Planar high-thrust and low-thrust orbital transfers from Earth to Europa

We review analytical formulae for low-thrust orbital transfers from a circular initial orbit to a circular target orbit and to escape, using constant thrust applied in the same direction as the velocity vector, or in the opposite direction. The formulae give approximations for the maneuver time, final mass fraction, and evolution of the semimajor axis. For comparison, the associated results for high-thrust Hohmann and Oberth transfers are summarized. A simple computer program employing the aforementioned relationships is a useful tool for analysis of planar planetary and interplanetary space missions. This implementation yields fast and reasonably accurate approximations to trajectory performance boundaries. Consequently, the approach can provide trajectory analysis for each spacecraft configuration during the conceptual space mission design phase. As an example, a mission from Low-Earth Orbit (LEO) to Jupiter's moon Europa is analyzed.