Relative motion and autonomous rendezvous in Keplerian elliptic orbits

In this paper, the analytical closed-form solution of the Tschauner-Hempel equations that are used for rendezvous in elliptic orbits are studied and exploited. The solution is based on a state transition matrix that is completely explicit in time. Autonomous guidance algorithms to approach, to flyaround, and to depart from a target vehicle in elliptic orbits are exploited based on that solution. The algorithms are general and able to translate the chaser vehicle in any direction, decelerate while approaching the target vehicle, and accelerate when moving away. These guidance algorithms are based on the glideslope used in the past for rendezvous and proximity operations of the Space Shuttle with other vehicles. The algorithms are applied to the problem of terminal rendezvous near any Keplerian elliptic orbit in a Newtonian gravitational field showing the effects of target orbit eccentricity on the relative motion. These algorithms extend and generalize previously published solutions. Numerical simulations confirm the brevity and accuracy of the general solutions developed in the current paper.