ω𝛼) × r,where dL/dt is the rate of change of the orbital an-gular momentum of the subject body with respect toinertial frames, ω𝛼 is the angular velocity of the ro-tational motion of the subject body, and r is a posi-tion vector identifying a specific location on or withinthe subject body. The leading coefficient c is a cou-pling efficiency coefficient, to be determined throughcomparisons of model outcomes with observations,which is typically constrained (by error estimates fornumerical simulations of orbital motions) to be ex-tremely small. In contrast to conventional tidal fric-tion (i.e., “spin-orbit coupling”) models, the torquegiven by the above equation changes sign. This maylead to both positive and negative accelerations ofthe rotation. As with tidal friction, dissipative in-teractions within the body are an expected conse-quence, as are slow evolutionary changes in orbitalmotions (conserving total system angular momen-tum). Orbit-spin coupling is likely to be effective

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over far larger distances than may be the case fortidal friction, where the torques have a dependenceon the inverse 6th power of distance. Two studies in-corporating the CTA within atmospheric general cir-culation models have appeared [Plan Space Sci. 141,45, 2017; Icarus 317, 649, 2019]. A key objective wasto determine whether the agreement between atmo-spheric observations and numerical modeling out-comes could be improved by including the CTA witha non-zero value of c. This question has been an-swered in the affirmative; the modified GCMs suc-cessfully reproduce Martian global dust storm con-ditions in the years in which such storms actuallyoccurred, with ‘hindcast’ success rates approaching80%. The orbit-spin coupling hypothesis offers manyopportunities for new research, both focusing on cur-rently open questions, and in connection with re-evaluations of the conclusions of prior studies.

Posters — Poster Presentations

P1 — A New Non-Recursive Approach forCalculating Satellite Orbital Positions

Leland Langston1,21 L2 Consulting (Highlands Ranch, Colorado, United States)2 Raytheon (Boston, Massachusetts, United States)

Away with M = E-esin(E) ! Determination of a satel-lite’s position is usually accomplished by solvingKepler’s equation using a recursive or iterative ap-proach to solve the transcendental equation, fol-lowed by using Gauss’s equation. This approach iseffective, but requires multiple calculations that taketime to perform. Furthermore, iterative procedurescannot be easily implemented in spread sheets orother similar calculating methods. Solving Kepler’sequation in an iterative fashion has been the meansof calculating the orbital positions of celestial bod-ies in elliptical orbits for almost 400 years. This pa-per develops a non-recursive technique for achiev-ing the same objective. In addition, a set of ancil-lary equations for calculating the radial and tangen-tial velocity of a planet or satellite is presented. Thisapproach is simple, can be implemented within aspread sheet and greatly reduces the execution timein critical real-time digital signal processing applica-tions.

P2 — Derivation of Cosmic Acceleration GivenInward Unbounded Light-Speed in the HubbleExpansion

Thomas Chamberlain1

1 University of California, Berkeley (Los Angeles, California, UnitedStates)

This work discusses how replacement of Einstein’spostulated isotropic light-speed in special relativityby inward unbounded light-speed - with c/2 out-ward, in accordance with Einstein’s “round trip ax-iom” - in the Hubble expansion gives an emergent,outward increasing cosmic time-dilation that allowsa derivation of cosmic acceleration, meaningful toleading order in the local universe. Special relativ-ity is revised in this deeper theory resulting in extraterms (e.g., in the Maxwell equations) which never-theless uphold empirical accuracy.

A follow-on relativistic joining of outward cos-mic time-dilation with inward (baryon-based) grav-itational time dilation allows derivation of emergentcosmic deceleration with a leading order r1/2 de-pendence. For distances less than about 100 mil-lion light-years (in the present epoch) emergent cos-mic deceleration exceeds cosmic acceleration and be-comes increasingly dominant.

The present deepening of special and general rela-tivity may be falsified. Here I claim that applicationof the theory will substantially reduce the need forboth “dark energy” and “dark matter” in the ΛCDMmodel. Should the need for “dark matter” in ex-plaining wide-binary star rotation flattening [shownsuperfluous in the talk], spiral galaxy rotation flat-tening [shown superfluous in the talk], “too fast”galaxy-cluster dynamics and growth, as well as theCMB power spectrum not drop from ∼5× total bary-onic matter to well below total baryonic matter, thetheoretical development may be considered falsified.Similarly, should “dark energy” in explaining cosmicacceleration remain necessary [shown superfluous inthe talk], the theory may be considered falsified. Inthis theoretical deepening , the many important suc-cesses of special and general relativity are preserved.

