Abstract: An inner satellite which is a proof mass freely flying in the shield cavity of the outer satellite does not suffer the external disturbances, such as air drag and solar pressure, and follows a purely gravitational orbit. The gravitational attraction on the inner satellite due to the outer satellite is a significant disturbance source to the purely gravitational orbit. The analysis model was deduced from the relative motion equation of formation flying to calculate the effect of gravitational attraction to purely gravitational orbit. With the outer satellite spinning to modulate the gravitational attraction, the function of reducing the effect of gravitational attraction was analyzed. It indicates that spinning of the outer satellite can evidently reduce the long-period effect of gravitational attraction disturbance. The departures of the inner satellite from the purely gravitational orbit due to the gravitational attraction were calculated for the Inner Formation Flying System with the outer satellite spinning or not. The comparison shows that the days departure can be reduced by about five to seven orders of magnitude if the outer satellite is rotated.

Key words: Purely gravitational orbit, Inner satellite, Outer satellite, Gravitational attraction disturbance, Inner formation flying system