ОСВІТЛЕНІСТЬ ШТУЧНИХ СУПУТНИКІВ ЗЕМЛІ НА КОЛОВИХ ОРБІТАХ

The purpose of the work is to build an updated model of the illumination of artificial satellites in circular Earth orbits and to study the duration and nature of solar illumination in orbits with different inclinations and altitudes throughout the year. The mathematical model uses the equation of the circular cone of the shadow, built taking into account the movement of the Sun relative to the Earth. The center of the cross section of the base of the cone coincides with the center of the Earth. The motion of the satellite is simulated by Kepler’s orbit. The computer model makes it possible to determine with a given accuracy the duration of the satellite’s stay in the Earth’s shadow. Simulation of the duration of illumination of satellites at two altitudes has been performed: 5,000 km and 35,786 km (geosynchronous orbit altitude) throughout the year. Curves of the duration of the satellites’ stay in the shadow are given. The shape of the curves varies from a nearly straight line for inclined orbits 25°, then they become periodic, and then divide into two parts, resembling the shape of a parabola. Among all the possible inclinations of the orbits of satellites, extreme ones have been detected. These are orbits with an angle of inclination 23°26', which defines a straight orbit. On them, an artificial satellite falls into the Earth’s shadow throughout the year at each orbit. The second group of extreme orbits are orbits with inclinations, in which the satellite falls into the shadow only near the time of the equinoxes. Shortest duration of stay of satellites in the shadow moving in orbits with an angle of inclination 113°26'. Falling into the shadow lasts from 15.02 to 23.04 and from 19.08 to 27.10 for an altitude of 5,000 km, and from 12.03 to 28.03 and from 14.09 to 01.10 for an altitude of 35,786 km. The results of the simulations will allow us to clarify the effect of sunlight and solar wind pressure on the motion of satellites over time. This will allow the use of additional satellite accelerations resulting from radiative impact to change the orbits of space debris and clean up near-Earth space.