Utilization of a Solar Sail to Perform a Lunar Cubesat Science Mission

Utilization of a Solar Sail to Perform a Lunar CubeSat Science Mission

2nd Interplanetary CubeSat Workshop Ithaca, New York May 28 -29, 2013

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 1 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 m 2 sails have been deployed on the ground in demonstrations by NASA and DLR 1 • Recent and upcoming Earth-orbiting solar sail technology demonstration flights 2-4: IKAROS Spacecraft (JAXA) 2

Name Organization Sail Size Date Spacecraft IKAROS JAXA 200 m 2 June 2010 Custom

NanoSail-D2 NASA/AFRL 10 m 2 January 2011 3U CubeSat

CubeSail NASA/CU 25 m 2 Planned 2013 3U CubeSat Aerospace/ Univ. of Illinois DeOrbitSail Univ. of Surrey 25 m 2 Planned 2014 3U CubeSat

LightSail TM -1 Planetary 32 m 2 Planned 2015 3U CubeSat Society NanoSail-D2 Spacecraft (NASA) 3 3 Concept of Operations

1.) Launch 2.) Deliver to Moon 3.) Deploy 6U 4.) Cruise Phase in on MPCV CubeSat from MPCV Lunar Circular Orbit

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

4 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

Moon

Earth yi

Moon Orbit Sun Inclination: 5.145° xi

*Not to scale Image Source: Oracle Education Foundation ThinkQuest article 6 http://library.thinkquest.org/29033/begin/earthsunmoon.htm Earth-Moon (EM) Frame Concept

L4 x

Earth L3 L1Moon L2 x x x

L5 x

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

7 z y i i Earth -Moon (EM) Frame Concept T

xi θ Sun vector to solar sail

zem x z em zi em

i ωem

yem

Moon Orbit Inclination i = 5.145°

Image Source: Oracle Education Foundation ThinkQuest article 8 *Not to scale http://library.thinkquest.org/29033/begin/earthsunmoon.htm . Solar Sail Thrust Determination

-3 x 10 Solar sail thrust as a function of tilt angle and reflectivity 1 From Space Mission 0.86 reflectivity 0.9 6 0.97 reflectivity Analysis and Design : 0.8

0.7 -6 RA 2 Tsail = 9.113 x 10 sin (θ (t)) [N] 0.6 D2 0.5

Thrust (N) 0.4

Where: 0.3 – R = fraction of incident light 0.2 reflected by sail 0.1 0 0 20 40 60 80 100 120 140 160 180 (Aluminum ranges 0.86-0.97; Sail tilt angle from Sun-Earth line (deg) absolute max = 1) Example thrust values with – A = sail area (m 2) representative input parameters – D = distance to Sun in AU D = 1.0026; A = 100 m 2 R = 0.86 – Θ(t) = sail tilt angle Max T = 7.80 x 10 -4 N (varies with respect to time) 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 9 Inertial Equations of Motion (in SCI frame)

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

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

10 Solar Sail Thrust Control

•Thrust off when moving toward Sun •Thrust on when moving away from Sun

LightSail-1 Attitude Control System Orbit Raising Mode 7 11 Orbit Raising Maneuver

4 x 10 Earth-Moon System w/ origin at c.m.

• Simulation starts with Earth center of mass 6 Moon center of mass Release Trajectory spacecraft in 110 km Final point before sail unfurl Solar sail trajectory L1 circular Low-Lunar Orbit 4 L2 Moon Surface • Solar sail deployed after 2 checkout phase • Sail force causes orbit to 0 Y-axis(km) spiral out slowly from Moon -2 • Orbit remains nearly circular until escape from -4

lunar gravity after 858 days -6

3.2 3.4 3.6 3.8 4 4.2 4.4 5 X-axis (km) x 10

12 Orbit Raising Maneuver

4 x 10 Earth-Moon System w/ origin at c.m.

Spiral outward Earth center of mass 6 Moon center of mass from lunar orbit Release Trajectory Final point before sail unfurl Solar sail trajectory L1 4 L2 Moon Surface

0 Y-axisY-axis(km) (km)

-2

-4

-6

3.2 3.4 3.6 3.8 4 4.2 4.4 13 5 X-axis (km) x 10 Orbit Raising Maneuver

4 x 10 Earth-Moon System w/ origin at c.m.

Wide range of Earth center of mass 6 Moon center of mass altitudes is covered Release Trajectory (desired condition) Final point before sail unfurl Solar sail trajectory L1 4 L2 Moon Surface

0 Y-axisY-axis(km) (km)

-2 Orbit stretches about halfway to Lunar L2 point -4 (desired condition)

-6

3.2 3.4 3.6 3.8 4 4.2 4.4 14 5 X-axis (km) x 10 Orbit Raising Maneuver

4 x 10 Earth-Moon System w/ origin at c.m.

