Epicycles and oscillations: The dynamics of the LISA orbits

This paper presents a modern treatment of epicycle theory, which is an exact series representation of Keplerian motion, and uses that theory to develop the first analytic method for analyzing the higher order dynamics of the LISA orbits. LISA, the Laser Interferometer Space Antenna mission, uses a constellation of three spacecraft in heliocentric space and takes advantage of particular solutions of the Clohessy-Wiltshire equations, a first-order approximation of gravitational dynamics, to keep the constellation an equilateral triangle. The higher-order analysis presented here suggests a modification of the basic LISA orbit architecture which may improve the stability of the constellation.