Satellite orbit under influence of a drag - analytical approach

Abstract

A satellite orbiting around an isolated spherical planet with no atmosphere would indefinitely follow the same elliptic orbit, without any variation of the trajectory. However, for the case of real Earth this simple picture is greatly altered by perturbing forces, usually classified into two major groups: (i) Perturbations of the total gravity field that acts on the satellite. These effects can appear due to gravitational attraction of Sun and Moon (gravity effects of other celestial bodies are negligible), but also as a result of the variation of Earth’s gravitational attraction, caused by flattening at the poles and other departures from spherical symmetry, such as the ”pear-shape” effect. When analyzing satellite dynamics, the total gravity perturbation is considered to be the sum of all particular contributions, independent on the satellite mass, size or geometry. (ii) Non-gravitational effects, proportional to the area-to-mass ratio of the satellite. Here we primarily consider the air drag, caused by rapid movement of a satellite through the upper atmosphere, but also effects of the solar radiation pressure. For most satellites, these are two types of force that induce major perturbations in the orbits. Many other perturbations exist, but do not normally produce large changes and will therefore be ignored here, as we aim to provide basic description. These neglected perturbations appear, among other causes, due to: upper-atmosphere winds, solar radiation reflected from Earth, Earth tides and ocean tides, precession of the Earth’s axis in space, resonance with Earth’s gravitational field and relativity effects. Although these effects will be ignored, it should be noted that they can be important for some special satellites. Parameters of the satellite orbit and its motion are given in Table 1. Several elements in the table are not self-explanatory. First, the drag coefficient Cd is a parameter that describes aerodynamic properties and is determined by the satellite geometry. The model for calculation of this coefficient, which would widely be accepted in the community, still does not exist. Values in the interval 2.1-2.3 were obtained for spherical satellites by most of the