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<p>In this paper, we propose and apply a novel numerical approach for modeling the gravitational field by solving the coupled interior-exterior boundary value problem (BVP) using the finite element method (FEM). To this end, we construct a finite computational domain encompassing the selected celestial object and a bounded portion of its exterior, within which the BVP is formulated. This problem consists of the Poisson equation for the gravitational potential, along with a Dirichlet boundary condition (BC) prescribed on the boundary. In this case, since the boundary is placed far from the object so that the Dirichlet BC is nearly zero, the only key input for the computation is the 3D model of the celestial body and its density. The solution is derived using the FEM, which is particularly effective for handling highly irregular or complex surface geometries. The numerical experiments include a test case involving a homogeneous sphere to demonstrate the second-order accuracy of the proposed approach as well as simulations of the gravitational fields of two selected asteroids, namely 25143 Itokawa and 433 Eros, and the comet 67P/Churyumov-Gerasimenko. These simulations yield detailed three-dimensional distributions of both gravitational potential and gravitational acceleration within the entire computational domain.</p>

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Gravitational field modeling of irregularly shaped bodies by solving the coupled interior-exterior boundary value problem

  • 期刊论文

  • 发表日期：

    2025年12月8日

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  • Marek Macák,
  • Zuzana Minarechová,
  • Karol Mikula

摘要

In this paper, we propose and apply a novel numerical approach for modeling the gravitational field by solving the coupled interior-exterior boundary value problem (BVP) using the finite element method (FEM). To this end, we construct a finite computational domain encompassing the selected celestial object and a bounded portion of its exterior, within which the BVP is formulated. This problem consists of the Poisson equation for the gravitational potential, along with a Dirichlet boundary condition (BC) prescribed on the boundary. In this case, since the boundary is placed far from the object so that the Dirichlet BC is nearly zero, the only key input for the computation is the 3D model of the celestial body and its density. The solution is derived using the FEM, which is particularly effective for handling highly irregular or complex surface geometries. The numerical experiments include a test case involving a homogeneous sphere to demonstrate the second-order accuracy of the proposed approach as well as simulations of the gravitational fields of two selected asteroids, namely 25143 Itokawa and 433 Eros, and the comet 67P/Churyumov-Gerasimenko. These simulations yield detailed three-dimensional distributions of both gravitational potential and gravitational acceleration within the entire computational domain.