“…The artificial satellites, in their motion around the Earth, can sometimes enter the Moon's shadow. 1,2 The probability of the satellite's entry the Moon's shadow can not be considered small, 3,4 as it is equal to 5% for the near-equatorial orbits with semi-major axes of 10-15 radii of the Earth. The problem of precomputing the Luni-Solar eclipses for the geostationary satellites was considered by several authors.…”