An approach for finding long period elliptical orbits for precursor SEI missions

Precursors for Solar System Exploration Initiative (SEI) missions may require long period elliptical orbits about a planet. These orbits will typically have periods on the order of tens to hundreds of days. Some potential uses for these orbits may include the following: studying the effects of galactic cosmic radiation, parking orbits for engineering and operational test of systems, and ferrying orbits between libration points and low altitude orbits. This report presents an approach that can be used to find these orbits. The approach consists of three major steps. First, it uses a restricted three-body targeting algorithm to determine the initial conditions which satisfy certain desired final conditions in a system of two massive primaries. Then the initial conditions are transformed to an inertial coordinate system for use by a special perturbation method. Finally, using the special perturbation method, other perturbations (e.g., sun third body and solar radiation pressure) can be easily incorporated to determine their effects on the nominal trajectory. An algorithm potentially suitable for on-board guidance will also be discussed. This algorithm uses an analytic method relying on Chebyshev polynomials to compute the desired position and velocity of the satellite as a function of time. Together with navigation updates, this algorithm can be implemented to predict the size and timing for AV corrections.