Rendezvous of a continuous low-thrust cubesat with a satellite**This paper is dedicated to our colleague Michel Dudeck who died on 2017 April 10th.

Abstract

We give in this paper a new method optimizing continuously the direction of a low continuous thrust to have rendezvous of a cubesat with a given satellite. We study the rendezvous of a cubesat B, with a satellite A, on an elliptic orbit around the Earth. The cubesat B, with 3 kg mass and low-thrust motor, is on a circular orbit around the Earth. The rendezvous is obtained by making the coincidence between the angular momentum vector and the eccentricity vector of B respectively with those of A, then by adjusting the position of B, at the initial instant of thrusting or by convenient choice of this instant. The thrust acceleration is supposed to be constant. The thrust is continuous and its direction is continuously oriented to optimize the time necessary to make the coincidence between the two orbits. A numerical application is given where A is the satellite ‘Almasat-1’.