Abstract
The Gravity Recovery and Interior Laboratory (GRAIL) mission to the Moon utilized an integrated scientific measurement system comprised of flight, ground, mission, and data system elements in order to meet the end-to-end performance required to achieve its scientific objectives. Modeling and simulation efforts were carried out early in the mission that influenced and optimized the design, implementation, and testing of these elements. Because the two prime scientific observables, range between the two spacecraft and range rates between each spacecraft and ground stations, can be affected by the performance of any element of the mission, we treated every element as part of an extended science instrument, a science system. All simulations and modeling took into account the design and configuration of each element to compute the expected performance and error budgets. In the process, scientific requirements were converted to engineering specifications that became the primary drivers for development and testing. Extensive simulations demonstrated that the scientific objectives could in most cases be met with significant margin. Errors are grouped into dynamic or kinematic sources and the largest source of non-gravitational error comes from spacecraft thermal radiation. With all error models included, the baseline solution shows that estimation of the lunar gravity field is robust against both dynamic and kinematic errors and a nominal field of degree 300 or better could be achieved according to the scaled Kaula rule for the Moon. The core signature is more sensitive to modeling errors and can be recovered with a small margin.
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Abbreviations
- AGC:
-
Automatic Gain Control
- AMD:
-
Angular Momentum Desaturation
- C&DH:
-
Command & Data Handler
- CBE:
-
Current Best Estimate
- CG:
-
Center of Gravity
- CPU:
-
Central Processing Unit
- DSN:
-
Deep Space Network
- DOWR:
-
Dual One-way Range
- ECM:
-
Eccentricity Correction Maneuver
- EOP:
-
Earth Orientation Platform
- ET:
-
Ephemeris Time
- GPS:
-
Global Positioning System
- GR-A:
-
GRAIL-A Spacecraft (Ebb)
- GR-B:
-
GRAIL-B Spacecraft (Flow)
- GRACE:
-
Gravity Recovery and Climate Experiment
- GRAIL:
-
Gravity Recovery and Interior Laboratory
- GSFC:
-
Goddard Space Flight Center
- ICRF:
-
International Celestial Reference Frame
- IERS:
-
International Earth Rotation and Reference Systems Service
- IR:
-
Infra Red
- IPU:
-
Instrument Processing Unit (GRACE mission)
- JPL:
-
Jet Propulsion Laboratory
- KBR:
-
Ka-Band Ranging
- KBRR:
-
Ka-Band Range-Rate
- LGRS:
-
Lunar Gravity Ranging System
- LLR:
-
Lunar Laser Ranging
- LOI:
-
Lunar Orbit Insertion
- LOS:
-
Line of Sight
- LP:
-
Lunar Prospector
- mGal:
-
milliGal (where 1 Gal=0.01 m s−2)
- MGS:
-
Mars Global Surveyor
- MIT:
-
Massachusetts Institute of Technology
- MOS:
-
Mission Operations System
- MIRAGE:
-
Multiple Interferometric Ranging and GPS Ensemble
- MMDOM:
-
Multi-mission Distributed Object Manager
- MONTE:
-
Mission-analysis, Operations, and Navigation Toolkit Environment
- MPST:
-
Mission Planning and Sequence Team
- MRO:
-
Mars Reconnaissance Orbiter
- MWA:
-
Microwave Assembly
- NASA:
-
National Aeronautics and Space Administration
- ODP:
-
Orbit Determination Program
- OPR:
-
Orbital Period Reduction
- OSC:
-
Onboard Spacecraft Clocks
- OTM:
-
Orbit Trim Maneuver
- PDS:
-
Planetary Data System
- PM:
-
Primary Mission
- PPS:
-
Pulse Per Second
- RSB:
-
Radio Science Beacon
- RSR:
-
Radio Science Receiver
- SCT:
-
Spacecraft Team
- SDS:
-
Science Data System
- SIS:
-
Software Interface Specification
- SRIF:
-
Square Root Information Filter
- SRP:
-
Solar Radiation Pressure
- TAI:
-
International Atomic Time
- TCM:
-
Trajectory Correction Maneuver
- TDB:
-
Barycentric Dynamic Time
- TDS:
-
Telemetry Delivery System
- TDT:
-
Terrestrial Dynamic Time
- TLC:
-
Trans-Lunar Cruise
- TSF:
-
Transition to Science Formation
- TSM:
-
Transition to Science Maneuver
- TTS:
-
Time Transfer System
- USO:
-
Ultra-stable Oscillator
- UTC:
-
Universal Time Coordinated
- VLBI:
-
Very Long Baseline Interferometry
References
S. Aoki, H. Kinoshita, Note on the relation between the equinox and Guinot’s non-rotating origin. Celest. Mech. 29, 335–360 (1983)
S. Aoki, B. Guinot, G.K. Kaplan, H. Kinoshita, D. McCarthy, P.K. Seidelmann, The new definition of universal time. Astron. Astrophys. 105, 359–361 (1982)