Earth center of mass 6 Moon center of mass Release Trajectory Final point before sail unfurl Solar sail trajectory L1 4 L2 Moon Surface

0 Y-axisY-axis(km) (km)

-2 Escapes from lunar gravity and passes near -4 L2 after 858 days (2 years, 4 months)

-6

3.2 3.4 3.6 3.8 4 4.2 4.4 15 5 X-axis (km) x 10 Unstable L2 Halo Orbit

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

16 Unstable L2 Halo Orbit

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

Uncontrolled: Uncontrolled: 1 period (11.7 days) 12.5 periods (146.22 days)

17 Unstable L2 Halo Orbit Uncontrolled Trajectory Comparison

Uncontrolled: 1 period (11.7 days)

Earth-Moon Halo Orbit in x-z plane Earth-Moon Halo Orbit in x-y plane 0.05 Trajectory Trajectory 0.1 L1 L1 L2 L2 0 Moon Moon 0.05

-0.05

-0.1 Y location (d.u.) Z location (d.u.)

-0.05

-0.15

-0.1 -0.2

0.85 0.9 0.95 1 1.05 1.1 1.15 0.85 0.9 0.95 1 1.05 1.1 1.15 X location (d.u.) X location (d.u.) 18 Uncontrolled: 12.5 periods (146.22 days) Unstable L2 Halo Orbit

Uncontrolled trajectory escapes lunar gravity after 175 days Earth-Moon Halo Orbit in x-z plane

Trajectory L1 1 L2 Moon

0.5

0 Earth ZZ locationlocation (d.u.) (d.u.)

-0.5

-1

-2 -1.5 -1 -0.5 0 0.5 1 X location (d.u.) 19 Stable L2 Halo Orbit (LQR Control Force)

• 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:

• Linear state feedback controller using gain matrix K obtained via linear quadratic regulator (LQR) method 8 • Compares state at each timestep to reference state (full period solution of uncontrolled L2 halo orbit) 20 Stable L2 Halo Orbit (LQR Control Force)

Ideal LQR Control vs. Uncontrolled Trajectory Comparison

Earth-Moon Halo Orbit (controlled) Trajectory L1 L2 Moon 0.05

-0.05

-0.1

ZZ locationlocation (d.u.) (d.u.) -0.15

0.1 1.1 0 1

-0.1 0.9 Y location (d.u.) X location (d.u.)

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

21 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 shadow 9 – Observations into polar craters 10 – Constellations to measure fields and particles with simultaneous spatial and temporal resolutions 9 – Telecom relay from small science packages emplaced out of Earth view on lunar farside and in some polar craters 10

• 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 • 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)

• 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 Lightsey [email protected]

JPL POC : Robert L. Staehle robert.l.staehle@jpl.nasa.gov

25 References

1Vulpetti, 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!”, 25 th 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. 6Wertz, J. R., Everett, D. F., and Puschell, J. J. (eds.), Space Mission Engineering: The New SMAD , 1 st ed., Microcosm Press, Hawthorne, CA, 2011, pp. 554-558.

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

10 Staehle, 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 Planetary Systems Corp. 6U (<100 ms per impulse) deployment • Total Possible Release ΔV: mechanism with 11.5-21.5 m/s deployable solar panels

Source : Planetary Systems Corporation 28 Bevo-2 flight thruster design gas release test Canisterized Satellite Dispenser (CSD) Data Sheet Earth/Moon Initial Condition

Total Lunar Eclipse: April 15, 2014, 7:46 UTC • Initial condition selected at a time when Sun, Moon, and Sun vector (x ) sci Earth are all aligned (i.e. a solar or lunar eclipse) • At this point, the Moon will be located at the ascending Moon Orbit node of its orbit about Earth Inclination: 5.145° relative to the ecliptic plane • Total lunar eclipse on April 15, 2014 (7:46 UTC) was chosen arbitrarily • X-axis of SCI frame is aligned *Not to scale 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.

Image Sources: http://commons.wikimedia.org/wiki/File: Geometry_of_a_ Lunar_Eclipse.svg ; http://starryskies.com/The_sky/events/lunar-2003/eclipse2.html ; 29 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)

Moon Orbit about Earth : (z-axis rotation) Moon Orbit Inclination : zem (Inclined) yem (initial) i =5.145° (x-axis rotation) yem (t) i zem (Ecliptic)

Φ(t)

xem (initial)

yem (Ecliptic)

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

0.6

0.5

0.4

0.3

Orbit Orbit Orbit Eccentricity Eccentricity 0.2

0.1

0 0 100 200 300 400 500 600 700 800 Time (days) 32 Orbit Raising Maneuver

4 x 10 6 L2 = 5.9845e4 km from Moon

2 Semi-Major Semi-Major Semi-Major AxisAxis (km) (km)

0 0 100 200 300 400 500 600 700 800 Time (days) 33