E/I-vector separation for safe switching of the GRACE formation

Abstract

After more than three years in orbit, a longitude swap maneuver was required to exchange the leading and trailing spacecraft of the GRACE formation. While the two satellites are nominally separated by about 220 km in along-track direction, a close encounter took place during the swap sequence. Based on the successful use for co-location of geo-stationary satellites, the concept of eccentricity/inclination vector separation has been suggested for safe proximity operations in this mission phase. Taking care of the natural evolution of the relative orbital elements of GRACE 1 and 2, optimum maneuver dates were identified. By proper timing of the maneuvers a safe limit for the minimum distance during the encounter could be guaranteed even in case of arbitrary thruster performance errors. This allowed the use of a fuel optimal maneuver sequence with individual drift start and stop maneuvers. The paper provides a conceptual outline and mathematical description of the e/i-vector separation for spacecraft formations in low Earth orbit and discusses the GRACE longitude swap maneuvers.