Comparative Analysis of Methods for Modeling the Gravitational Potential of Complex Shaped Bodies

摘要

The correct modeling of the gravitational field of small celestial bodies is an urgent problem in solving the problems of approaching, landing on, and researching these bodies. There are a number of different methods for describing the gravitational field, each of which has its own advantages and disadvantages. This paper considers and presents the results of a comparative analysis of the three most well-known methods for representing the gravitational potential: the polyhedron model, the mascon model, and expansion in spherical harmonics. A technique for comparing the accuracy and computational complexity of these methods for an asteroid whose shape is assumed to be known and whose mass is uniformly distributed over the volume is developed and implemented. The analysis shows that the method of expansion in spherical harmonics is computationally more advantageous when calculating the gravitational potential for a large number of sample points, but it is the least accurate of the three methods presented in this study. The mascon method is the fastest and is more accurate for a small number of sample points. The polyhedron method is the most computationally expensive, but it is also the most accurate method and can be used as the reference for calculating the gravitational potential of a homogeneous body.