EART160 Planetary Sciences

Francis Nimmo

Course Overview• Foundation class for Planetary Sciences pathway• Introduction to formation and evolution of planetary

bodies in this Solar System• Focus on surfaces, interiors and atmospheres of

planetary bodies, especially solid ones

Course Outline• Week 1 – Introduction, highlights, missions, solar

system formation, cosmochemistry• Week 2 – Terrestrial planet surfaces (1)• Week 3 – Terrestrial planet surfaces (2)• Week 4 – Terrestrial planet interiors• Week 5 – Midterm; Planetary atmospheres• Week 6 – Orbital dynamics• Week 7 –Giant planets & extra-solar planets• Week 8 - Satellites• Week 9 – Asteroids, Meteorites and Comets • Week 10 – Recap. and putting it all together; Final

Logistics• Website: http://www.es.ucsc.edu/~fnimmo/eart160• Optional text – Hartmann, Moons & Planets, 5th ed.• Prerequisites –

– One of: Math 11B or 19B; and– One of: Phys 6A or Phys 5A.

• WARNING: I am going to assume a good working knowledge of single-variable calculus and freshman physics. You will need to be able to set up and solve “word problems”. Don’t be under any illusions – this is a quantitative course.

• Grading – based on weekly homeworks (40%), midterm (20%), final (40%).

• Homeworks due on Fridays (not this week)• Plagiarism – see Syllabus for policy (posted on web)• Office hours – MWF 12:10-1:10 (A219 E&MS) or by

appointment (email: fnimmo@es.ucsc.edu)• Questions? - Yes please!

Expectations• Homework typically consists of 3 questions

• If it’s taking you more than 1 hour per question on average, you’ve got a problem – come and see me

• Late homework penalized by 10% per day

• Midterm/finals consist of short (compulsory) and long (pick from a list) questions

• Showing up and asking questions are usually routes to a good grade

Summer Research Opportunities• There are many programs, usually paid, for summer

undergraduate research positions in planetary science• Most of the deadlines are within the next month!• There is a list of some of these programs on the class

website

http://es.ucsc.edu/~fnimmo/eart160

There are also going to be many planetary sciences talks this term – searching for a new professor!

This Week• Introductory stuff• Highlights• Formation of the solar system and planets:

• What is the Solar System made of?• How and how fast did the planets form?• How have they evolved subsequently?• [How typical is our Solar System?]

Don’t hesitate to ask questions – it’s what I’m here for

Highlights (1)1. The surface of Titan 2. New craters on Mars

Why do we care?

What is thefluid?

Highlights (2)3. Subsurface oceans 4. An unexpected particle

How do we know?

How did it form?

Highlights (3)5. Enceladus geysers 6. Direct imaging of exoplanets

250 km diameter

What is the energy source?

HR8799

Any Earths out there?

Mission HighlightsPhoenix (Mars) Lunar frenzy

Kaguya (Japan) Chandrayaan-1 (India)

Chang’e (China)

Mercury, the last unknown (MESSENGER)

Selected MissionsMission Target Dates Agency NotesCassini/Huygens Saturn 1997- NASA/ESA Doppler shift . . .

M.E.R. Mars 2003- NASA Still going . . .

Mars Express Mars 2003- ESA First Mars radar

MESSENGER Mercury 2004- NASA Third flyby

Rosetta Comet 2004- ESA

Deep Impact Comet 2005 NASA What next?

M.R.O. Mars 2005- NASA 30cm resolution!

New Horizons Pluto 2006- NASA Jupiter flyby

Dawn Vesta/Ceres 2007- NASA Vesta 2011

L.R.O./GRAIL Moon 2009/2011 NASA Lunar orbiters

Kepler Exoplanets 2009 NASA

M.S.L. Mars 2013(?) NASA $300m overrun

BepiColombo Mercury 2013 ESA

What does the Solar System consist of?

• The Sun 99.85% of the mass (78% H, 20% He)

• Nine Eight Planets

• Satellites• A bunch of other junk (comets, asteroids, Kuiper

Belt Objects etc.)

Where is everything?

J S U N P

1 AU is the mean Sun-Earth distance = 150 million kmNearest star (Proxima Centauri) is 4.2 LY=265,000 AU

KB

Me V E Ma

Note log scales!

