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T LATEST DEVELOPMENTS IN LUNAR GRAVITY FIELD RECOVERY

WITHIN THE PROJECT GRAZIL

S. Krauss1, H. Wirnsberger1, B. Klinger2, T. Mayr-Gürr2, O. Baur1,3

1Space Research Institute/ÖAW, Austria; 2Institute of Geodesy/TU Graz, Austria; 3 now at Airbus Defense and Space GmbH, Germany

The project GRAZIL addresses the highly accurate recovery of thelunar gravity field using inter-satellite Ka-band ranging (KBR)measurements collected by Gravity Recovery And InteriorLaboratory (GRAIL) mission. Dynamic precise orbit determinationis an indispensable task in order to recover the lunar gravity field.The concept of variational equations is adopted to determine theorbit of the two GRAIL satellites. As far as lunar gravity fieldrecovery is concerned, we apply an integral equation approachusing short orbital arcs. We present the latest developmentswithin the project GRAZIL. Results are validated against GRAILproducts released by other institutions.

RESULTS AND MODEL EVALUATION

External solutions

• JPL lunar gravity field model (GL660B)

• NASA-GSFC lunar gravity field model (GRGM660PRIM)

• AIUB lunar gravity field model (AIUB-GRL200b)

Validation types

• Free-air gravity anomalies

REFERENCES

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METHODS OVERVIEW

Orbit determination (OD) of GRAIL-A and GRAIL-B

• Based on variational equations

• Consistent force modeling

• DSN radio science data (S-band, X-band)

• Allows for a fully independent solution

Gravity filed recovery (GFR)

• Based on short-arc approach [7]

• Ka-band ranging data (primary mission)

• Heritage of the gravity field mission GRACE

To avoid spectral aliasing, short wavelength signals are reduced from the KBR data using the GL0660B lunar gravity model

Lunar gravity field recovery is a huge computational challenge

High performance computer clustering at the IWF

• 32 independent computer nodes (40 cores each)

• 128 GB RAM per node (4 TB in total)

ORBIT CHARACTERISTICS

Altitude

• ~55 km (± 35km)

Inclination

• 89.9° (w.r.t. lunar equator)

Revolution period

• 113 minutes

Separation distance

• 82-218 km

FORCE MODEL AND PARAMETRIZATION

NON CONSERVATIVE FORCE MODEL

Satellite plate macro model [2]

Modeled accelerations acting on GRAIL-A between low andhigh solar angle phase

Force modeling

• 3rd body accelerations

• Solid Moon tides

• Relativistic accelerations

• Solar radiation pressure

• Albedo

• Emissivity

Arc-length

• OD: 1.25 days

• GFR: 70 minutes

Satellite design

• 28-plate macro model

Empirical parameters

• 4x / rev. (along, cross)

Time bias

ORBIT RESIDUALS

Level1b position and velocity used as pseudo-observations

Implementation of DSN Doppler tracking data is presentlyunder development

Macro model not applied, scale factor estimated

GRAIL-A orbit residuals to Level1b data (GNI1b release04)

RMS values of post-fit residuals show the importanceof appropriate non conservative force modeling

• Degree variances

Orbital altitude (left) and separation distance (right) betweenthe GRAIL satellites during the primary mission phase.

GrazLGM300c GL0660B - GrazLGM300c

[mGal] [mGal]

(1) Arnold, D., et al., 2015: Icarus, 261, 182-192.(2) Fahnestock, E.G., 2012: AIAA/AAS, Astrodyn. Specialist Conference.(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) Krauss, S. et al., 2015: VGI Special Report, 103, 156-161.(6) Lemoine, F.G. et al., 2014: J. Geophys. Res. (Planets), 118, 1676-1698.(7) Mayer-Gürr, T., 2006: PhD Thesis, University of Bonn.

We acknowledge the financial support for the project GRAZILby the Austrian Research Promotion Agency (FFG).