Skip to main content
Log in

The Scientific Measurement System of the Gravity Recovery and Interior Laboratory (GRAIL) Mission

  • Published:
Space Science Reviews Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

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)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • 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)

    ADS  Google Scholar 

  • 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)

    Article  ADS  Google Scholar 

  • S.W. Asmar, Radio as a science tool. Proc. IEEE 98, 10 (2010)

    Article  Google Scholar 

  • 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

    Google Scholar 

  • 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)

    Google Scholar 

  • E.G. Fahnestock, Comprehensive gravity and dynamics model determination of binary asteroid systems, in American Astronomical Society, DPS Meeting 41, #50.11 (2009)

    Google Scholar 

  • 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

    Google Scholar 

  • 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)

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • W.A. Heiskanen, H. Moritz, Physical geodesy. Bull. Géod. 86(1), 491–492 (1967)

    Article  Google Scholar 

  • 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

    Google Scholar 

  • W.M. Kaula, Theory of Satellite Geodesy (Blaisdell, Waltham, 1966). 124 pp.

    Google Scholar 

  • 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)

    Article  ADS  Google Scholar 

  • 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)

    Article  ADS  Google Scholar 

  • 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)

    Book  MATH  Google Scholar 

  • 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

    Google Scholar 

  • 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)

    ADS  Google Scholar 

  • 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)

    Article  ADS  Google Scholar 

  • D.D. McCarthy, G. Petit (eds.), IERS Conventions, IERS Technical Note, vol. 32 (2003)

    Google Scholar 

  • T.D. Moyer, Formulation for Observed and Computed Values of Deep Space Network Data Types for Navigation (Wiley, Hoboken, 2003). 576 pp.

    Book  Google Scholar 

  • X.X. Newhall, J.G. Williams, Estimation of the lunar physical librations. Celest. Mech. Dyn. Astron. 66, 21–30 (1997)

    Article  ADS  Google Scholar 

  • 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)

    Article  ADS  Google Scholar 

  • S. Pines, Uniform representation of the gravitational potential and its derivatives. AIAA J. 11, 1508–1511 (1973)

    Article  ADS  MATH  Google Scholar 

  • 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

    Google Scholar 

  • P.K. Seidelmann, 1980 IAU theory of nutation: the final report of the IAU working group on nutation. Celest. Mech. 27, 79–106 (1982)

    Article  MathSciNet  ADS  Google Scholar 

  • B.D. Tapley, B. Schutz, G. Born, Statistical Orbit Determination (Elsevier, Boston, 2004a). 547 pp.

    Google Scholar 

  • 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)

    Article  ADS  Google Scholar 

  • J.M. Wahr, The forced nutations of an elliptical, rotating, elastic, and oceanless Earth. Geophys. J. R. Astron. Soc. 64, 705–727 (1981)

    Article  ADS  MATH  Google Scholar 

  • 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

    Article  ADS  Google Scholar 

  • J.G. Williams, A scheme for lunar inner core detection. Geophys. Res. Lett. 34, L03202 (2007). doi:10.1029/2006GL028185

    Article  ADS  Google Scholar 

  • 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)

    Article  ADS  Google Scholar 

  • 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

Download references

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.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Sami W. Asmar.

Rights and permissions

Reprints and permissions

About this article

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11214-013-9962-0

Keywords

Navigation