Inner solar system

5 AU1.5 AU

Outer solar system

30 AU

Note logarithmic scales!Me V MaE

Gas giants Ice giants Terrestrial planets

Basic dataDistance (AU)

Porbital (yrs)

Protation

(days)

Mass (1024kg)

Radius (km)

(g cm-3)

Sun - - 24.7 2x106 695950 1.41

Mercury 0.38 0.24 58.6 0.33 2437 5.43

Venus 0.72 0.62 243.0R 4.87 6052 5.24

Earth 1.00 1.00 1.00 5.97 6371 5.52

Mars 1.52 1.88 1.03 0.64 3390 3.93

Jupiter 5.20 11.86 0.41 1899 71492 1.33

Saturn 9.57 29.60 0.44 568 60268 0.68

Uranus 19.19 84.06 0.72R 86.6 24973 1.32

Neptune 30.07 165.9 0.67 102.4 24764 1.64

Pluto 39.54 248.6 6.39R 0.013 1152 2.05See e.g. Lodders and Fegley, Planetary Scientist’s Companion

Solar System Formation

• The basic characteristics of this Solar System – composition, mass distribution, angular momentum distribution – are mainly determined by the manner in which the solar system originally formed

• So to understand the subsequent evolution of the planets (and other objects), we need to understand how they formed

In the beginning . . .• Elements are generated by nucleosynthesis within stars• Heavier elements (up to Fe) are formed by fusion of

lighter elements: H -> He -> C -> O• Elements beyond Fe are produced by nuclei absorbing

neutrons• Elements are scattered during stellar explosions (supernovae) and form clouds of material (nebulae) ready to form the next generation of stars and planets

Elem

ental abundance(log scale)

From Albarede, Geochemistry: An introduction

Solar System Formation - Overview• Some event (e.g. nearby supernova) triggers

gravitational collapse of a cloud (nebula) of dust and gas• As the nebula collapses, it forms a spinning disk (due to

conservation of angular momentum)• The collapse releases gravitational energy, which heats

the centre; this central hot portion forms a star• The outer, cooler particles suffer repeated collisions,

building planet-sized bodies from dust grains (accretion)• Young stellar activity (T-Tauri phase) blows off any

remaining gas and leaves an embryonic solar system• These argument suggest that the planets and the Sun

should all have (more or less) the same composition• Comets and meteorites are important because they are

relatively pristine remnants of the original nebula

Jeans Collapse• A perturbation will cause the density to increase locally• Increased density -> increased gravity -> more material

gets sucked in -> runaway process (Jeans collapse)

Gravitational potential energy R

GM 2

~Collapsing cloud

R

M,

Thermal energy M

kTkTN ~~

Equating these two and using M~R3 we get:

2~

RG

kTcrit

Does this make sense?

Example: R=60 light years T=50 K gives crit~10-20 kg m-3 This is 6 atoms per c.c. (a few times the typical interstellar value)

M=mass =densityk=Boltzmann’s constant=atomic weightN=no. of atomsT=temperature (K)

Sequence of events• 1. Nebular disk formation• 2. Initial coagulation

(~10km, ~104 yrs)• 3. Runaway growth (to

Moon size, ~105 yrs)• 4. Orderly growth (to

Mars size, ~106 yrs), gas loss (?)

• 5. Late-stage collisions (~107-8 yrs)

Accretion timescales (1)

Planet density

PlanetesimalSwarm, density s

RfR

vorb

fvRdtdM s2~/

• Consider a protoplanet moving through a planetesimal swarm. We have where v is the relative velocity and f is a factor which arises because the gravitational cross-sectional area exceeds the real c.s.a.

f is the Safronov number:

))/8(1(

))/(1(22

2

vRG

vvf e

Where doesthis come from?

where ve is the escape velocity, G is the gravitational constant, is the planet density. So:

))/8(1(~/ 222 vRGvRdtdM s

Accretion timescales (2)• Two end-members:

– 8GR2 << v2 so dM/dt ~ R2 which means all bodies increase in radius at same rate – orderly growth

– 8GR2 >> v2 so dM/dt ~ R4 which means largest bodies grow fastest – runaway growth

– So beyond some critical size (~Moon-size), the largest bodies will grow fastest and accrete the bulk of the mass

a, AU s,g cm-2 n, s-1 , Myr

1 10 2x10-7 5

5 1 2x10-8 500

25 0.1 2x10-9 50,000

Approximate timescales to form an Earth-like planet. Here we are using f=10, =5.5 g/cc. In practice, f will increase as R increases. Here is the nebular density per unit area and n is 2/orbital period.

Note that forming Neptune is problematic!

