Optimal rendezvous trajectory between Sample Return Orbiter and Orbiting Sample Container in a Mars Sample Return mission

A trajectory optimization problem is examined to determine the most fuel-efficient rendezvous trajectory between spacecrafts in different orbits. To explore the whole range of feasible solutions, the wait time and the total time of flight are treated as free parameters while the initial and transfer orbits are not restricted to a particular one. To improve the accuracy of the numerical computation, the Kepler's time of flight equation is posed in terms of universal variables while the Lagrange coefficients are employed to obtain three-dimensional orbit information. The optimal rendezvous trajectory is then obtained enforcing the determined necessary conditions to be satisfied given only the initial state vectors of the involved spacecrafts. Two optimal rendezvous trajectories between a Sample Return Orbiter (SRO) and an Orbiting Sample Container (OS) are computed in the context of a future Mars Sample Return mission to demonstrate the reliability of the proposed solution. Finally, orbital perturbations due to the real shape of planet Mars and the solar radiation pressure are taken into account to determine the additional energy required to compensate these perturbations while performing the rendezvous manoeuvre.