D.F. Argus, R.G. Gordon, No-net-rotation model of current plate velocities incorporating plate motion model NUVEL-1. Geophys. Res. Lett. 18, 2039–2042 (1991)
S.W. Asmar, Radio as a science tool. Proc. IEEE 98, 10 (2010)
S.W. Asmar, J.W. Armstrong, L. Iess, P. Tortora, Spacecraft Doppler tracking: noise budget and achievable accuracy in precision radio science observations. Radio Sci. 40 (2005). doi:10.1029/2004RS003101
J.G. Beerer, G.G. Havens, Operation the dual-orbiter GRAIL mission to measure the Moon’s gravity, in SpaceOps 2012 Conference, Stockholm, Sweden, June 2012
C. Boucher, Z. Altamimi, L. Duhem, Results and analysis of the ITRF93. IERS Technical Note, 18, Observatoire de Paris, 1994
C. Dunn, W. Bertiger, Y. Bar-Sever, S. Desai, B. Haines, D. Kuang, G. Franklin, I. Harris, G. Kruizinga, T. Meehan, S. Nandi, D. Nguyen, T. Rogstad, J.B. Thomas, J. Tien, L. Romans, M. Watkins, S.C. Wu, S. Bettadpur, J. Kim, Instrument of GRACE: GPS augments gravity measurements. GPS World 14, 16–28 (2003)
E.G. Fahnestock, Comprehensive gravity and dynamics model determination of binary asteroid systems, in American Astronomical Society, DPS Meeting 41, #50.11 (2009)
E.G. Fahnestock, R.S. Park, D.-N. Yuan, A.S. Konopliv, Spacecraft thermal and optical modeling impacts on estimation of the GRAIL lunar gravity field, in AIAA/AAS Astrodynamics Specialist Conference, Minneapolis, MN, AIAA, August 13–16, 2012, pp. 2012–4428
R. Floberhagen, P. Visser, F. Weischede, Lunar albedo forces modeling and its effect on low lunar orbit and gravity field determination. Adv. Space Res. 23, 378–733 (1999)
W.M. Folkner, DSN station locations and uncertainties. JPL TDA Progress Report, 42-128, 1-34, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, 1996
W.M. Folkner, J.A. Steppe, S.H. Oliveau, Earth orientation parameter file description and usage. Interoffice Memorandum 335.1-11-93 (internal document), Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, 1993
J. Guinn, P. Wolff, TOPEX/Poseidon operational orbit determination results using global positioning satellites, in AAS/AIAA Astrodynamics Specialists Conference (1993). AAS-93-573
S. Hatch, R. Roncoli, T. Sweetser, GRAIL trajectory design: lunar orbit insertion through science, in AIAA Guidance, Navigation, and Control Conference, Toronto, Ontario, Canada, August 2010. AIAA 2010-8385
W.A. Heiskanen, H. Moritz, Physical geodesy. Bull. Géod. 86(1), 491–492 (1967)
T.L. Hoffman, GRAIL: gravity mapping the Moon, in Aerospace Conference, 2009 IEEE, Big Sky, MT, 7–14 March 2009. ISBN 978-1-4244-2622-5
W.M. Kaula, Theory of Satellite Geodesy (Blaisdell, Waltham, 1966). 124 pp.
J. Kim, Simulation study of a low-low satellite-to-satellite tracking mission. Ph.D. dissertation, Univ. of Texas at Austin, May 2000
J. Kim, B. Tapley, Error analysis of a low-low satellite-to-satellite tracking mission. J. Guid. Control Dyn. 25(6), 1100–1106 (2002)
W.M. Klipstein, B.W. Arnold, D.G. Enzer, A.A. Ruiz, J.Y. Yien, R.T. Wang, C.E. Dunn, The lunar gravity ranging system for the gravity recovery and interior laboratory (GRAIL) mission. Space Sci. Rev. (2013, this issue)
A.S. Konopliv, S.W. Asmar, E. Carranza, D.N. Yuan, W.L. Sjogren, Recent gravity models as a result of the lunar prospector mission. Icarus 150, 1–18 (2001)
F.T. Krogh, Changing stepsize in the integration of differential equations using modified divided differences. JPL Tech. Mem. No. 312, Section 914 (internal document), Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, 1973
C.L. Lawson, R.J. Hanson, Solving Least Squares Problems. SIAM Classics in Applied Mathematics, vol. 15 (Society for Industrial and Applied Mathematics, Philadelphia, 1995)
R. Leavitt, A. Salama, Design and implementation of software algorithms for TOPEX/POSEIDON ephemeris representation, in AIAA/AAS Astrodynamics Specialists Conference (1993). AAS-93-724
J.H. Lieske, T. Lederle, W. Fricke, B. Morando, Expressions for the precession quantities based upon the IAU (1976) system of astronomical constants. Astron. Astrophys. 58, 1–16 (1977)
A.J. Mannucci, B.D. Wilson, D.-N. Yuan, C.H. Ho, U.J. Lindqwister, T.F. Runge, A global mapping technique for GPS-derived ionospheric total electron content measurements. Radio Sci. 33(3), 565–582 (1998)
D.D. McCarthy, G. Petit (eds.), IERS Conventions, IERS Technical Note, vol. 32 (2003)
T.D. Moyer, Formulation for Observed and Computed Values of Deep Space Network Data Types for Navigation (Wiley, Hoboken, 2003). 576 pp.
