utilization of a solar sail to perform a lunar cubesat ... · pdf fileutilization of a solar...

Utilization of a Solar Sail to Perform

a Lunar CubeSat Science Mission

2nd Interplanetary CubeSat Workshop

Ithaca, New York

May 28-29, 2013

1

The University of Texas at Austin (UT): Texas Spacecraft Laboratory (TSL)

Peter Z. Schulte Undergraduate Research Assistant

E. Glenn Lightsey Professor

Katharine M. Brumbaugh Graduate Research Assistant

Jet Propulsion Laboratory, California Institute of Technology (JPL)

Robert L. Staehle Assistant Manager for Advanced Concepts, Instruments Division

May 28-29, 2013

Overview

• Demonstrate use of solar sail propulsion to enable unique lunar

science missions

• Six-unit (6U) CubeSat configuration with spacecraft mass ≈ 12 kg

• Deliver as secondary payload to circular Low-Lunar Orbit (LLO)

• Deploy solar sail and raise orbit to accomplish science objectives

• Show an example destination: enter an L2 halo orbit

2

Solar Sail Technology

• Constant low-thrust propulsion with reduced

mass and limited propellant use

• Several 400 m2 sails have been deployed on the

ground in demonstrations by NASA and DLR1

• Recent and upcoming Earth-orbiting solar sail

technology demonstration flights2-4: IKAROS Spacecraft (JAXA)2

3

NanoSail-D2 Spacecraft (NASA)3

Name Organization Sail Size Date Spacecraft

IKAROS JAXA 200 m2 June 2010 Custom

NanoSail-D2 NASA/AFRL 10 m2 January 2011 3U CubeSat

CubeSail NASA/CU

Aerospace/

Univ. of Illinois

25 m2 Planned 2013 3U CubeSat

DeOrbitSail Univ. of Surrey 25 m2 Planned 2014 3U CubeSat

LightSailTM-1 Planetary

Society

32 m2 Planned 2015 3U CubeSat

1.) Launch 2.) Deliver to Moon

on MPCV

3.) Deploy 6U

CubeSat from MPCV

4.) Cruise Phase in

Lunar Circular Orbit

5.) Deploy Solar Sail 6.) Orbit Raising 7.) Transfer to L2 8.) Halo Orbit at L2

Concept of Operations

4

5.) Deploy Solar Sail 6.) Orbit Raising 7.) Transfer to L2 8.) Halo Orbit at L2

Image Sources: Panels 1,2, and 4 - various public NASA websites. Panel 3 - Canisterized Satellite Dispenser Data Sheet, p. 15,

Planetary Systems Corporation website, http://www.planetarysystemscorp.com/#!__downloads

Trajectory Study Methodology

• Developed numerical simulation in MATLAB to evaluate trajectory

• Primary simulation based in Sun-Centered Inertial (SCI) frame

• For simplicity of interpretation, input and output values were

provided in the Earth-Moon (EM) rotating reference frame

5

Sun-Centered Inertial (SCI) Frame Concept

Earth

Moon

yi

Sunxi

zi

*Not to scale

Moon Orbit

Inclination: 5.145°

6Image Source: Oracle Education Foundation ThinkQuest article

http://library.thinkquest.org/29033/begin/earthsunmoon.htm

xx

x

x

Earth-Moon (EM) Frame Concept

Earth MoonL1 L2L3

L4

xx

x

x

7

Earth-Moon rotating reference frame showing locations of Lagrange Points (L1 through L5)5

L5

xi

yi

zi

Sun vector to solar sail

xem

zem

ωem

θ

T

zizem

i

Earth-Moon (EM) Frame Concept

yem

Moon Orbit

Inclination

i = 5.145°

*Not to scale8Image Source: Oracle Education Foundation ThinkQuest article

http://library.thinkquest.org/29033/begin/earthsunmoon.htm.

