Dynamics and control of spacecraft formations: Challenges and some solutions
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Presented is an analytic method to establish J2invariant relative orbits, that is, relative orbit motions that do not drift apart. Working with mean orbit elements, the secular relative drift of the longitude of the ascending node and the argument of latitude between two neighboring orbits are set equal. Two first order conditions constrain the differences between the chief and deputy momenta elements (semi-major axis, eccentricity and inclination angle), while the other three angular differences (ascending node, argument of perigee and mean anomaly), can be chosen at will. Several challenges in designing such relative orbits are discussed. For near polar orbits or near circular orbits enforcing the equal nodal rate condition may result in impractically large relative orbits if a difference in inclination angle is prescribed. In the latter case, compensating for a difference in inclination angle becomes exceedingly difficult as the eccentricity approaches zero. The third issue discussed is the relative argument of perigee and mean anomaly drift. While this drift has little or no effect on the relative orbit geometry for small or near-zero eccentricities, for larger eccentricities it causes the relative orbit to enlarge and contract over time. A simple control solution to this issue is presented. Further, convenient expressions are presented which allow for quick annual fuel budget estimations. For given initial orbit element differences, these formulas estimate what Δv is required to compensate for the J2induced relative drift.