Preliminary Study of Geosynchronous Orbit Transfers from LEO using Invariant Manifolds

The invariant manifolds of libration point orbits (LPOs) in the Sun-Earth/Moon system are used to construct lowenergy transfers from Low Earth Orbits (LEOs) to geosynchronous orbits. A maneuver is performed in LEO to insert onto a stable manifold trajectory of an LPO. The spacecraft travels to the host LPO and then follows an unstable manifold trajectory back to a geosynchronous orbit, where an orbit insertion maneuver is performed. The maneuver costs of the transfers that employ invariant manifolds are compared to those using traditional techniques. Potential ∆V savings for transfers involving inclination changes are presented. INTRODUCTION The geosynchronous orbit (semimajor axis ≈ 42,164 km) is utilized for a wide spectrum of applications ranging from communications and television broadcasting to important defense and intelligence applications. Approximately 400 spacecraft with geosynchronous orbital elements are publicly available from the Celestrak website, which is managed by the U.S. Air Force.1 Many methods have been developed for transfers between orbits. The minimum two-impulse transfer between circular coplanar orbits is the well known Hohmann transfer, which is a half ellipse originating and terminating at opposite apsides.2 In practice, a launch vehicle may inject the spacecraft onto the Hohmann transfer orbit with a perigee equivalent to a Low Earth Orbit (LEO) and an apogee at the geosynchronous radius. The inclination of this transfer trajectory is typically similar to the inclination of the launch site. Once at apogee, one or more maneuvers are necessary to circularize the orbit and to achieve the desired inclination. Inclination changes can be very expensive. For example, the maneuver to change from a geosynchronous orbit at 28◦ to an equatorial geostationary orbit is roughly 1.5 km/s. The cost is approximately 2.55 km/s to transfer from a geosynchronous orbit at 49◦ (the minimum launch inclination achievable by Baikonur) to a geostationary orbit. The fuel mass required to perform such large maneuvers limits the dry mass of the spacecraft and thus can impact the lifetime, payload, and revenue of a mission. ∗Post-Doctoral Research Associate, The Colorado Center for Astrodynamics Research, University of Colorado, Boulder, CO 80309. †Research Associate, The Colorado Center for Astrodynamics Research, University of Colorado, Boulder, CO 80309. ‡Director, The Colorado Center for Astrodynamics Research, University of Colorado, Boulder, CO 80309.