Relative Motion between Satellites on Neighbouring Keplerian Orbits

P L Palmer & E Imre

In this paper we explore the relative motion between two satellites on Keplerian
orbits. We assume that the orbital elements defining the Keplerian ellipses for the two
satellites are similar so that we may neglect differences in these elements to second
order. Analytic solutions for the relative motion are presented which conserve relevant
quantities related to the Keplerian motions and we discuss in detail the choice of
initial conditions to improve the order of the approximations involved. Finally we
present results that compare our analytic results with differences of Keplerian orbits to
determine the accuracy of the approximation, which is shown to be much greater than
anticipated. An advantage of the approach presented over previous work in this area,
is that the relative motion is described in an inertial frame and not a rotating frame.
This enables the effects of perturbations on the relative motion to be incorporated in
a straight-forward manner.

Paper: Relative Kepler Motion

Ref: Palmer, P.L. & Imre, E , AIAA J Guidance, Control & Dynamics, 30, No. 2 , pp. 521 – 528, 2007.

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