P3 — Geocentric Proper Orbital Elements

Aaron Jay Rosengren1; Claudio Bombardelli2; DavideAmato3

1 Aerospace and Mechanical Engineering, University of Arizona(Tucson, Arizona, United States)

2 Technical University of Madrid (UPM) (Madrid, Spain)3 University of Colorado (Boulder, Colorado, United States)

As near-Earth space gets more and more congested,the need for a classification scheme based uponscientific taxonomy is needed to properly identify,group, and discriminate resident space objects, ashas been advocated recently. Debris or not debris

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is one of the fundamental questions that has moti-vated these efforts over the past few years, yet thecurrent approaches all suffer from one essential fea-ture: dynamical ambiguity. Any attempt to classifyspace debris, say, into families cannot be based onthe osculating elements, which, being in continualchange as functions of time, do not clearly discloseany characteristic feature of the initial orbit or statevector. Mean orbital elements, such as those pro-vided by the two-line element sets of the space objectcatalog, also do not leave a dynamical fingerprint ofthe object’s inherent state, since they vary over longer(secular) timescales. It is striking that astrodynami-cal taxonomists have not hitherto looked beyond ourterrestrial abode for the proper solution to this com-pelling genealogy problem; namely, to the asteroidbelt, where small-body taxonomists now enjoy onehundred years of astronomical heritage. Asteroidfamilies consist of swarms of fragments generated af-ter energetic interasteroidal collisions in the distantpast that result in the breakup of their progenitors.They are dynamically recognized by searching forclusters in the three-dimensional space of proper ele-ments; parameters characterizing the asteroid orbitsthat are very close to fundamental invariants of mo-tion, and thus keep a dynamical record of the initialproximity of the orbits generated by a catastrophicfragmentation event. The concept of proper elementshas already been applied with success to the natu-ral satellite systems of the outer planets; but the or-bits of artificial Earth satellites and space debris, andtheir dynamical environments, differ so markedlyfrom the classical problems presented by nature, ren-dering many of the time-honored methods of Solar-System celestial mechanics inapplicable. Here, wepresent a theory of proper orbital elements in the cir-cumterrestrial context. This talk is dedicate to thememory of Andrea Milani, an encyclopedia of astro-nomical insight.

P4 — Cosinusoidal Potential as a PossibleSolution to the Planet IX Problem

David Farnham Bartlett1; John Cumalat11 Physics, University of Colorado (Boulder, Colorado, United States)

Einstein’s 1918 paper extended his classic 1916 pa-per on General Relativity. In this extension Einsteinachieved a steady state universe by adding the cos-mological constant term to his general covariant the-ory. Einstein also showed that even non-relativistictheory could achieve a steady state universe if onemade a linear modification to Poisson’s equation. Hecalled the addition of a term ko

2 φ to Poisson’s equa-tion a ”foil”, not to be taken seriously. Here φ is the

gravitational potential and ko is a constant havingthe dimensions of an inverse length. We choose toadd a length scale ko

−1 to the general formalism ofGR, thus creating a specific example of f(R) gravity.(Here R is the Ricci Scalar). If ko

2 is negative the po-tential of a point mass is φ = -GM/r Cos[ko r]. Weexpress ko in terms of the constants c, G, h-bar, themass of the electron, and α = 1/137: ko = Sqrt[3 G c]m2 α4 / h-bar3/2. This ko yields a wavelength λo = 2pi/ko = 383 pc, a length which is long compared tothe dimensions of the solar system, but short enoughto permit flat rotation curves for galaxies. Expressedas an energy, ko = 10−25 eV, an energy so small as tobe consistent with the current limit on the identity ofspeeds of gravitational and electromagnetic waves.Our modification leads to an oscillating universe in-stead of the big bang. It also gives very strong lo-cal tidal forces which can explain the observed influ-ence of the galactic center on the aphelia of planets,comets, and large members of the Kuiper Belt. Wealso choose a smaller kem = (1/3) ko for the mass ofthe photon.

P5 — Formation of Exponential Profiles fromStellar Scattering Investigated with N-bodySimulations

Jian Wu1; Curtis Struck1; Elena D’Onghia2; Bruce G.Elmegreen3

1 Iowa State University (Ames, Iowa, United States)2 University of Wisconsin-Madison (Madison, Wisconsin, United

States)3 Thomas J. Watson Research Center (Yorktown Heights, New York,

United States)

The exponential shape of radial surface brightnessprofiles of disk galaxies has been observed andknown for decades. However, the physical mecha-nism of its formation is not well understood. Distur-bances from bars and spiral arms, viscous accretionof gas, and interaction with surrounding galaxies canaccount for an exponential disk, but these existingtheories all have limitations. Experiments with theN-body simulation code GADGET-2 show that ex-ponential profiles can form out of various initial stel-lar density distributions in a disk containing massivescattering centers, which in a real galaxy can be mas-sive clouds or stellar clusters. The timescale of theprofile evolution is influenced by scattering centerproperties including mass, orbital radius, and spa-tial number density. Cold disks with local gravita-tional instabilities can trigger temporary phase mix-ing and violent relaxation, which accelerate profilechanges towards an exponential. This may be re-

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sponsible for fast establishment of exponential pro-files in disturbed dwarf galaxies.

