Construction of J2-Invariant Periodic Relative Motion in Highly Elliptical Orbits

Two satellites with mean orbital elements which differ only in terms of right ascension of the ascending node, argument of perigee, and mean anomaly are notable for having the same mean orbital element secular drift rates due to the J2 perturbation. The relative orbits which result from this configuration are discounted in the literature for not providing sufficiently many degrees of freedom with which to design relative orbit geometries suitable for real world missions. However, this paper will explore a variety of useful geometries which result from this limited design space, and provide analytical formulas for the differences between chief and deputy mean orbital elements as a function of the desired orbit geometry and inertial chief orbit. These include in-track-centered, quadrant-time-centered, offset-circular, rectilinear, boomerang-shaped, and cross-track only geometries.