New State Transition Matrix for Relative Motion on an Arbitrary Keplerian Orbit

A new formation of the relative state transition matrix has been developed for the spacecraft relative motion without using the Tschauner-Hempel solutions. The relative state transition matrix is obtained by expressing the inertial two-body state transition matrix in the rotating frame through a series of coordinate transformations. Two different approaches are used for exploiting the inertial two-body state transition matrix. One is to use the parametric linearization technique in terms of the orbital elements. The other one is to adopt the universal variables and Lagrange coefficients to achieve the same goal. This new state transition matrix for spacecraft relative motion is time explicit and universally applicable to elliptic, parabolic, and hyperbolic orbits. The numerical results demonstrate that the new state transition matrix can achieve high-precision state propagation for spacecraft relative motion.