P6 — Simulations of Multi-component SplashBridges in Direct Galaxy Collisions

Travis R. Yeager11 Physics and Astronomy, Iowa State University (Ames, Iowa,

United States)

We use an inelastic particle code with shocks andcooling calculated on a subgrid level to study the gasin direct collisions between galaxy discs. The inter-stellar media (ISM) of the discs are modeled withcontinuous thermal phases. The models producemany unique structures, which are collectively calledsplash bridges. They range from central bridge discsto swirled sheets, which resemble those observed ininteracting galaxies. These morphologies are sensi-tive to the rotation, relative mass, disc offsets, andthe gas structure in the discs. In the case of theTaffy galaxies - NGC 12914/15, extensive observa-tions have revealed radio continuum emitting gas,HI gas, hot X-rays from hot diffuse gas and moreH2 than exists in the Milky Way coexisting in thebridge. The origins of the H2 and large asymmet-ric distribution of ISM are not clear. We show thatfor small disc impact parameters, multiple phases ofISM with densities over many orders of magnitudecan be removed from their host galaxies into a Taffy-like bridge. The orientation of the discs initial over-lap can have a great effect on the distributions of eachphase of ISM after the collision. In some cases, themodels also predict the creation of a possible ‘darkgalaxy,’ a large flat region of dense ISM far from thestellar disc potential of either galaxy. Another im-portant parameter, currently being modeled, is therelative angle between the discs upon impact. A li-brary of expected splash bridge morphologies canbe a powerful resource for future observations con-ducted on interacting galaxies.

P7 — High-resolution profiles of the Uranian ringsfrom Voyager 2 radio occultation observations

Richard G. French1; Sophia Flury1; Jolene Fong1; RyanMaguire1; Glenn Steranka1; Colleen McGhee-French1

1 Astronomy, Wellesley College (Wellesley, Massachusetts, UnitedStates)

On January 24, 1986, the radio occultation of Voyager2 provided a detailed portrait of the nine main Ura-nian rings during both ingress and egress, revealingcomplex structural details at 50-m resolution (λ=3.6cm), after reconstruction from the diffraction-limited

observations (Gresh et al. 1989, Icarus 78,131-168).With the success of the Cassini mission in obtain-ing hundreds of high-resolution occultation profilesof Saturn’s rings, there is renewed interest in explor-ing the narrow sharp-edged Uranian rings as analogsof Saturn’s own ringlets, several of which are hometo density waves and excited normal modes. Tosearch for evidence of similar features in the Uranianrings, we have returned to the original raw Voyager2 Uranus radio occultation data (kindly provided byDick Simpson) and used our open-source Pythoncode (hosted on GitHub at https://github.com/NASA-Planetary-Science/rss_ringoccs) to pro-duced diffraction-reconstructed profiles of all 18 ringdetections. Our 50-m resolution profiles are in ex-cellent agreement with those provided by the origi-nal Voyager team to NASA’s Planetary Data System,confirming the validity of our implementation of thediffraction reconstruction technique pioneered byMarouf et al. (1986 Icarus 68, 120-166). We have ex-tended this effort to produce 20-m resolution opticalprofiles, with the goal of searching for regular fine-scale structure within the Uranian rings. Althoughnoise-limited at high optical depths, the new profilesexhibit quasiperiodic structure within some of therings, which we quantify using Morlet wavelet spec-trograms. In a related effort, we have successfully re-produced Gresh et al.’s detection of an anomalouslystrong scattered signal from the egress ε ring event,which has prompted us to search for similar signa-tures in the vicinity of Saturn’s own broad (100-km)wide ringlets. Our open-source radio science ringoccultation analysis code, rss_ringoccs, was devel-oped with support from JPL provided by the Cassinimission to Saturn.

P8 — Collisional fragmentation as a source forearly martian impactors

Carlisle A. Wishard1; David A. Minton11 Earth, Atmospheric, and Planetary Science, Purdue University

(West Lafayette, Indiana, United States)

Many previous models of solar system evolutionhave suggested that the craters seen on the most an-cient surfaces in the inner solar system were cre-ated by a late dynamical instability in the outer so-lar system. Clement et al. (2018) showed that anearly dynamical instability, prior to the end of terres-trial planet accretion, could satisfy many constraintsplaced on the architecture of the solar system as well,or better than, a late dynamical instability. Theirmodel successfully replicates the structure of the in-ner and outer solar system but does not currentlyprovide a source for inner solar system impactors.

