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

Transcription

1 Utilization of a Solar Sail to Perform a Lunar CubeSat Science Mission 2 nd 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

2 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

3 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 June2010 Custom NanoSail-D2 NASA/AFRL 10 m 2 January2011 3U CubeSat CubeSail NASA/CU Aerospace/ Univ. of Illinois 25 m 2 Planned2013 3U CubeSat DeOrbitSail Univ. of Surrey 25 m 2 Planned2014 3U CubeSat LightSail TM -1 Planetary Society 32 m 2 Planned U CubeSat NanoSail-D2 Spacecraft (NASA) 3 3

4 Concept of Operations 1.) Launch 2.) Deliver to Moon on MPCV 3.)Deploy 6U CubeSat from MPCV 4.) CruisePhase in 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 -CanisterizedSatellite Dispenser Data Sheet, p. 15, Planetary Systems Corporation website, downloads 4

5 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

6 Sun-Centered Inertial (SCI) Frame Concept Moon y i Earth Sun Moon Orbit Inclination: x i z i Image Source: Oracle Education Foundation ThinkQuestarticle *Not to scale 6

7 Earth-Moon (EM) Frame Concept L4 x L3 x Earth L1 x Moon L2 x L5 x Earth-Moon rotating reference frame showing locations of Lagrange Points (L1 through L5) 5 7

8 y i z i Earth-Moon (EM) Frame Concept T x i Sun vector to solar sail θ z em z i z em x em i ω em y em Moon Orbit Inclination i= *Not to scale Image Source: Oracle Education Foundation ThinkQuestarticle 8

9 Solar Sail Thrust Determination From Space Mission Analysis and Design 6 : Tsail = Where: x 10 RA D 2 2 sin ( θ ( t)) R = fraction of incident light reflected by sail [N] (Aluminum ranges ; absolute max = 1) A = sail area (m 2 ) D = distance to Sun in AU Θ(t) = sail tilt angle (varies with respect to time) Thrust (N) x 10-3 Solar sail thrust as a function of tilt angle and reflectivity 0.86 reflectivity 0.97 reflectivity Sail tilt angle from Sun-Earth line (deg) Example thrust values with representative input parameters D = ; A = 100 m 2 R = 0.86 Max T = 7.80 x 10-4 N AvgT = 3.90 x 10-4 N R = 0.97 Max T = x 10-4 N AvgT = 4.40 x 10-4 N 9

10 Inertial Equations of Motion (in SCI frame) *Sail force is along direction of the thrust vector (û t ) Assumes Sun is always visible to entire sail (ignore shadowing) 10

11 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

12 Orbit Raising Maneuver Simulation starts with spacecraft in 110 km circular Low-Lunar Orbit Solar sail deployed after checkout phase Sail force causes orbit to spiral out slowly from Moon Orbit remains nearly circular until escape from lunar gravity after 858 days Y-axis (km) x 10 4 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 X-axis (km) x

13 Orbit Raising Maneuver Spiral outward from lunar orbit 6 4 x 10 4 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 2 ) Y-axis (km) X-axis (km) x

14 Orbit Raising Maneuver 6 4 x 10 4 Wide range of altitudes is covered (desired condition) 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 2 ) Y-axis (km) Orbit stretches about halfway to Lunar L2 point (desired condition) X-axis (km) x

15 Orbit Raising Maneuver x 10 4 Earth-Moon System w/ origin at c.m. 6 4 Earth center of mass Moon center of mass Release Trajectory Final point before sail unfurl Solar sail trajectory L1 L2 Moon Surface 2 ) Y-axis (km) Escapes from lunar gravity and passes near L2 after 858 days (2 years, 4 months) X-axis (km) x

16 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

17 Unstable L2 Halo Orbit 1 d.u. = distance from Earth to Moon (384,000 km) Uncontrolled: 1 period (11.7 days) Uncontrolled: 12.5 periods ( days) 17

18 Unstable L2 Halo Orbit Uncontrolled Trajectory Comparison Uncontrolled: 1 period (11.7 days) Trajectory L1 L2 Moon Earth-Moon Halo Orbit in x-y plane Earth-Moon Halo Orbit in x-z plane Trajectory L1 L2 Moon Y location (d.u.) 0 Z location (d.u.) X location (d.u.) Uncontrolled: 12.5 periods ( days) X location (d.u.) 18

19 Unstable L2 Halo Orbit Uncontrolled trajectory escapes lunar gravity after 175 days Earth-Moon Halo Orbit in x-z plane 1 Trajectory L1 L2 Moon 0.5 Z location (d.u..) 0 Earth X location (d.u.) 19

20 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 Kobtained via linear quadratic regulator (LQR) method 8 Compares state at each timestep to reference state (full period solution of uncontrolled L2 halo orbit) 20

21 Stable L2 Halo Orbit (LQR Control Force) Ideal LQR Control vs. Uncontrolled Trajectory Comparison 0.05 Earth-Moon Halo Orbit (controlled) Trajectory L1 L2 Moon Z location (d.u.) Y location (d.u.) X location (d.u.) Controlled: 50 periods (1.6 years) Uncontrolled: 12.5 periods ( days) 21

22 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 farsideand 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

23 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

24 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

25 Contact Information Primary Author: Peter Z. Schulte UT POC: E. Glenn Lightsey JPL POC: Robert L. Staehle 25

26 References 1 Vulpetti, G., Johnson, L., and Matloff, G.L., Solar Sails: A Novel Approach to Interplanetary Travel, Praxis Publishing, Ltd., New York, 2008, pp. 59, 106, Sawada, 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 , AIAA, Denver, CO, Alhorn, 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, Johnson, 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 McInnes, 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 Wertz, 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 Biddy, C. LightSail-1: Solar Sail Design and Qualification, The Planetary Society/Stellar Exploration, Inc., 41 st Aerospace Mechanism Symposium, Pasadena, CA, Wie, B., Space Vehicle Dynamics and Control, AIAA Education Series, AIAA, Reston, VA, 1998, pp , Staehle, 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: 10 Staehle, R.L., Anderson, B., Betts, B., Blaney, D., Chow, C., et al. Interplanetary CubeSatsArchitecture and Missions, 1st International Workshop on LunarCubes, Palo Alto, CA,

27 Backup 27

28 Potential V At Release from MPCV Max ejection V from deployment mechanism with 12 kg mass = 1.5 m/s Cold Gas Thruster: net m/s ΔV at 1W (<100 ms per impulse) Total Possible Release ΔV: Planetary Systems Corp. 6U deployment mechanism with m/s deployable solar panels Bevo-2 flight thruster design gas release test Source: Planetary Systems Corporation 28 Canisterized Satellite Dispenser (CSD) Data Sheet

29 Earth/Moon Initial Condition Total Lunar Eclipse: April 15, 2014, 7:46 UTC *Not to scale Sun vector (x sci ) Moon Orbit Inclination: Image Sources: Geometry_of_a_ Lunar_Eclipse.svg; chart_close-2014apr15. png 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 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. 29

30 Coordinate Transformations (EM SCI) Location of Earth-Moon system center of mass 30

31 Coordinate Transformations (EM SCI) z em (Inclined) i z em (Ecliptic) Moon Orbit Inclination: i=5.145 (x-axis rotation) Moon Orbit about Earth: (z-axis rotation) y em (t) y em(initial) Φ(t) x em(initial) y em (Ecliptic) Image Source: 31

32 Orbit Raising Maneuver Orbit Eccentr ricity Time (days) 32

33 Orbit Raising Maneuver 6 x 104 L2 = e4 km from Moon 5 is (km) Semi-Major Axi Time (days) 33