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STUDIES OF PHOBOS’ ORBIT, ROTATION, AND SHAPE USING SPACECRAFT 
IMAGE DATA 
K. Willner, J. Oberst, B. Giese, M. Wâhlisch, K-D. Matz, T. Roatsch, H. Hoffmann 
German Aerospace Center 
Institute of Planetary Research, Planetary Geodesy 
Runtherfordstr. 2, 12489 Berlin, Germany 
- konrad.willner@dlr.de 
http://www.dlr.de/pf 
Commission IV, WG IV/7 
KEY WORDS: Phobos, Control Point Network, Shape, Orbit Model, Astrometric Observations 
ABSTRACT: 
Images obtained by the High Resolution Stereo Camera (HRSC) and the Super Resolution Channel (SRC) on the European Mars 
Express (MEX) spacecraft have renewed the interest in Phobos, the larger of the two Martian satellites. We are involved in a 
comprehensive study in geodesy and cartography of this small irregular (13.4 x 11.2 x 9.2 km) satellite. We focus on astrometric 
measurements to refine and validate the current Phobos orbit models, on an update of the Phobos control point network to study 
rotational and global shape parameters, and a global Digital Terrain Model in high resolution. 
1. INTRODUCTION 
In 1877 Asaph Hall, an astronomer at the United States Naval 
Observatory, discovered the Martian moons Phobos and 
Deimos. Phobos, the larger of the two moons, is orbiting with a 
mean distance of 9375 km to the center of Mars, deep in the 
gravitational field of the planet. Hence, Phobos’ long term 
orbital evolution may reveal constraints on the elastic properties 
of the Martian interior. Up to the current date Phobos’ orbit is 
being studied by means of ground-based observations during 
Mars oppositions on a several kilometers accuracy level 
(Morley, 1989, Veiga, submitted). Mariner 9 obtained the first 
spacecraft images of Phobos, which were used to determine 
Phobos’ position with an accuracy of 3 to 10 km (Duxbury and 
Callahan, 1989a). Further observations by the Viking orbiters 
led to similar accuracies for positional observations (Duxbury 
and Callahan, 1988) as well as to a control point network 
(Duxbury and Callahan, 1989b) and shape and surface models 
(Duxbury, 1991). In 1989, the Russian Phobos 2 Mission made 
37 positional observations of Phobos with an estimated 
accuracy of 2 km (Kolyuka et al., 1991). A decade later, MGS 
(Mars Global Surveyor) revisited Phobos. MOLA (Mars Orbiter 
Laser Altimeter) range measurements to Phobos (Banerdt and 
Neumann, 1999) and positional observations of Phobos’ 
shadow (Neumann et al., 2004) were carried out. With the 
observation of Phobos eclipse events from the Mars Exploration 
Rovers, discrepancies of 12 km to the orbit prediction models 
were reported (Bell et al., 2005). These discrepancies were later 
confirmed by a number of flyby observations obtained by the 
SRC on Mars Express (MEX) (Oberst et al., 2006). Motivated 
by the large number of new observations and the uncertainties 
of orbit data, JPL (Jacobson and Rush, 2006) and ROB (Lainey 
et al., 2007) released new orbit models. Studying the geodesy 
and cartography of Phobos we validated available orbit 
prediction models by means of comparison with new SRC flyby 
observations. Furthermore an independent and global control 
point network was determined on the basis of SRC and Viking 
Orbiter image data. The control point network is used to study 
rotational parameters of Phobos and will be used to derive 
physical parameters such as volume and bulk density of Phobos. 
2. MARS EXPRESS PHOBOS FLYBYS AND SRC 
IMAGING 
Mars Express is orbiting Mars in a highly elliptical nearly polar 
orbit. With an apoapsis of near 10,000 km, the orbit is reaching 
well beyond the nearly circular and equatorial Phobos orbit 
with a mean radius of 9375 km. As the orbit periods of MEX 
and Phobos are similar, there are usually epochs of close 
Phobos encounters in consecutive flybys followed by periods 
with no close Phobos approaches (Oberst et al., 2008). The SRC 
is used to obtain high resolution images of Phobos during close 
flyby encounters. Owing to its large focal length of 988.5 mm, 
images resolve with 10 m/pxl at a distance of 1000 km. Until 
April 2008 a total of 92 successful flyby maneuvers were 
performed, from which image data were returned. The mean 
flyby distance of orbits where useful SRC images were obtained 
is at about 2000 km (with a minimum range to Phobos of 590 
km and a maximum range of 11,000 km). Hence, image 
resolutions vary between 5 m/pxl and 100 m/pxl but are mainly 
better than 20 m/pxl (see Figures 1 and 2). For a detailed 
description of the camera and MEX orbital parameters see 
(Oberst et al., 2008) and (Jaumann et al., 2007), respectively. 
3. ORBIT VALIDATION 
3.1 Flyby sequences 
During a Phobos flyby, the camera systems are pointed at one 
fixed inertial point in the celestial sphere. The HRSC needs to 
operate at least one line sensor due to technical constraints but 
usually scans the sky for Phobos with several line sensors for 
stereo imaging. In addition, a sequence of 8 SRC images is 
obtained during one flyby. The first and the last SRC images of