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In this work, we show that collisional fragmen-tation during the accretion of the terrestrial plan-ets can provide a source for inner solar system im-pactors. Impacts between growing terrestrial plan-ets and smaller bodies, like planetesimals and plane-tary embryos, generate collisional debris. This debriscreates a source of impactors that is localized andpreferentially impacts one terrestrial planet over an-other. While previous work has been done to incor-porate fragmentation into an early instability model(Clement et al. 2019), in this work we address the ef-fects of fragmentation on the cratering history of theinner solar system, with a focus on Mars.

The cratering chronology of Mars is derived fromthe lunar cratering chronology, with the underlyingassumption being that both bodies share a commonimpactor source. A consequence of this assumptionis that the lunar cratering chronology is mirrored onMars. In this work, we aim to separate the crater-ing histories of the Moon and Mars using the resultsof n-body simulations of terrestrial planet formation,after the occurrence of an early outer solar system in-stability, as described by Clement et al. (2018). Thesesimulations are then coupled with collisional evolu-tion and cratering models. We will explore possiblemartian cratering chronologies that are not derivedfrom the lunar cratering chronology and comparedthese possible cratering chronologies to the observ-able martian cratering history.

P9 — Re-examining the rings of Uranus in theVoyager 2 images

Robert Chancia1; Matthew Hedman11 Physics, University of Idaho (Moscow, Idaho, United States)

We examine the decades-old Voyager 2 images of theUranian rings and present the results of our searchfor evidence of known and expected perturbationsfrom nearby moons. The ε, δ, γ, and η rings areknown to fall near resonances with the small innermoons of Uranus. The narrow rings’ resonant in-teractions with moons give rise to oscillating edgepositions causing variations in width, that can re-sult in azimuthal brightness variations. Structuresresulting from high-wavenumber resonances withCordelia, Ophelia, and Cressida have been detectedin the rings’ radial positions and widths using eitherextensive sets of occultation observations or withbrightness variations in more recent Hubble data,but there have not yet been comparable results re-ported for each ring using the higher resolution Voy-ager imaging data. Measured azimuthal variationsin the integrated reflectance of the rings may pro-vide estimates of a perturbing moon’s mass, a physi-

cal characteristic that remains poorly constrained forthe inner Uranian moons.

P10 — Vertical Mass Segregation in EccentricNuclear Disks

Hayden Foote1; Ann-Marie Madigan1; AlekseyGenerozov1

1 Astrophysical and Planetary Sciences, University of ColoradoBoulder (Boulder, Colorado, United States)

Eccentric nuclear disks are a type of nuclear star clus-ter in which the stars lie on apsidally-aligned orbitsin a disk around the central supermassive black hole.These disks can produce a high rate of tidal disrup-tion events (TDEs) via secular gravitational torques.Here, we show that eccentric nuclear disks exhibitstrong vertical mass segregation, in which massivestars sink to low inclinations through dynamical fric-tion with a more numerous population of lighterstars. This results in a much higher TDE rate perstar among the heavy stars (∼0.10) than the light stars(∼0.06).

P11 — The planar rigid two-body problem

Margrethe Wold1; John Thomas Conway1; Alex Ho11 Department of Engineering Sciences, Universtity of Agder (Grim-

stad, Norway)

We report on ongoing work to model the motionof two extended, rigid bodies of constant density,and present preliminary results for the case of twospheroids and two disks sharing a common equato-rial plane. Our method evaluates the mutual gravi-tational potential between the two bodies as surfaceintegrals of analytical expressions (MacMillan 1930),thereby avoiding expanding the potential in spheri-cal harmonics. The method is exact to within the ge-ometry of the bodies, and does not suffer from trun-cation errors, and it can also be used for close en-counters. We solve the equations of motion in thecenter of mass system using a Runge-Kutta integra-tor, and show examples of trajectories for the twobodies as well as how their energy and momentumevolves over time.

P12 — VPLanet: The Virtual Planet Simulator

Rory Barnes1,2; Rodrigo Luger2,3; Russell Deitrick2,4;Peter Driscoll2,5; Thomas Quinn1,2; David Fleming1,2;Hayden Smotherman1,2; Diego McDonald1; CaitlynWilhelm1,2; Rodolfo Garcia1,2; Patrick Barth6; Ben-jamin Guyer1; Victoria Meadows1,2; Cecilia Bitz1,2;

34

Pramod Gupta1,2; Shawn Domagal-Goldman7,2; JohnArmstrong8; David Crsip9

1 Astronomy, University of Washington (Seattle, Washington,United States)

2 NASA Virtual Planetary Laboratory (Seattle, Washington, UnitedStates)

3 Center for Computational Astrophysics (New York, New York,United States)

4 University of Bern (Bern, Switzerland)5 Carnegie Institute for Science (Washington, District of Columbia,

United States)6 Max Planck Institute for Astronomy (Heidelberg, Germany)7 Goddard Space Flight Center (Greenbelt, Maryland, United

States)8 Webet St. University (Ogden, Utah, United States)9 Jet Propulsion Laboratory (Pasadena, California, United States)