From Space Mission

Analysis and Design6:

Where:– R = fraction of incident light

))((2

sin2

-610 x 9.113 Tsail t

D

RAθ=

Solar Sail Thrust Determination

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1x 10

-3

Thru

st

(N)

Solar sail thrust as a function of tilt angle and reflectivity

0.86 reflectivity

0.97 reflectivity

[N]

– R = fraction of incident light

reflected by sail

(Aluminum ranges 0.86-0.97;

absolute max = 1)

– A = sail area (m2)

– D = distance to Sun in AU

– Θ(t) = sail tilt angle

(varies with respect to time)

9

0 20 40 60 80 100 120 140 160 1800

0.1

0.2

Sail tilt angle from Sun-Earth line (deg)

Example thrust values with

representative input parameters

D = 1.0026; A = 100 m2

R = 0.86

Max T = 7.80 x 10-4 N

Avg T = 3.90 x 10-4 N

R = 0.97

Max T = 8.7945 x 10-4 N

Avg T = 4.40 x 10-4 N

Inertial Equations of Motion (in SCI frame)

10

*Sail force is along direction of the thrust vector (ût)

Assumes Sun is always visible to entire sail (ignore shadowing)

•Thrust off when moving toward Sun

•Thrust on when moving away from Sun

Solar Sail Thrust Control

LightSail-1 Attitude Control System Orbit Raising Mode7 11

Orbit Raising Maneuver

• Simulation starts with

spacecraft in 110 km

circular Low-Lunar Orbit

• Solar sail deployed after

checkout phase2

4

6

x 104 Earth-Moon System w/ origin at c.m.

Earth center of mass

Moon center of mass

Release Trajectory

Final point before sail unfurl

Solar sail trajectory

L1

L2

Moon Surface

checkout phase

• Sail force causes orbit to

spiral out slowly from Moon

• Orbit remains nearly

circular until escape from

lunar gravity after 858 days

12

3.2 3.4 3.6 3.8 4 4.2 4.4

x 105

-6

-4

-2

0

X-axis (km)

Y-a

xis

(km

)

2

4

6

x 104

Y-a

xis

(km

)

Earth-Moon System w/ origin at c.m.


Moon center of mass

Release Trajectory



L1

L2

Moon Surface


Spiral outward

from lunar orbit

3.2 3.4 3.6 3.8 4 4.2 4.4

x 105

-6

-4

-2

0

X-axis (km)

Y-a

xis

(km

)

13

2

4

6

x 104

Y-a

xis

(km

)



Moon center of mass

Release Trajectory



L1

L2

Moon Surface


Wide range of

altitudes is covered

(desired condition)

3.2 3.4 3.6 3.8 4 4.2 4.4

x 105

-6

-4

-2

0

X-axis (km)

Y-a

xis

(km

)

14

Orbit stretches about

halfway to Lunar L2 point

(desired condition)

2

4

6

x 104

Y-a

xis

(km

)



Moon center of mass

Release Trajectory



L1

L2

Moon Surface


3.2 3.4 3.6 3.8 4 4.2 4.4

x 105

-6

-4

-2

0

X-axis (km)

Y-a

xis

(km

)

15

Escapes from lunar

gravity and passes near

L2 after 858 days

(2 years, 4 months)

• Assume optimal transfer trajectory exists orbit raising

trajectory to L2 halo orbit

• Differential correction procedure used to determine initial

conditions for an L2 halo orbit

• Uncontrolled Three-Body Motion (Circular Restricted Three-

Unstable L2 Halo Orbit

• Uncontrolled Three-Body Motion (Circular Restricted Three-

Body Problem) in EM frame (Equations from Ref. 8):

16


1 d.u. = distance from Earth to Moon (384,000 km)

17

Uncontrolled:

12.5 periods (146.22 days)

Uncontrolled:

1 period (11.7 days)

Uncontrolled Trajectory Comparison


0.85 0.9 0.95 1 1.05 1.1 1.15

-0.1

-0.05

0

0.05

0.1

X location (d.u.)

Y location (

d.u

.)

Earth-Moon Halo Orbit in x-y plane

Trajectory

L1

L2

Moon

0.85 0.9 0.95 1 1.05 1.1 1.15

-0.2

-0.15

-0.1

-0.05

0

0.05

X location (d.u.)

Z location (

d.u

.)

Earth-Moon Halo Orbit in x-z plane

Trajectory

L1

L2

Moon

Uncontrolled: 1 period (11.7 days)

Uncontrolled: 12.5 periods (146.22 days)18

0.5

1

Z location (

d.u

.)Earth-Moon Halo Orbit in x-z plane

Trajectory

L1

L2

Moon


Uncontrolled trajectory escapes lunar gravity after 175 days

-2 -1.5 -1 -0.5 0 0.5 1

-1

-0.5

0

X location (d.u.)

