Disturbing function in the analytical theory of the motion of Phobos

A new theory of the motion of Phobos – the moon of Mars – is created. The accuracy of this theory is to within one meter of the mean motion of Phobos over one year which is the best result obtained so far for the analytical approach. The perturbational analysis is of main interest. The elements of the physical interactions which are the most essential for the motion of Phobos are specified. The theory is based on the two fixed gravitational centers problem. Analytical functions of this problem are expressed as a series of the third order with respect to the J2 and J3/J2 zonal harmonics of Mars. This theory takes into account the interaction of Phobos with the potential of Mars consisting of very many elements. The zonal harmonics of order ≤ 12 and tesseral harmonics of order ≤ 6 are considered. Interactions of Phobos with the Sun, Jupiter, Deimos – another moon of Mars, and the tidal potential of the Sun are taken into account. The influence of all the elements of the perturbational function on the accuracy for determining the position of Phobos is presented. The numerical integration allows to illustrate the influence of all perturbations (of the ones which have been taken into account and of the ones which have been neglected) on the mean motion of Phobos.