•Growth timescale increases with increasing distance (why?):

Late-Stage Accretion• Once each planet has swept up debris out of the area where its

gravity dominates that of the Sun (its feeding zone, or Hill sphere), accretion slows down drastically

• Size of planets at this point is determined by the radius of the Hill sphere and local nebular density, ~ Mars-size at 1 AU

• Collisions now only occur because of mutual perturbations between planets, timescale ~107-8 yrs

Agnor et al. Icarus 1999

Complications• 1) Timing of gas loss

– Presence of gas tends to cause planets to spiral inwards, hence timing of gas loss is important

– Since outer planets can accrete gas if large enough, the relative timescales of planetary growth and gas loss are important

• 2) “Snow line”– More solid material is available beyond the snow line, which allows planets to

grow more rapidly

• 3) Jupiter formation– Jupiter is so massive that it significantly perturbs the nearby area e.g. it

scattered so much material from the asteroid belt that a planet never formed there

– It must have formed early, while the nebular gas was still present. How?

Timescale Summary

Runaway growth

Orderly growth

Late-stage accretion(Giant impacts. Gas loss?)

Dust grains

~Moon-size(planetesimal)

~Mars-size(embryo)

~Earth-size(planet)

~1 Myr

~0.1 Myr

~10-100 Myr

Observations (1)• Early stages of solar system formation can be imaged directly – dust

disks have large surface area, radiate effectively in the infra-red

• Unfortunately, once planets form, the IR signal disappears, so until very recently we couldn’t detect planets (now we know of ~150)

• Timescale of clearing of nebula (~1-10 Myr) is known because young stellar ages are easy to determine from mass/luminosity relationship.

This is a Hubble image of a young solarsystem. You can see the vertical greenplasma jet which is guided by the star’smagnetic field. The white zones are gasand dust, being illuminated from inside bythe young star. The dark central zone is where the dust is so optically thick that the light is not being transmitted.

Thick disk

Observations (2)• We can use the present-

day observed planetary masses and compositions to reconstruct how much mass was there initially – the minimum mass solar nebula

• This gives us a constraint on the initial nebula conditions e.g. how rapidly did its density fall off with distance?

• The picture gets more complicated if the planets have moved . . .

• The observed change in planetary compositions with distance gives us another clue – silicates and iron close to the Sun, volatile elements more common further out

An Artist’s Impression

The young Sun gas/dustnebula

solid planetesimals

Cartoon of Nebular Processes

• Scale height increases radially (why?)

• Temperatures decrease radially – consequence of lower irradiation, and

lower surface density and optical depth leading to more efficient cooling

Polar jets

Stellar magnetic field (sweeps innermost disk clear, reduces stellar spin rate)

Disk cools by radiation

Dust grains Infallingmaterial

Nebula disk(dust/gas)

Hot, high

Cold, low

What is the nebular composition?• Why do we care? It will control what the planets are

made of!• How do we know?

– Composition of the Sun (photosphere)

– Primitive meteorites (see below)

– (Remote sensing of other solar systems - not yet very useful)

• An important result is that the solar photosphere and the primitive meteorites give very similar answers: this gives us confidence that our estimates of nebular composition are correct

Solar photosphere• Visible surface of the Sun

• Assumed to represent the bulk solar composition (is this a good assumption?)

• Compositions are obtained by spectroscopy

• Only source of information on the most volatile elements (which are depleted in meteorites): H,C,N,O

Note sunspots(roughly Earth-size)

1.4

mil

lion

km

Primitive Meteorites• Meteorites fall to Earth and can be analyzed• Radiometric dating techniques suggest that they formed

during solar system formation (4.56 Gyr B.P.)• Carbonaceous (CI) chondrites contain chondrules and

do not appear to have been significantly altered

1cm chondrules

• They are also rich in volatile elements

• Compositions are very similar to Comet Halley, also assumed to be ancient, unaltered and volatile-rich

Meteorites vs. Photosphere

Basaltic Volcanism Terrestrial Planets, 1981

• This plot shows the striking similarity between meteoritic and photospheric compositions

• Note that volatiles (N,C,O) are enriched in photosphere relative to meteorites

• We can use this information to obtain a best-guess nebular composition

Nebular Composition• Based on solar photosphere and chondrite compositions,

we can come up with a best-guess at the nebular composition (here relative to 106 Si atoms):

Data from Lodders and Fegley, Planetary Scientist’s Companion, CUP, 1998This is for all elements with relative abundances > 105 atoms.

Element H He C N O Ne Mg Si S Ar Fe

Log10 (No. Atoms)

10.44 9.44 7.00 6.42 7.32 6.52 6.0 6.0 5.65 5.05 5.95

Condens.

