Europlanet Science Congress 2021
Virtual meeting
13 – 24 September 2021
Europlanet Science Congress 2021
Virtual meeting
13 September – 24 September 2021
EPSC Abstracts
Vol. 15, EPSC2021-370, 2021
Europlanet Science Congress 2021
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.

Artificial terrain on Phobos: Assessing the influence on local gravity using the Wedge-Pentahedra Method

Matthias Noeker1,2, Özgür Karatekin1, Birgit Ritter1, and Elisa Tasev1
Matthias Noeker et al.
  • 1Royal Observatory of Belgium, Brussels, Belgium (
  • 2Université catholique de Louvain, Ottignies-Louvain-la-Neuve, Belgium


The origin and composition of the Martian moon Phobos is still subject to scientific discussions that are not yet free of doubt. Visiting the inner Martian moon with a spacecraft promises to provide more insights on these questions. One future mission to visit Phobos is the Japanese Martian Moon eXplorer (MMX) mission, e.g. [1]. Such a mission, including the free-fall landing of a rover and a touch-and-go sample acquisition manoeuvre, demands a good knowledge of the (local) gravity field. Moreover, a surface gravimeter GRASS [2], was considered in the early phase of the mission on the rover to investigate the local surroundings influence on the resulting gravity. We investigate the influence of a local, artificial, high-resolution digital elevation model (DEM), superimposed on the lower-resolution Phobos shape file on the local surface gravity. For this, we have developed the Wedge-Pentahedra Method that allows analysis of the local (surface) gravity.



For Small Solar System Bodies and natural, non-spherical satellites (hereafter: small bodies) we have, even if visited by spacecraft, only limited resolutions on the global shape files. The development of space exploratory gravimeter for small bodies GRASS [2], but also planned small body landings [1,3] and touch-and-go sample acquisition manoeuvres demand an analysis of the local terrain on the resulting (near-) surface gravity. Traditionally, the gravity of any polyhedron with (assumed) homogeneous density is computed using the polyhedral method (PM) by Werner & Scheeres [4]. This global approach makes it difficult to include a local (2D) DEM in the surrounding of the landing point and to vary the proximity material density. We developed the Wedge-Pentahedra Method (WPM) that allows to incorporate any DEM on a small body surface and to vary the density at a resolution identical to the DEM resolution.

In this study, we use the global shape file of Phobos from [5] and the artificial, scalable DEM for the MMX landing site kindly provided by [6]. We localise the problem by defining a (specific or random) landing point on the Phobian surface as shown in Figure 1. On this local, lower-resolution surface, we now project the high-resolution DEM, where the original elevation value is arbitrary and therefore scaled to control the DEM amplitude.

With the DEM in place, the WPM is implemented using the high-resolution surface. Firstly, a triangulation of the DEM surface is performed. Then, from each of these triangles, a wedge is created by projecting the triangle downwards to a defined elevation (Figure 2). The gravity of each wedge is then computed with the PM. The advantage here is that the density of each wedge can be varied and, moreso, the wedges can be dissected vertically allowing density variation in all dimensions, limited only by the DEM resolution. 

The influence of the DEM can now be found by comparing the gravity of the smooth (original) surface and the DEM surface. To avoid differences due to a different grid size, the smooth surface is in fact the DEM surface, but scaled by zero (Figure 3 (a) and (b), respectively). Generally, single features will be much larger than the average DEM topography, creating some unrealistically large features for larger scale factors. This can be solved with cutoff-constraints, as needed.