The Martian Moon Phobos – A Geodetic Analysis of its Motion, Orientation, Shape and Physical Parameters

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, deep in the gravity field of the planet. 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 fly-by 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 fly-by observations were in agreement with the ephemerides models within the error bands. Offsets were rather consistent and systematic indicating that Phobos is ahead of its predicted position by approximately 2 km. To be able to model the irregular shape of Phobos by means of different techniques - namely a digital terrain model and a model based on spherical harmonic functions - 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 +/-17 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 coeffcients 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 5689km³ and a corresponding bulk density of 1.85 g/cm³ were determined. The results were in good agreement, but signiffcantly improved accuracy compared to previous estimates 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 bounds. 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.