The Method to Determine Spherical Harmonic Model of Asteroid based on Polyhedron

In order to obtain sufficiently accurate spherical harmonic model of asteroid’s gravity field during the design stage of asteroid exploration mission which we can benefit from to design the orbit trajectory or the landing trajectory, the author of this paper proposed a method to determine the spherical harmonic model of asteroid’s gravity field based on polyhedron model. Firstly, this method reconstructed the distributing conditions of outer gravity filed of asteroid using polyhedron model, and then chose the gravitational potential of some specific point as virtual observation. Secondly, according to the definition of the spherical harmonic model, the relationship between virtual observation and spherical harmonic coefficients can be determined. Finally, as this relationship is given, the over-determined equations can be solved to obtain the spherical harmonic coefficients in different orders of asteroid’s gravity field. Comparing to the traditional method which is approximating the asteroid to a triaxial ellipsoid to determining the spherical harmonic model, the method of this paper can substantially increase the accuracy of gravity field model. Through the comparison between this paper and the spherical harmonic coefficients of asteroid 433Eros which is solved by NEAR probe’s orbital data we can see that the maximum error of this paper’s result is 6% at most. Whereas the maximum error of triaxial ellipsoid model can be 29.61%, which can fully indicate that the method we use has the higher accuracy which can be used to provide more accurate gravity filed model to the orbit design of the pre-mission of asteroid detection. Keywords-Modeling of Gravity; spherical harmonic model; polyhedron model ; spherical harmonic coefficients