Z location (

d.u

.)

19

Earth

• Develop an ideal controller to stabilize L2 halo orbit using an

unconstrained, arbitrary control force

• Added ideal control acceleration to three-body motion in EM frame:

Stable L2 Halo Orbit (LQR Control Force)

20

• Linear state feedback controller using gain matrix K obtained via linear

quadratic regulator (LQR) method8

• Compares state at each timestep to reference state (full period solution of

uncontrolled L2 halo orbit)

-0.05

0

0.05

Earth-Moon Halo Orbit (controlled)

Z location (

d.u

.)

Trajectory

L1

L2

Moon

Stable L2 Halo Orbit (LQR Control Force)

Ideal LQR Control vs. Uncontrolled Trajectory Comparison

0.9

1

1.1

-0.1

0

0.1

-0.15

-0.1

X location (d.u.)Y location (d.u.)

Z location (

d.u

.)

21

Uncontrolled: 12.5 periods (146.22 days)Controlled: 50 periods (1.6 years)

Candidate Science Mission Applications Enabled

• Significant orbital maneuvering capability of an inexpensive

s/c in lunar orbits could be used for:

– Radio survey and mapping of Moon’s radio shadow9

– Observations into polar craters10

– Constellations to measure fields and particles with simultaneous

spatial and temporal resolutions9

– Telecom relay from small science packages emplaced out of Earth view – Telecom relay from small science packages emplaced out of Earth view

on lunar farside and in some polar craters10

• If you can raise from 110 km circular orbit to escape, the same

propulsion technique can be used to go from incoming V-

infinity to any orbit

22

Summary

• Developed models to calculate solar sail thrust force based on angle to the sun, inertial position and velocity, sail material properties, and physical area of sail

• Created simulation to propagate trajectories in Sun-Centered Inertial (SCI) frame, but provided initial conditions and plotted results in Earth-Moon (EM) rotating reference frame

• Assumed 6U CubeSat can be delivered to a lunar circular orbit by another Moon-bound spacecraft

• Assumed 6U CubeSat can be delivered to a lunar circular orbit by another Moon-bound spacecraft

• Modeled solar sail propulsion to demonstrate orbit raising

• Determined L2 halo orbit can be stabilized; will consider using solar sail for this maneuver

• Established proof of concept for a solar sail orbit raising mission at the Moon with low-mass, low-cost spacecraft (time scale 2-3 years)

23

Future Work

• Design optimal control laws for solar sail pointing

– Orbit raising maneuver

– Transfer to L2 halo orbit

– L2 halo orbit stabilization

• Design optimal transfer trajectory

(from orbit raising trajectory to L2 halo orbit)(from orbit raising trajectory to L2 halo orbit)

• Implement solar sail visible and radio shadowing functions for

increased simulation fidelity

24

Contact Information

Primary Author: Peter Z. Schulte

[email protected]

UT POC: E. Glenn LightseyUT POC: E. Glenn Lightsey

[email protected]

JPL POC: Robert L. Staehle

[email protected]

25

References1Vulpetti, G., Johnson, L., and Matloff, G.L., Solar Sails: A Novel Approach to Interplanetary Travel, Praxis Publishing, Ltd., New York, 2008, pp. 59, 106, 135-9.

2Sawada, H., Mori, O., Okuizumi, N., Shirasawa, Y., Miyazaki, Y., et al., “Mission Report on The Solar Power Sail Deployment Demonstration of IKAROS,” 52nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, AIAA 2011-1887, AIAA, Denver, CO, 2011.

3Alhorn, D.C., Casas, J.P., Agasid, E.F., Adams, C.L., Laue, G., et al., “NanoSail-D: The Small Satellite That Could!”, 25th

Annual AIAA/USU Conference on Small Satellites, SSC11-VI-1, AIAA, Logan, UT, 2011.

4Johnson, L., Young, R., Barnes, N., Friedman, L., Lappas, V., McInnes, C., “Solar Sails: Technology And Demonstration Status,” International Journal of Aeronatuical & Space Science, Vol. 13, No. 4, 2012, pp. 421-427.

