On the maximal and minimal distances of flying-around satellite formation

The purpose of this paper is to present the obtained analytic solutions of maximal and minimal inter-satellite distances for flying-around satellite formation.

The relative motion equation is used to express the inter-satellite distance as the function of the orbital elements of two participating satellites for the flying-around satellite formation. Then by taking the derivative of the distance function with respect to the true anomaly, some possible extreme value points are obtained. According to the detailed analysis, the maximal and minimal distance solutions are found. By a reverse process, the expected initial differential orbital elements that generate the required extreme inter-satellite distances are also obtained.

The maximal and minimal distances of the flying-around formation can be analytically written as the functions of three initial orbital elements differences, i.e. the differential orbital inclination, the differential eccentricity and the differential right ascension. For the given maximal and minimal distances, there are lots of solutions of the initial differential orbital elements, which can produce the expected relative motions.

The solutions of the maximal and minimal inter-satellite distances are only accurate for the circular or near circular reference orbit. For the elliptic reference orbit, there is a need to develop new methods to find the analytic solutions.

The results here can be applied to design the factual flying-around formation with dimension requirements in mission analysis stage.

By using the solutions presented in this paper, the engineers can design the expected flying-around formation with required maximal and minimal inter-satellite distances in a very easy way.