Spacecraft Formation Flying

5.6 Elliptic Reference Orbits

For circular reference orbits, the choice of the independent variable of either time or true anomaly leads to the same form of the equations of motion. This is not the case for elliptic reference orbits. Time-explicit solutions are attractive since Kepler’s equation need not be solved to produce results at specified points of time. However, true-anomaly-based solutions have certain advantages, especially near the perigee, and are more suitable for long-term motion prediction for elliptic orbits.

5.6.1 Time as the independent variable: Melton’s STM

Melton [109] has developed expansions of the STM in powers of eccentricity, in both Cartesian as well as cylindrical coordinate systems. A brief outline of his approach ...