A new state transition matrix is described for the nonlinear problem of relative motion on an arbitrary elliptical orbit. A linearization is performed, leading to a set of linear differential equations with time-dependent coef cients. A new and simpler solution to those equations is represented in a convenient state transition matrix form. This new state transition matrix is valid for arbitrary elliptical orbits of 0 · · e < < 1. The state propagation using the new state transition matrix shows good agreement with numerical results. Nomenclature a cd = acceleration due to forces other than the inverse square gravity term on the chaser spacecraft, for example, solar pressure, air drag, higher gravity terms, etc. a f = acceleration due to thrust forces on the chaser spacecraft a td = acceleration due to forces other than the inverse square gravity term on the target spacecraft, for example, solar pressure, air drag, higher gravity terms, etc. c = ½ cos µ e = eccentricity of target orbit h = orbital angular momentum of target orbit k = p .h=p 2 / R = vector from the center of gravity to the target spacecraft r = vector from the target spacecraft to the chaser spacecraft s = ½ sin µ Koji Yamanaka was born in 1968 in Mie Prefecture, Japan. He received his M.S. in aeronautical engineering in 1992 from Nagoya University. He has been working for the National Space Development Agency of Japan since then. He has worked on the automated rendezvous experiment of Engineering Test Satellite VII, Japanese lunar lander, and currently on the H-II Transfer Vehicle project, which is a space station logistic support vehicle. His research interests are in the area of automated rendezvous and formation ying. He is a member of AIAA. Finn Ankersen was born in 1958 in Aalborg, Denmark. He received his M.Sc. in electrical engineering in 1985 from Aalborg University, with a specialization in automaticcontrol systems there and at the Massachusetts Institute of Technology. He worked for a year in the software industry before joining the European Space Agency Research and Technology Center in the Netherlands, where he holds a senior position in the spacecraft guidance, navigation, and control technical section. His research interests are in the area of multivariable robust control, system identi cation, mathematical modeling and design, and simulation tools design for space systems and electrooptical mechanical systems.

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