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The wedge-pentahedra method (WPM): Topographic reduction of local terrain in the context of solar system surface gravimetry and robotic exploration

In classical gravimetry, different corrections are applied, e.g. to correct for the measurement elevation above a reference plane and the gravitational attraction of the material lying between the measurement point and reference plane. Additionally, and especially in non-flat regions, a correction for the topography is generally needed. While this contribution is relatively small on spherical celestial objects, it can be more important for irregularly shaped bodies, such as small bodies or some natural satellites. With the surface gravity being much smaller, the relative importance of the topographic correction increases, while the approximation errors of the surface will become larger. In this work, the novel Wedge-Pentahedra Method (WPM) for topographic correction for (near-) surface gravimetric measurements and simulations is presented that allows precise topographic corrections for asteroids and natural satellites. For a first study, the WPM is applied to the Martian moon Phobos. Taking an exemplary surface location, a high-resolution artificial terrain is added to the surrounding, and the gravitational influence of this topography compared to the original surface is assessed. It is found that the influence of topography on the surface gravity of a small body such as Phobos can be in the order of a few percent, making it an important correction not only for surface gravity science, but likewise for landing and surface operations, to best ensure the mission success. Therefore, the here presented WPM opens a manifold of possible future applications in the context of Solar System exploration, regarding both space science and space technology.