Optimal Two-Impulse Cotangent Rendezvous Between Coplanar Elliptical Orbits

Abstract

This paper studies the two-impulse cotangent rendezvous problem between two coplanar elliptical orbits. This problem requires the same flight time for two spacecraft and a cotangent transfer between the initial and final orbits. For two coplanar circular orbits, the closed-form solution is obtained and its total cost is equal to that of the Hohmann transfer. However, for two coplanar elliptical orbits, the solutions are obtained only by a numerical iterative algorithm. There are many solutions for the multiple-revolution case. Moreover, the minimum-fuel two-impulse cotangent transfer can be expressed as the true anomaly of final orbit. With the minimum-fuel transfer, a simple method for the optimal revolution numbers is proposed based on the first-order Taylor series expansion of the flight-time equation. Then, the minimum-fuel two-impulse cotangent rendezvous is obtained by calculating and comparing two or four candidates. Two numerical examples are provided to apply the proposed technique for all solutions and the minimum-fuel solution to the two-impulse cotangent rendezvous problem.