Influence of the Gravitational Fields of the Moon and the Sun on Long-Period Variations in the Proper Rotation of “Midas” Satellites

We report the results of an analysis of the variation of the proper rotation of several destabilized satellites over many-year long time intervals. The cause of the cyclic variations of the proper rotation period of “Midas-7” satellite, which has been orbiting the Earth since 1963 at an altitude of 3700 km, have long been unclear. These variations could not be explained either by the influence of the terrestrial atmosphere and terrestrial magnetic field, or by solar activity. Based on the results of 40-year long observations of “Midas-4,” “Midas-6,”, and “Midas-7” satellites it was established that their proper rotation exhibits not only dissipative braking variations, but also long-period variations with the periods of 477 days (“Midas-4”), 466 days (“Midas-6”), and 346 days (“Midas-7”) with different amplitudes. These variations in the case of the above satellites have well-defined resonance nature. An explanation of the processes found is proposed based on the results of this study and simulations of the observed orbital dynamics of the satellites. Long-period variations of the proper spacecraft rotation arise as a result of the combined effect of the gravitational fields of the Earth, Moon, and Sun depending on the orientation of their orbital planes in space. The amplitudes of such variations is determined by the inclination of satellite orbits to the equator: the closer it is to the pole (i.e., to 90?), the stronger the effect.