Near-Parallel Equivalence Satellite Orbits

Equivalence orbits of satellites are formed by combining two (or possibly more) motion references of satellite orbits. For this purpose, the different motion references can be combined arbitrarily. In all cases mean and true equivalences are distinguished. The mean equivalence orbits are obtained from the comparison of mean motions or mean orbital periods. The mean motions are formed with mean epoch elements in expressions of secular motion influences. Closer to reality are true equivalence orbits. They are formed with true period times. These are formed according to the respective motion reference by calculation of the true orbit angle over one orbit. Also in this case, mean epoch orbit parameters (elements) are calculated. In both cases, multiple iterations must be performed. This process can be performed with an analytical or a numerical orbit model. This usually requires an initial value for the semimajor axis. This can be formed as an approximate value with sufficient accuracy from expressions of the mean motions. The orbits coupled in this way can present interesting special properties.