Spacecraft Formation Flying

7.4 Averaged Relative Motion

The previous developments in this chapter made use of the mean elements extensively. One can, for convenience, define and compute mean motion variables from the differential mean elements instead of the differential osculating elements. However, since the averages of the short-periodic variations in the elements do not necessarily equal zero, errors of $\mathcal{O}\left(J_2\right)$ can result due to a direct substitution of the differential mean elements into the expressions for the motion variables. Sengupta et al. [125] have obtained corrections to the mean motion variables, resulting in the so-called “averaged” expressions for the relative ...