The number of impulses in the coplanar problem of energy-optimized flight between close Keplerian orbits

The objective of the study is to determine the maximum number of impulses for the energy-optimized transfer between closely adjacent elliptic Keplerian orbits. It is shown that for an arbitrary eccentricity of the adjacent orbits, only single-impulse transfers are optimum with respect to energy. An analysis is also made of the coplanar problem of a minimum-energy impulse maneuver for avoiding the intersection of close elliptic Keplerian orbits. It is shown that only single-impulse maneuvers are optimum for an orbit eccentricity of less than 0.7748, while optimum two-impulse maneuvers exist for larger eccentricities.