We present a software package called VPLanet thatcan simulate numerous aspects of planetary systemevolution for billions of years, with a focus on hab-itable worlds. In this initial version, eleven indepen-dent models for internal, atmospheric, rotational, or-bital, stellar, and galactic processes are included andcoupled to self-consistently simulate terrestrial plan-ets, gaseous planets, and stars. We describe thesemodels and reproduce observations and/or past re-sults. In our framework, only the relevant physicsis applied to each member of the system, facilitat-ing the rapid simulation of a wide range of plane-tary systems. A key feature of VPLanet is that theuser can determine at runtime which physics to ap-ply to an individual object, so a single executable cansimulate the diverse phenomena that are importantacross a wide range of planetary and stellar systems.This flexibility is enabled by matrices and vectors offunction pointers that are dynamically allocated andpopulated based on user input. VPLanet is publiclyavailable and the repository contains extensive doc-umentation and numerous examples, with code in-tegrity maintained through continuous integrationand periodic scanning for memory issues.

P13 — Effect of the Yarkovsky transverseparameter on radar astrometry for asteroid (99942)Apophis

Jorge Antonio Perez-Hernandez1; Luis Benet11 Non-linear Physics, ICF-UNAM (Tlalpan, Mexico City, Mexico)

We present results regarding the Yarkovsky effect onApophis, using time-delay and Doppler shift radarastrometry obtained from Goldstone and Areciboduring its 2012-2013 close approach with the Earth[1]. Using TaylorIntegration.jl [2], we compute our

own ephemerides for a dynamical model of the So-lar System and Apophis. The bodies included arethe Sun, the eight planets, the Moon and Ceres,and Apophis as a (massless) test particle. We con-sider post-Newtonian accelerations between all bod-ies, oblateness effects from the Earth’s J2, J3 and J4zonal harmonics, oblateness effects from the Sun’s J2zonal harmonic, and a kinematic model for the ori-entation of the Earth rotational axis. In the equa-tions of motion for Apophis we include a non-gravitational acceleration term accounting for thetransversal Yarkovsky effect. We take the initial con-ditions for Apophis from JPL’s solution #199 [3] atthe reference epoch September 24, 2008 00:00:00.0(TDB). For the rest of the Solar System bodies con-sidered, we take initial conditions from the DE430ephemerides at the same reference epoch (for Ceres,we used initial conditions from Horizons). Afterreducing the relativistic and solar corona contribu-tions to the radar astrometry based on our dynami-cal model, and exploiting automatic differentiationtechniques, we obtain the O-C residuals of time-delay and Doppler shift as polynomial expressionswhich depend on the parameter A2. Using these ex-pressions, we describe the influence of the Yarkovskyparameter, and propose the nominal value A2=-5.68443×10−14au/day2, which minimizes the meansquare residuals.

References: [1] Brozović, M., et al., 2018, Gold-stone and Arecibo radar observations of (99942)Apophis in 2012–2013. Icarus, 300, 115-128.[2] Pérez-Hernández J. A., Benet L., 2018, Tay-lorIntegration.jl: ODE integration using Taylor’smethod in Julia, https://github.com/PerezHz/TaylorIntegration.jl [3] JPL’s solution #199 forApophis was downloaded in SPK format using thesmb_spk script provided by JPL at ftp://ssd.jpl.nasa.gov/pub/ssd/SCRIPTS/. Retrieved March 30,2019.

P14 — Non-hierarchical Triple Dynamics andApplications to Planet Nine

Hareesh Gautham Bhaskar1; Gongjie Li1; MatthewPayne2; Samuel Hadden2; Matthew J. Holman2

1 Physics, Georgia Institute of Technology (Atlanta, Georgia, UnitedStates)

2 Harvard-Smithsonian Center for Astrophysics (Cambridge, Mas-sachusetts, United States)

Three-body interactions have wide applications inastrophysics. For instance, Kozai-Lidov oscillationfor hierarchical triples has been studied extensivelyand applied to a wide range of astrophysical topics.

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However, non-hierarchical triples also play a domi-nant role but it is less explored. In this work we con-sider the secular dynamics of a test particle inside anon-hierarchical configuration with two massive ob-jects. We find the resonances and chaotic regions us-ing surface of sections, and we identify regions ofphase space that allows large eccentricity and incli-nation variations. In the end, we apply our under-standing to the distribution of extreme TNO underthe perturbation of a possible Planet Nine.

