Analytical model of satellite motion in almost circular orbits under the influence of zonal harmonics of geopotential

The article deals with the movement of satellites in low near-circular orbits of the Earth. An analytical model is constructed, which consists of formulas describing the change of the osculating elements and averaged equations. An algorithm for constructing a second approximation of the influence of zonal harmonics of the geopotential on the movement of satellites in almost circular orbits is presented. For the second and third zonal harmonics, formulas are given for the osculating and average elements describing the motion of the satellite in the second approximation in small parameters. The introduction of special variables for almost circular orbits made it possible to significantly simplify the procedure for constructing the second approximation of the influence of zonal harmonics. The article provides a justification for the accuracy of the analytical model for the considered orbits. The constructed model of changes in the average elements of the orbit describes the basic principles of motion. With a sufficiently high accuracy, this model describes the changes in the average elements of the orbit with simple analytical formulas and is convenient for analyzing the properties of orbits and pre-selecting a reference orbit for a specific mission.