Mascon gravitation model using a shaped polyhedral source

Abstract

In the last two decades, new computational tools have been developed in order to aid space missions to orbit around irregular small bodies. One of the techniques consists in rebuilding their shape in tetrahedral polyhedron. This method is well suited to determine the shape and estimate certain physical features of asteroids. However, a large computational effort is necessary depending on the quantity of triangular faces chosen. Another method is based on a representation of the central body in terms of mascons (discrete spherical masses). The main advantage of the method is its simplicity which makes the calculation faster. Nevertheless, the errors are non-negligible when the attraction expressions are calculated near the surface of the body. In this work, we carry out a study to develop a new code that determines the centre of mass of each tetrahedron of a shaped polyhedral source and evaluates the gravitational potential function and its first- and second-order derivatives. We performed a series of tests and compared the results with the classical polyhedron method. We found good agreement between our determination of the attraction expressions close to the surface, and the same determination by the classical polyhedron method. However, this agreement does not occur inside the body. Our model appears to be more accurate in representing the potential very close to the body's surface when we divide the tetrahedron in three parts. Finally, we have found that in terms of CPU time requirements, the execution of our code is much faster compared with the polyhedron method.