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.

Dynamics in the vicinity of (101955) Bennu: solar radiation pressure effects in equatorial orbits

“…In this work, we modeled the gravity field of the asteroid (101955) Bennu using the new approach of mascon gravitation, developed by Chanut et al (2015a), where the Mascon gravity framework (Geissler et al 1997) was applied using the shaped polyhedral source (Werner 1994). We tested this model analysing the equilibria near (101955) Bennu when the solar radiation pressure is not accounted for.…”

“…However, recently Wang et al (2016) have shown that within the limits of density and rotation defined by Chesley et al (2014), the centre points can become linearly stable by changing the topological structure from case 5 to case 1 ). In Aljbaae et al (2017), we presented the corrected form of the second order derivatives of Chanut et al (2015a). We solved the linearized state equations in the neighbourhood of the equilibrium points ), and we show the unnormalized eigenvalues and their stability type in Table 5.…”

“…Other factors, such as the solar radiation pressure, can make periodic motions about those equilibrium points to be unstable (Xin et al 2016), but this point will not be investigated in the paper. Another important point is that the running time shown in Table 6 indicated that the classical polyhedron model of gravitation is not very well suited for the division into several different density layers, while the Mascon mathematical model described in Chanut et al (2015a) seems more appliable for this purpose. Unlike the tsoulis method, in the mascon model case, the calculations are done only one time for the total potential, independently of each layer density.…”

“…In this section, we numerically test and analyse the evolution of the dynamics of equatorial, direct orbits, considering the 3-D gravitational perturbation and the solar radiation pressure (SRP) close to the asteroid (101955) Bennu. As done in the previous section, we choose the Mascon gravity tensor implemented by Chanut et al (2015a), with each tetrahedron divided into ten equal thickness layers (Mascon 10). The path of the spacecraft is calculated using the equations of motion (Eqs.…”

“…Representation of a tetrahedron with vertex 0 at the origin and the vectors u, v and w coming out from this vertex(Chanut et al 2015a). …”