Temp (K)

180 -- 78 120 -- -- 1340 1529 674 40 1337

• Blue are volatile, red are refractory• Most important refractory elements are Mg, Si, Fe, S

Planetary Compositions• Which elements actually condense will depend on the

local nebular conditions (temperature)• E.g. volatile species will only be stable beyond a “snow

line”. This is why the inner planets are rock-rich and the outer planets gas- and ice-rich

• The compounds formed from the elements will be determined by temperature (see next slide)

• The rates at which reactions occur are also governed by temperature. In the outer solar system, reaction rates may be so slow that the equilibrium condensation compounds are not produced

Three kinds of planets . . .• Nebular material can be divided into “gas” (mainly

H/He), “ice” (CH4,H2O,NH3 etc.) and “rock” (including metals)

• Planets tend to be dominated by one of these three end-members

• Proportions of gas/ice/rock are roughly 100/1/0.1• The compounds which actually condense will depend on the local nebular conditions (temperature)• E.g. volatile species will only be stable beyond a “snow line”. This is why the inner planets are rock-rich and the outer planets gas- and ice-rich

Gas-rich

Ice-rich

Rock-rich

Temperature and Condensation

Temperature profiles in a young (T Tauri) stellar nebula, D’Alessio et al., A.J. 1998

Nebular conditions can be used to predict what components of the solar nebula will be present as gases or solids:

Condensation behaviour of most abundant elements of solar nebula e.g. C is stable as CO above 1000K, CH4 above 60K, and then condenses to CH4.6H2O.From Lissauer and DePater, Planetary Sciences

Mid-plane

Photosphere

Earth Saturn

Terrestrial (silicate) planets

• Consist mainly of silicates ((Fe,Mg)SiO4) and iron (plus FeS)

• Mercury is iron-rich, perhaps because it lost its mantle during a giant impact (more on this later)

• Volatile elements (H2O,CO2 etc.) uncommon in the inner solar system because of the initially hot nebular conditions

• Some volatiles may have been supplied later by comets

• Satellites like Ganymede have similar structures but have an ice layer on top (volatiles are more common in the outer nebula)

Mercury

Venus Earth

Moon

Mars

Ganymede

Io

Gas and Ice Giants• Jupiter and Saturn consist mainly of He/H with a

rock-ice core of ~10 Earth masses• Their cores grew fast enough that they captured the

nebular gas before it was blown off• Uranus and Neptune are primarily ices

(CH4,H2O,NH3 etc.) covered with a thick He/H atmosphere

• Their cores grew more slowly and captured less gas

Figure from Guillot, Physics Today, (2004). Sizes are to scale. Yellow is molecular hydrogen, red is metallic hydrogen, ices are blue, rock is grey. Note that ices are not just water ice, but also frozen methane, ammonia etc.

90% H/He

75% H/He

10% H/He

10% H/He

How old is the solar system?• We date the solar system using the decay of long-lived radioactive

nuclides e.g. 238U-206Pb (4.47 Gyr), 235U-207Pb (0.70 Gyr)• These nuclides were formed during the supernova which supplied

the elements making up the original nebula• The oldest objects are certain meteorites, which have an age of

4550 Myr B.P. (see figure)

• Some meteorites once contained live 26Al, which has a half-life of only 0.7 Myr. So these meteorites must have formed within a few Myr of 26Al production (in the supernova).• So the solar system itself is also 4550 Myr old Meteorite isochron (from Albarede,

Geochemistry: An Introduction)

Summary• Solar system formation involved collapse of a large gas

cloud, triggered by a supernova (which also generated many of the elements)

• Solar system originally consisted of gas:ice:rock in ratio 100:1:0.1 (solar photosphere; primitive meteorites)

• Initial nebula was dense and hot near the sun, thinner, colder further out

• Inner planets are mainly rock; outer planets (beyond the snow line) also include ice and (if massive enough) gas

• Planets grow by collisions; Mars-sized bodies formed within ~1 Myr of solar system formation

• Late-stage accretion is slow and involved large impacts

Important Concepts• Minimum mass solar nebula• Stellar nucleosynthesis• Solar photosphere• Jeans collapse• T-Tauri phase & gas loss• CI chondrite• Accretion• Escape velocity• Snow line• Planetesimals• Runaway growth• Astronomical unit (AU)

End of Lecture

Forming Jupiters• Individual gas giants probably form by gas accreting

onto a pre-existing large solid planet• How big does the initial solid planet have to be?

Gravitational P.E. per unitmass of gas R

GM~R

Thermal energy per unit mass of gas

kTN~

Equating these two and using M~R3 we get:

2/12/3

~

G

NkTM crit

Does this make sense?

M=mass =densityk=Boltzmann’s constantN=no. of atoms per kgT=temperature (K)

M,Solid core

Gas

Example: =5000 kg m-3 T=1000 K gives Mcrit~ 6x1023 kg (=Earth)This is actually a bit low – real value is more like 8-10 MEarth