Metrics on the Relative Spacecraft Motion Invariant Manifold.

This paper establishes a methodology for obtaining the general solution to the spacecraft relative motion problem by utilizing Cartesian configuration space in conjunction with classical orbital elements. The geometry of the relative motion configuration space is analyzed, and the relative motion invariant manifold is determined. Most importantly, the geometric structure of the relative motion problem is used to derive useful metrics for quantification of the minimum, maximum, and mean distance between spacecraft for commensurable and non-commensurable mean motions. A number of analytic solutions, as well as useful examples, are provided, illustrating the calculated bounds. A few particular cases are given that yield simple solutions. [ABSTRACT FROM AUTHOR]