P15 — Nbody Simulations of Self ConfiningRinglets

Joseph Hahn1; Douglas P. Hamilton2; ThomasRimlinger2; Yuxi Lu2

1 Space Science Institute (Cedar Park, Texas, United States)2 Univerisity of Maryland (College Park, Maryland, United States)

Nbody simulations are used to explore whether nar-row eccentric planetary rings might be self confining.In our experiments, the epi_int_lite Nbody code isused to evolve a viscous and self-gravitating ringletthat is represented as a pair of gravitating stream-lines that interact via their mutual gravities and vis-cous friction. We find that the streamline’s seculargravitational perturbations causes the streamline’seccentricity gradient e’=a(de/da) to grow over timewhile the ringlet’s internal friction causes the stream-lines to spread radially. And in certain circum-stances, the simulated ringlet’s eccentricity gradientapproaches the critical value e’=√3/2=0.877, whichzeros the orbit-averaged viscous torque that adja-cent streamlines exert on each other (Borderies et al1982). When that happens, the simulated ringlet’s ra-dial spreading slows dramatically but is not entirelyhalted. Rather, our simulated ringlet still spreadsalbeit very slowly while executing low-amplitudelibrations about the equilibrium state described inBorderies et al (1983). So our simulations show thata ringlet’s secular gravitational perturbations candrive an unconfined viscous ringlet very close to thee’=√3/2=0.877 threshold, which suggests that nar-row eccentric planetary rings might be self-confiningwithout the need for any shepherd satellites. But itis unclear today whether the low-amplitude librationand slow spreading seen in our simulation is real orsomehow an artifact of subtleties in the epi_int_litecode or choice of initial conditions.

P16 — Identifying Three-body Resonances inKepler’s Extrasolar Planetary Systems

Abigail Graham1; Darin A. Ragozzine1; Jack Lissauer2;Daniel Jontof-Hutter3; Jason Rowe4; Daniel Fabrycky5

1 Brigham Young University (Provo, Utah, United States)2 NASA Ames (Mountain View, California, United States)3 University of the Pacific (Stockton, California, United States)4 Bishop’s University (Sherbrooke, Quebec, Canada)5 The University of Chicago (Chicago, Illinois, United States)

The Kepler Space Telescope discovered over 200 sys-tems with three or more known exoplanet candi-dates. Previous studies have found that some ex-oplanetary systems contain three-body mean mo-tion resonances which offer valuable insights intothe formation, evolution, and dynamics of exoplane-tary systems. Using the precise orbital periods fromKepler exoplanetary systems, we search for candi-date three-body resonances by identifying commen-surabilities in every possible set of three planet can-didates. Since there are many opportunities forrandom three-body alignments, we assess the falsealarm probability for the candidate three-body res-onances in order to identify the most dynamicallysignificant cases. Even though Kepler periods areknown precisely (typically to one part in 100,000), wefind that the observational uncertainties in the peri-ods are important for identifying real three-body res-onances. We will present the findings of our searchfor statistically significant Kepler three-body reso-nances.

P17 — Towards a Photodynamical Analysis ofKepler’s Multiply-Transiting Systems

Vatsala Sharma1; Darin Ragozzine1; Daniel Fabrycky2;Sean Mills3

1 Physics and Astronomy, Brigham Young University (Provo, Utah,United States)

2 University of Chicago (Chicago, Illinois, United States)3 The California Institute of Technology (Pasadena, California,

United States)

The Kepler Space Telescope discovered about 700systems with multiple transiting exoplanets (about1700 planet candidates) over a four year period. Insystems of multiple transiting planets, planet-planetgravitational interactions can sometimes be detectedby observing that the transits do not occur strictlyperiodically (sometimes called Transit Timing Vari-ations or TTVs). Until now, planetary interactionshave not been typically included in the determina-tion of the full set of light curve parameters. Weseek to increase the amount of information extractedfrom these exoplanetary systems with a more de-tailed analysis. In particular, by fitting the transit-ing light curves, we can better constrain exoplan-etary masses (along with other orbital properties).In combination with the measured radii, these light

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curves reveal densities of exoplanets that are cru-cial for understanding their formation, evolution,and habitability. We have started a new investiga-tion aimed at these more precise measurements byconnecting n-body integrations directly to the mea-sured light curve (skipping the step of measuring in-dividual transit times), using our new PhotoDynam-ical Multi-planet Model, PhoDyMM. Coupled witha Bayesian parameter inference method (DifferentialEvolution Markov Chain Monte Carlo), we plan toapply PhoDyMM to all 700+ systems of Kepler mul-tiple transiting planets in order to infer physical andorbital parameters using the best existing data. Wewill present early results from this large project fo-cused on the details of our specific methodology andapplication to test cases.

