Geodesy and Cartography of Phobos
Final Report Abstract
Mars is accompanied by two small natural satellites. Deimos, the smaller of the two, is orbiting at a greater distance from Mars while Phobos revolves around the planet at a mean altitude of approximately 6,000km with respect to the Martian surface and thus deep in the gravity field of Mars. An in-depth study of the irregular shaped moon Phobos was commenced due to remaining questions on its orbital motion, shape, and physical parameters based on new high resolution images of the Super Resolution Channel (SRC) and the High Resolution Stereo Camera (HRSC) which are part of the European Mars Express Mission (MEX). Parameters of ephemerides models were questioned after the finding of large discrepancies of Phobos' position to astrometric observations. During the course of this study astrometric measurements were made in flyby images of Phobos and through observations of Phobos' shadow on the Martian surface. While results of the latter analysis led to largely scattered differences compared to orbit prediction models with high uncertainties, the flyby observations were in agreement with the ephemerides models within the error bands. Offsets were consistent and systematic indicating that Phobos is ahead of its predicted position by approximately 2 km. As a basis for Phobos shape model representations, a new global control point network was established. The 665 object point coordinates with respect to the Phobos body-fixed coordinate frame were determined through observations in 53 SRC and 16 Viking Orbiter images. Coordinates of the object points were computed by means of a least-squares bundle block adjustment. The overall accuracy was estimated to be in the order of ±18 m. The control network proved to be a valuable tool to observe the forced libration amplitude – a superimposed oscillation on the rotation of Phobos due to interactions between the irregularly shaped Phobos and the gravity field of Mars. A global digital terrain model (DTM), which is based on stereo images of the HRSC and Viking Orbiter images, was computed and was used to ortho-rectify SRC and Viking images. Based on the ortho-rectified images an accurate map of Phobos was prepared. Since the DTM representation of Phobos' shape is rather inefficient to obtain physical parameters, the coefficients of the surface spherical harmonic function to degree and order 17 were determined through the control point coordinates. The analytical expression for Phobos was used to re-estimate the volume, bulk density of Phobos and the moment of inertia tensor. A volume of 5689 km3 and a corresponding bulk density of 1.85 g/cm3 were determined with a significantly improved accuracy and being in good agreement with previous estimations of these values. The moments of inertia were primarily computed assuming a homogeneous mass distribution within Phobos. The principle moments of inertia can be put in relation to the forced libration amplitude. The modeled forced libration amplitude agrees well with the observed value within its error bands. Applying simple two layer mass distribution models, exact agreement between observation and model of the forced libration amplitude could only be achieved assuming extreme model parameters. This suggests a more complex mass distribution within Phobos. In October 2008, DLR, ESA, and FU-Berlin released results of the shape modelling and cartographic processing to the press. The press release can be found under http://www.dlr.de/en/desktopdefault.aspx/tabid-3432/7418_read-13776/7418_page-3/
Publications
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"Position measurements of Phobos shadows in HRSC and MOC images and implications for the Phobos orbit",'First European Planetary Science Conference', 2006
Willner, K., Bendig, J., Oberst, J., Wählisch, M., Matz, K.-D. and Roatsch, T.
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"A new astrometric measurement technique for Phobos using background stars and surface control points", ISPRS WG IV/7: Extraterrestrial Mapping Workshop - Advances in Planetary Mapping 2007 , in IV/7, I. W., ed.,'Extraterrestrial Mapping Workshop Advances in Planetary Mapping 2007', 2007
Willner, K., Oberst, J., Matz, K.-D., Roatsch, T. and Hoffmann, H.
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"Observations of Phobos' Orbit and Rotation Using Images of SRC on Mars Express", European Mars Science & Exploration Conference: Mars Express and ExoMars Abstract Book, 'European Mars Science and Exploration Conference: Mars Express & ExoMars', European Space Agency, European Space and Technology Centre (ESTEC), 2007, pp. 139 - 139
Willner, K., Oberst, J., Matz, K.-D., Wählisch, M., Giese, B., Roatsch, T., Hoffmann, H. and Neukum, G.
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"Ongoing Observations of Phobos and Deimos by the HRSC Experiment on Mars Express", Proceedings of the conference held November 5- 8, 2007 in Moffett Field, California (1377),'First International Conference on the Exploration of Phobos and Deimos', 2007, pp. 20 - 20
Hoffmann, H., Willner, K., Oberst, J., Giese, B., Gwinner, K., Matz, K.-D., Roatsch, T., Jaumann, R., Duxbury, T. C. and Neukum, G.
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"Validation of the Phobos Orbit and Control Point Network with HRSC and SRC on Mars Express", XXIII International Cartographic Conference, 'XXIII International Cartographic Conference', 2007, pp. CD-ROM
Willner, K., Oberst, J., Wählisch, M., Matz, K.-D., Roatsch, T. and Bendig, J.
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"Validation of the Phobos orbit with HRSC and SRC on Mars Express", '71. Jahrestagung der Deutschen Physikalischen Gesellschaft und DPG Frühjahrstagung des Arbeitskreises Festkörperphysik', 2007
Willner, K., Oberst, J., Wählisch, M., Matz, K.-D. and Roatsch, T.
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Observations of Phobos and its shadow: Implications for the Phobos orbit", 'SPP 1115 Colloquium 2007 (4. Colloquium)', 2007
Willner, K., Oberst, J., Wählisch, M., Matz, K.-D. and Roatsch, T.
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"New astrometric observations of Phobos with the SRC on Mars Express", Astronomy and Astrophysics (:488), 2008, pp. 361 - 364
Willner, K., Oberst, J., Wählisch, M., Matz, K.-D., Hoffmann, H., Roatsch, T., Jaumann, R. and Mertens, V.
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"Observations of Phobos by the HRSC on Mars Express", 1st International Conference IAA-RACT "Space for Humanity", '1st International Conference IAA-RACT', 2008
Willner, K., Oberst, J., Wählisch, M., Hoffmann, H., Matz, K.-D., Roatsch, T., Jaumann, R., Duxbury, T. and Neukum, G.
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"Observations of Phobos' Orbit, Rotation and Shape Using SRC on Mars Express and Viking Orbiter Images",'SPP 1115 Colloquium 2008 (5. Colloquium)', 2008
Willner, K., Oberst, J., Giese, B., Matz, K.-D., Wählisch, M., Roatsch, T. and Hoffmann, H.
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"Studies of Phobos' orbit, rotation, and shape using Spacecraft image data", Proceedings ISPRS 2008 Beijing XXXVII(Part B4),'ISPRS 2008 Beijing', The International Archives of the Photogrammetry, 2008, pp. 981 - 986
Willner, K., Oberst, J., Giese, B., Wählisch, M., Matz, K.-D., Roatsch, T. and Hoffmann, H.
