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T FIRST INDEPENDENT LUNAR GRAVITY FIELD SOLUTION IN THE

FRAMEWORK OF PROJECT GRAZIL

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FRAMEWORK OF PROJECT GRAZIL

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Harald Wirnsberger1, Sandro Krauss1, Beate Klinger2, Torsten Mayer-Gürr2

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1Space Research Institute, Austrian Academy of Sciences; 2Institute of Geodesy, Graz University of Technology

The twin satellite mission Gravity Recovery and Interior Laboratory (GRAIL) aims to recovering the lunar gravity field by means of intersatellite Ka-bandranging (KBR) observations. In order to exploit the potential of KBR data, absolute position information of the two probes is required. Hitherto, the Grazranging (KBR) observations. In order to exploit the potential of KBR data, absolute position information of the two probes is required. Hitherto, the Grazlunar gravity field models (GrazLGM) relies on the official orbit products provided by NASA. In this contribution, we present for the first time a completelyindependent Graz lunar gravity field model to spherical harmonic degree and order 420. The reduced dynamic orbits of the two probes are determinedindependent Graz lunar gravity field model to spherical harmonic degree and order 420. The reduced dynamic orbits of the two probes are determinedusing variational equations following a batch least squares differential adjustment process. These orbits are based on S-band radiometric tracking datacollected by the Deep Space Network (DSN) and are used for the independent GRAIL gravity field recovery. To reveal a highly accurate lunar gravity field,collected by the Deep Space Network (DSN) and are used for the independent GRAIL gravity field recovery. To reveal a highly accurate lunar gravity field,an integral equation approach using short orbital arcs is adopted to process the KBR data. A comparison to state-of-the-art lunar gravity models computedat NASA-GSFC, NASA-JPL and AIUB demonstrate the progress of Graz lunar gravity field models derived within the project GRAZIL.at NASA-GSFC, NASA-JPL and AIUB demonstrate the progress of Graz lunar gravity field models derived within the project GRAZIL.

RESULTS AND MODEL EVALUATIONORBIT DETERMINATION (POD) GRAVITY FIELD RECOVERY (GFR) RESULTS AND MODEL EVALUATION� External solutions exploiting GRAIL data:

ORBIT DETERMINATION (POD) � Allows for a fully independent solution

GRAVITY FIELD RECOVERY (GFR)� requires absolute position of GRAIL-A (Ebb) and GRAIL-B (Flow)

NASA-GSFC: GRGM660PM [5]� POD based on variational equations

� Batch least squares differential corrector (IWF software)

� GFR based on short-arc integral equation approach

� Processing strategy inherited from GRACE (TUG software)

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NASA-JPL: GL0420A [4]GL0660B [4]

� Batch least squares differential corrector (IWF software)

� DSN two-way radiometric tracking data in S-Band

� Processing strategy inherited from GRACE (TUG software)

� Inter-satellite ranging data in Ka-Band (KBR)

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GL0660B [4]

AIUB: GRL200A [1]

� DSN two-way radiometric tracking data in S-Band � Inter-satellite ranging data in Ka-Band (KBR)

Iterative procedure POD - GFR:Comparison to official orbit product GNI1B (includes KBR data)AIUB: GRL200A [1]

GRL200B [1]Iterative procedure POD - GFR:

a-priori Model SGM150J [2]

Comparison to official orbit product GNI1B (includes KBR data)exemplary shown for Ebb:

Signal: GRGM660PM (US)a-priori Model SGM150J [2]

POD – S2 Release

Model – d/o = 200

Signal: GRGM660PM (US)

GL0660B (US)Model – d/o = 200

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GL0420A (US)200300300

SGM150J (JAP)

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POD L3-1 420iterative procedure leads to differences in the range of 10 m:

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POD L3-1 420

420 POD L5

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420 POD L5

POD N5 420GrazLGM200a [3]

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420 POD N6

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Post-fit residuals of DSN two-way tracking data:

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Post-fit residuals of DSN two-way tracking data:Free air gravity anomalies near side (left) and far side (right):

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GrazLGM420a � GrazLGM420a: Completely independent solution up to d/o 420

� GrazLGM420a+: GL0660B as background model for d/o > 420

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� GrazLGM420a+: GL0660B as background model for d/o > 420

REFERENCES[1] Arnold, D., et al., 2015: Icarus, 261, 182-192. G

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Residual RMS of last iteration is around 1.8mHz during PM phase: [1] Arnold, D., et al., 2015: Icarus, 261, 182-192.[2] Gossens, S., et al., 2011: J. Geod., 85, 487-504.[3] Klinger, B. et al., 2014: Planet. Space Sci., 91, 83-90.

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Residual RMS of last iteration is around 1.8mHz during PM phase:

[3] Klinger, B. et al., 2014: Planet. Space Sci., 91, 83-90.[4] Konopliv, A.S. et al., 2014: Geophys. Res. Lett., 41, 1452-1458.[5] Lemoine, F.G. et al., 2014: J. Geophys. Res. (Planets), 118, 1676-1698. IW

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[5] Lemoine, F.G. et al., 2014: J. Geophys. Res. (Planets), 118, 1676-1698. IWF

We acknowledge the financial support by the Austrian Research We acknowledge the financial support by the Austrian Research Promotion Agency (FFG) for funding the project GRAZIL.