P18 — Size frequency distributions of impactcraters on Saturn’s moons Tethys & Dione;implications for source impactors

Sierra Nichole Ferguson1; Alyssa Rhoden21 School of Earth and Space Exploration, Arizona State University

(Tempe, Arizona, United States)2 Southwest Research Institute (Boulder, Colorado, United States)

Currently the Saturnian satellites are thought to haveformed anywhere between 4.5 Gyr and 100 Myr. Oneconstraint on the ages of these satellites is the im-pactor flux that is creating the craters on the satel-lites. We completed regional scale mapping (imageresolutions of ∼250 m/pix or better) on Tethys andDione to investigate the distribution of small impactcraters (D < 5 km) and elliptical craters to investigatethe source population of impactors in the system.Major sources of impactors in the Saturnian systemare thought to consist of heliocentric and planeto-centric debris, each of which could have been activeat different periods in the history of these satellites.Our mapping on Tethys finds that we see an abun-dance of small impact features on the cumulative sizefrequency distribution (CSFD) and a steeper sloperelative to the younger mapped terrain. Younger ter-rain units have shallower slopes that agree with apotential heliocentric population at small diameters.We interpret this difference in slope to be a transi-tion from an initially planetocentric population thatfollows along with the Case B function from Zahnleet al. 2003, to a heliocentric population that matcheswell with Case A. We have also mapped the surfaceof Dione in four regions, each within a distinct geo-logic unit (unit descriptions via Kirchoff et al. 2015)using high-resolution Cassini data (image resolution∼250 m/pix). Analysis of Dione results finds similarsize-frequency distributions to what was observed

in Kirchoff et al. 2015 for the fractured terrain andsmooth terrain. Analysis of their potential sourcepopulations is ongoing and will be presented. Wepresent our size-frequency results so that we can en-gage in further discussion with the dynamics com-munity about the potential source populations forthese impact craters.

P19 — Comparison of predictions of asteroids’close encounters with the Earth

Daniel J. Hestroffer1; Anatoliy IVANTSOV2; WilliamTHUILLOT1; Josselin DESMARS3; Pedro DAVID1

1 IMCCE, Paris observatory (Paris, France)2 Space Sciences and Technologies Department, Akdeniz University

(Antalya, Turkey)3 LESIA/Paris observatory (PARIS, France)

Prediction of future close encounters of asteroidswith the Earth belongs to sensitive information asit has a direct relation to the possible collision withthe Earth. Observations of asteroids collected by theIAU Minor Planet Center (MPC) generally constitutethe same source of astrometric and radar measure-ments for orbital computations and subsequent closeapproaches. We report here on a cross-identificationof such events between different lists of predictionsprovided by the well-known world professional ser-vices: IAU MPC (Forthcoming Close Approaches ToThe Earth and the Running Tallies), the JPL Centerfor NEO Studies (CNEOS), the ESA SSA-NEO Coor-dination Centre (NEOCC) through its Space Situa-tional Awareness Programme, and DynAstVO, thenewly opened service of IMCCE at Paris Observa-tory PADC centre. We have selected two one-yearwindows, separated by 4 months, for generating thelists of predictions. Each event that has declared cal-culated geocentric distance of close approach less orequal 0.05 AU in one of the lists was cross-identifiedwith the events in other sources. The comparisonswere made with respect to the orbital propagationsprovided by the JPL HORIZONS on-line solar sys-tem data and ephemeris computation service. It ap-pears that the actual predictions made by all theseservices can be significantly different, not only inepochs and distances of close encounters, but also inthe entry list of asteroids. We have found that in bothcomparison window cases, all the services producepredictions that agree in less than 50% cases with re-spect to the general set formed as a union of all ta-bles. The highest overlapping belongs to DynAstVOand NEOCC while the lowest to IAU/MPC. Thesedifferences in the prediction lists may be explainedby peculiarities of the algorithms used, frequency of

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the orbital updates, different weighting schemes ap-plied in the orbital determinations. We emphasisethe necessity of additional astrometric/radar mea-surements of potentially hazardous asteroids, espe-cially those which constitute the differences in suchpredictions.

P20 — Could there be an Undetected Inner PlanetNear the Stability Limit in Kepler-1647?

Ziqian Hong2; Billy Quarles1; Gongjie Li1; JeromeOrosz3

1 Georgia Institute of Technology (Atlanta, Georgia, United States)2 University of Science and Technology of China (Xiamen, China)3 San Diego State University (San Diego, California, United States)

Kepler-1647b is the most recently discovered planetthat transits two stars, i.e., a circumbinary planet(CBP). Due to its large orbital separation, Kepler-1647b stands out from the rest of the Kepler CBPs,which mostly reside on much tighter orbits nearthe stability limit. The large separation of Kepler-1647b challenges inward disk migration as a domi-nant formation pathway, suggested by the other Ke-pler CBPs. In this paper, we consider the possibil-ity of an undetected planet near the stability limitby examining observational consequences of such aplanet. We calculate the transit probability of theputative planet, transit timing variations (TTVs) ofthe known planet, and eclipsing timing variations(ETVs) of the host binary caused by the putativeplanet. We find the presence of a ≳30 M⊕ innerplanet to be highly unlikely near the stability limit.In addition, we provide future TTV observation win-dows, which will further constrain possible unde-tected planets with lower masses.