X.X. Newhall, J.G. Williams, Estimation of the lunar physical librations. Celest. Mech. Dyn. Astron. 66, 21–30 (1997)
R.S. Park, S.W. Asmar, E.G. Fahnestock, A.S. Konopliv, W. Lu, M.M. Watkins, Gravity recovery and interior laboratory simulations of static and temporal gravity field. J. Spacecr. Rockets 49, 390–400 (2012)
S. Pines, Uniform representation of the gravitational potential and its derivatives. AIAA J. 11, 1508–1511 (1973)
R. Roncoli, K. Fujii, Mission design overview for the gravity recovery and interior laboratory (GRAIL) mission, in AIAA Guidance, Navigation, and Control Conference, Toronto, Ontario, Canada, August 2010. AIAA 2010-8383
P.K. Seidelmann, 1980 IAU theory of nutation: the final report of the IAU working group on nutation. Celest. Mech. 27, 79–106 (1982)
B.D. Tapley, B. Schutz, G. Born, Statistical Orbit Determination (Elsevier, Boston, 2004a). 547 pp.
B.D. Tapley, S. Bettadpur, M. Watkins, C. Reigber, The gravity recovery and climate experiment: mission overview and early results. Geophys. Res. Lett. 31 (2004b). doi:10.1029/2004GL019920
B.J. Thomas, An analysis of gravity-field estimation based on intersatellite dual-1-way biased ranging. JPL Publication 98–15, May 1999
S.G. Turyshev, V.T. Toth, M.V. Sazhin, General relativistic observables of the GRAIL mission. Phys. Rev. D 87, 024020 (2013)
J.M. Wahr, The forced nutations of an elliptical, rotating, elastic, and oceanless Earth. Geophys. J. R. Astron. Soc. 64, 705–727 (1981)
R.C. Weber, P.-Y. Lin, E.J. Garnero, Q. Williams, P. Lognonne, Seismic detection of the lunar core. Science 331, 309–313 (2011). doi:10.1126/science.1199375
J.G. Williams, A scheme for lunar inner core detection. Geophys. Res. Lett. 34, L03202 (2007). doi:10.1029/2006GL028185
J.G. Williams, D.H. Boggs, W.M. Folkner, DE421 lunar orbit, physical librations, and surface coordinates. JPL IOM 335-JW, DB, WF-20080314-001, March 14, 2008
D.-N. Yuan, W. Sjogren, A. Konopliv, A. Kucinskas, Gravity field of mars: a 75th degree and order model. J. Geophys. Res. 106(E10), 23377–23401 (2001)
M.T. Zuber, D.E. Smith, D.H. Lehman, T.L. Hoffman, S.W. Asmar, M.M. Watkins, Gravity recovery and interior laboratory (GRAIL): mapping the lunar interior from crust to core. Space Sci. Rev. (2013, this issue). doi:10.1007/s11214-012-9952-7
Acknowledgements
The GRAIL mission is supported by the NASA Discovery Program under contracts to the Massachusetts Institute of Technology and the Jet Propulsion Laboratory. The work described in this paper was mostly carried out at Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. The authors thank colleagues who have contributed to this work or reviewed it, especially at JPL: Duncan McPherson, Ralph Roncoli, William Folkner, Kevin Barltrop, Charles Dunn, William Klipstein, Randy Dodge, William Bertch, Daniel Klein, Dong Shin, Stefan Esterhausin, Slava Turyshev, Tom Hoffman, Charles Bell, Hoppy Price, Neil Dahya, Joseph Beerer, Glen Havens, Robert Gounley, Ruth Fragoso, Susan Kurtik, Behzad Raofi, and Dolan Highsmith. From Lockheed Martin Space Systems Company (Denver): Stu Spath, Tim Linn, Ryan Olds, Dave Eckart, and Brad Haack, Kevin Johnson, Carey Parish, Chris May, Rob Chambers, Kristian Waldorff, Josh Wood, Piet Kallemeyn, Angus McMechan, Cavan Cuddy, and Steve Odiorne. From the NASA Goddard Space Flight Center: Frank Lemoine and David Rowlands, and from the University of Texas: Byron Tapley and Srinivas Bettadpur.
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Asmar, S.W., Konopliv, A.S., Watkins, M.M. et al. The Scientific Measurement System of the Gravity Recovery and Interior Laboratory (GRAIL) Mission. Space Sci Rev 178, 25–55 (2013). https://doi.org/10.1007/s11214-013-9962-0
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DOI: https://doi.org/10.1007/s11214-013-9962-0