Escape from Elliptic Orbit Using Constant Radial Thrust

HE classical problem of escape from a circular orbit using aconstant radial thrust was first proposed by Tsien [1] and thenrefined by Battin [2]. The same problem was then revisited byPrussing and Coversone [3], providing more analytical results andintroducing the concept of a potential-energy well. The aim of thisNote is to show that the available results for circular orbits can beextended to elliptic orbits. In particular, two main issues arepresented: 1) analytical expressions (in terms of propulsiveacceleration)fortheoccurrenceofanescapeconditionand2)simpleformulas for the maximum amplitude of the radial oscillation ifescapedoesnotoccur.Althoughthefollowingdiscussionisgeneral,amissionwithaconstantradialthrustmaybeinterpretedasaspecialcaseofminimagnetosphericplasmapropulsion[4](M2P2)inwhichthe M2P2 system uses a nuclear power source [5].