P21 — The Exact Boltzmann Most ProbableMonatomic Ideal Gas

Michael Cahill11 Physics & Astronomy, U WI Milwaukee/Washington County

(West Bend, Wisconsin, United States)

New results are presented for Boltzmann’s mostprobable dynamics of an ideal monatomic gas. Hiswork is pivotal in the dynamical foundations of stel-lar systems and planetary & satellite atmospheres.Velocity space is divided into Nc cells of equal vol-ume, cell j particles have population nj & kinetic en-ergy εj each. Particles of mass m remain intact in col-lisions so total population N is constant. A collisioncan change particle energy but total system kineticenergy Ê is constant. m, N & Ê are defining constantsof the gas. Macroscopic gas properties are due to its

macrostate, i.e. cell particle populations nj. A mi-crostate is given by each particle’s cell location. Ran-domizing particle collisions cause an equilibriummacrostate which is due to the largest number of mi-crostates obeying the N & Ê constraints. Boltzmann’sentropy S must then be maximized since it is the logof the microstates in a macrostate where S = ∑Nc

𝑗=1ln(nj!) (1). nj satisfying these conditions are found byLagrange’s multiplier method whose equations arein unitless form if energy multiplier B defines unit-less energies by ej = B εj, E = B Ê (2). The Nc + 2 La-grange unitless constrained extreme entropy equa-tions are A = ej + Ψ(nj + 1), N = ∑Nc

𝑗=1 nj, E = ∑Nc𝑗=1

ej nj} (3) where A is the population multiplier & Ψ(n)is the digamma function defined by Ψ(n) := d(ln((n-1)!)/dn. 2 approximations for the above situation areconsidered giving Case 1: the above exact case, usingBoltzmann’s entropy formula Case 2: is Boltzmann’suse of Stirling’s approximation in (1) giving A = ej +ln(nj) Case 3: directly approximates Ψ(nj + 1) givingA = ej + ln(exp(-γ) + nj), For large nj all cases obey A =ej + ln(nj) At nj = 0 case 1 & 3 allow any A > 0 but case2 has A = ∞ (3) gives {E, Nc, nj} of {A, N, ej}: A, nH(highest nj) or eH (highest ej) specify a macrostate eH= A + γ, eH = γ + Ψ(nH + 1), γ is Euler’s constant eHis a natural parameter for a nj(e) distribution. The gasterminates at {nj = 0, ej = eH} with any eH > 0 The fol-lowing quantities are determined: VH(m, eH) givesthe unitless phase space volume of gas phase pointsNc(eH, N) gives the number of cells Vc(eH, m, N) =VH/Nc gives the cell size C(eH) = E/Nc gives spe-cific heat ratio 3/2 for large enough eH

P22 — Planned archive of Uranus ring occultationobservations on NASA’s Planetary Data System

Colleen McGhee-French1; Richard G. French1; MitchGordon2

1 Astronomy, Wellesley College (Wellesley, Massachusetts, UnitedStates)

2 SETI Institute (Mountain View, California, United States)

Under NASA’s PDART (Planetary Data Archiving,Restoration, and Tools) program, we are in the pro-cess of submitting the entire set of known high-SNR Uranus ring occultation observations to NASA’sPlanetary Data System Ring-Moon Systems Node(RMS). These observations span more then 25 years(1977-2002), and include digitally-recorded aperturephotometry in the IR, several early events that wererecorded only on strip charts, additional high-SNRunpublished ground-based observations, two occul-tations observed from the Hubble Space Telescope,and two occultations observed using 2D imaging ar-rays. The archive will contain the full continuous

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time series observations of each occultation, as wellas high-resolution individual ring event profiles reg-istered on a radius scale based on a self-consistentring orbit model accounting for the inclinations andeccentricities of the rings, all fitted normal modes,and a derived Uranus pole direction. We will sub-mit all raw, intermediate, and higher order productsto the PDS, along with complete documentation andmachine-readable tables of key derived quantities foreach observed occultation and ring profile. This willenable intercomparison with other planetary rings,such as Saturn’s narrow ringlets, and allow system-atic searches to be made for previously undetectedrings or ring arcs in the Uranus system that may beassociated with the dusty sheets of material asso-ciated with the rings, as seen in Voyager forward-scattering images. Once the data have been ingestedinto PDS, they will be accessible from the RMS Node,including being fully supported by the node’s searchtool, OPUS. The results will be useful for studies ofthe dynamics and kinematics of the rings and theirinternal structure, and for setting limits of the gravi-tational harmonics of Uranus itself, and hence its in-ternal structure as well. Our target date for complet-ing this work is August 31, 2020, and we invite sug-gestions from potential users so that the archived re-sults will be as useful as possible to the entire scien-tific community. This work is supported by NASA’sPDART program.

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