Satellite equivalence orbits

Satellite equivalence orbits are orbits coupling two or more relative satellite motions. Equivalence orbits between tropical and meridional motion are direct orbits. They have exactly the period 2 sidereal days. As consequence of Kepler's third law the corresponding Keplerian mean semimajor axis is 66931.447 km and gives an impression of this special class of equivalence orbits. In this case the period is identical for all matching orbits and will be preserved by adjusting the orbital elements. Preset 5 orbital elements the sixth element has to be adjusted, e.g. the semimajor axis. The sum of right ascension and geographic longitude shows no secular variations, but only periodic variations due to periodic perturbations, the equation of the center and the reduction on to the equator. The equivalence between tropical and meridional motion offers an independent check of the consistency of the physical parameters. When computed with the Brouwer analytical orbit model, the groundtrack of such an equivalence orbit shows no or only small variations over long time intervals. Based on the theory developed, the paper extends the term equivalent orbits with respect to Hansen motion, anomalistic motion, draconitic motion, Sun-synodic motion, and Moon-synodic motion.