5McInnes, A.I.S., “Strategies for Solar Sail Mission Design in the Circular Restricted Three-Body Problem,” Master’s Thesis, School of Aeronautics and Astronautics, Purdue University, West Lafayette, IN, Aug. 2000.Thesis, School of Aeronautics and Astronautics, Purdue University, West Lafayette, IN, Aug. 2000.

6Wertz, J. R., Everett, D. F., and Puschell, J. J. (eds.), Space Mission Engineering: The New SMAD, 1st ed., Microcosm Press, Hawthorne, CA, 2011, pp. 554-558.

7Biddy, C. “LightSail-1: Solar Sail Design and Qualification,” The Planetary Society/Stellar Exploration, Inc., 41st

Aerospace Mechanism Symposium, Pasadena, CA, 2012.

8Wie, B., Space Vehicle Dynamics and Control, AIAA Education Series, AIAA, Reston, VA, 1998, pp. 240-255, 286-302.

9Staehle, R.L., Anderson, B., Betts, B., Blaney, D., Chow, C., et al. “Interplanetary CubeSats: Opening the Solar System to a Broad Community at Lower Cost,” Final Report of NIAC Phase 1 to NASA Office of the Chief Technologist, Jet Propulsion Laboratory, Pasadena, CA, 2012, URL: http://www.nasa.gov/pdf/716078main_Staehle_2011_PhI_CubeSat.pdf.

10Staehle, R.L., Anderson, B., Betts, B., Blaney, D., Chow, C., et al. “Interplanetary CubeSats Architecture and Missions,” 1st International Workshop on LunarCubes, Palo Alto, CA, 2012.

26

Backup

27

Potential ∆V At Release from MPCV

• Max ejection ∆V from deployment mechanism with 12 kg mass = 1.5 m/s

• Cold Gas Thruster:

net 10-20 m/s ΔV at 1W

(<100 ms per impulse)

• Total Possible Release ΔV:

Planetary

Systems Corp. 6U

deployment

mechanism with

deployable solar 11.5-21.5 m/s deployable solar

panels

Bevo-2 flight thruster design gas release testSource: Planetary Systems Corporation

Canisterized Satellite Dispenser (CSD) Data Sheet

28

Earth/Moon Initial Condition

Sun vector (xsci)

Moon Orbit

Inclination: 5.145°

• Initial condition selected at a

time when Sun, Moon, and

Earth are all aligned (i.e. a

solar or lunar eclipse)

• At this point, the Moon will

be located at the ascending

node of its orbit about Earth

relative to the ecliptic plane

Total lunar eclipse on April

Total Lunar Eclipse: April 15, 2014, 7:46 UTC

*Not to scale

• Total lunar eclipse on April

15, 2014 (7:46 UTC) was

chosen arbitrarily

• X-axis of SCI frame is aligned

with 4/15/2014 sun vector as

shown to the left

• Position of Earth and Moon

for all simulations are

propagated from this point

using circular orbits.

29Image Sources: http://commons.wikimedia.org/wiki/File: Geometry_of_a_

Lunar_Eclipse.svg; http://starryskies.com/The_sky/events/lunar-2003/eclipse2.html;

http://commons.wikimedia.org/wiki/File:Lunar_eclipse_ chart_close-2014Apr15. png

Coordinate Transformations (EM�SCI)

Location of Earth-Moon

system center of mass

30

Coordinate Transformations (EM�SCI)

31

izem (Inclined)

yem (Ecliptic)

zem (Ecliptic)

Moon Orbit Inclination:

i =5.145° (x-axis rotation) yem(t)

xem (initial)

yem (initial)

Moon Orbit about Earth:

(z-axis rotation)

Φ(t)

Image Source: http://scienceblogs.com/startswithabang/2009/07/21/the-best-eclipse-of-the-centur/


0.4

0.5

0.6

Orb

it E

ccentr

icity

32

0 100 200 300 400 500 600 700 8000

0.1

0.2

0.3

Time (days)

Orb

it E

ccentr

icity

4

5

6x 10

4

Sem

i-M

ajo

r A

xis

(km

)


L2 = 5.9845e4 km

from Moon

0 100 200 300 400 500 600 700 8000

1

2

3

Time (days)

Sem

i-M

ajo

r A

xis

(km

)

33

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