A comparative study of gravitational field modeling for 101955 Bennu

The poster presents the modeling of the gravitational field of the near-earth asteroid 101955 Bennu using two spectral-domain methods based on spherical harmonics and two numerical spatial-domain approaches. Due to its irregular shape, accurate gravitational field modeling represents a challenging task that is essential for precise orbit determination and spacecraft navigation. A mutual comparison of spectral- and spatial-domain methods is therefore vital. The spherical harmonic methods rely on two distinctive approaches. The first one is known as spectral gravity-forward modelling and produces a spherical harmonic series that is valid only outside the smallest sphere completely encompassing bennu. The second approach estimates an external spherical harmonic series from surface gravitational data using the least-squares method, making the series valid everywhere on and above the surface of bennu. Opposed to the spherical harmonic methods, two numerical approaches based on the finite element method are considered: the first solves the exterior boundary value problem (BVP) for the Laplace equation, while the second addresses a coupled interior–exterior BVP for the Poisson equation. Constant mass density is assumed in all experiments.

In the theoretical part of the poster, the fundamental principles of all applied methods are introduced. These approaches are subsequently implemented and tested in a series of numerical experiments. In the first experiment, gravitational acceleration evaluated on an approximated surface of the asteroid by spatial-domain gravity-forward modeling is prescribed as a boundary condition.

The convergence of the numerical solution toward the reference solution obtained from spherical harmonic functions is then analyzed. In the second experiment, a triangulated surface representation of the asteroid bennu is employed in order to assess the performance of the numerical methods on a more realistic geometry. The comparison focuses on the convergence rate, computational efficiency, and memory requirements of the individual approaches, providing insight into their applicability for gravitational field modeling of irregular small bodies.