Comparative analysis of methods for modeling the gravitational potential of complex shape bodies

Correct modeling of the celestial bodies gravitational field is the key problem for rendezvous, landing and research of these objects. There are a number of various methods for describing the gravitational field, each method has advantages and disadvantages. The paper considers and presents the comparative analysis results of the three most wellknown methods for representing the gravitational potential: the polyhedron model, the mascon model, and the spherical harmonics expansion. The approach for comparison of the accuracy and computational complexity of each method is suggested and realized. An asteroid of known shape and uniformly distributed mass is taken as the sample object. The analysis showed that the method of spherical harmonics expansion is computationally more advantageous when calculating the gravitational potential on a large number of trial points, but it is the least accurate of the three methods presented in the work. The mascon method on a small number of trial points takes the least time and has a higher accuracy. The polyhedron method is the most computationally expensive but it is the most accurate and can be used as a reference for calculating the gravitational potential for a homogeneous body.