Notes on logarithmic spiral trajectories generated by solar sails

The aim of this paper is to provide a systematic study about the possibility of inserting a solar sail spacecraft into a heliocentric logarithmic spiral trajectory. The required conditions in terms of solar sail (fixed) attitude, performance, and initial position are discussed. It is shown that the spiral trajectory is required to start from a specific point that depends on the solar sail performance and the parking orbit characteristics. Moreover, the evolution of the osculating orbital parameters are presented, and some potential mission scenarios involving logarithmic spirals are analyzed, including the rotation of the apse line and the phasing trajectories of a spacecraft placed along an elliptic orbit.