Using an Integral Index to Search for Orbits around Oblate Spheroids

Abstract An integral index is used in this manuscript to search for the least gravitationally perturbed orbits around an oblate spheroid. Although there are missions where perturbations are desired, such as Sun-synchronous orbits, near Keplerian orbits can be useful in some cases during the whole mission or partially, helping to keep the oscillations of the orbital parameters in the minimum possible level, which can be interesting to observe celestial bodies. These orbits are also good candidates to require a lower number of station-keeping maneuvers, helping to simplify the logistic of the mission. The index used is available in the literature and it is based on the integration of the accelerations suffered by a spacecraft over time. An oblate spheroid is used to represent the approximate shape of non-spherical bodies because it has a closed equation for the potential, which makes it ideal for the analysis proposed, and because it is a shape similar to what is found for several objects in the small bodies population. The Lagrange planetary equations are also used to map orbits that have a minimum rate of variation in their orbital elements, and compared with the results obtained with the integral index. The results show a very good agreement between the index and the variations of the orbital elements of the spacecraft, in particular in terms of locating the least perturbed orbits to place the spacecraft.