On the choice of orbits for spacecrafts

The problem of distribution of a given number of spacecrafts over a certain structured set of orbits consisting of n = pk orbits is considered. The solution to this problem is given under the condition that the set of possible orbits for spacecraft coincides with the number of spacecrafts. In addition, it is assumed that the given set is divided into disjoint subsets of orbits, and the number of orbits in the indicated subset is the same. In the situation under consideration, it is equal to some prime number p. Currently, several orbits are used to place satellites on them, depending on the tasks they solve. Geostationary orbit is used for live TV broadcasting. Low satellite orbits are used for communication between satellite phones. Their own orbits exist for satellites of navigation systems GPS, Navstar, GLONASS, military satellites, satellites for various scientific research. Naturally, under these conditions, the problem arises of structuring a set of orbits with some restrictions on the location of the spacecraft in given orbits, depending on the purpose of the spacecraft. The problem of the complexity of calculating the number of orbits under these constraints is considered.