Nonlinear Evolution of a Balloon Satellite Orbit

The motion of a spherically symmetric balloon satellite near the equatorial plane is considered. Taking the Earth's oblateness and solar light pressure into account, the integral of motion can be obtained under certain simplifications. The eccentricity is related to the solar angle which represents an angle between pericenter and the Sun. This analytical approximation describes a large and complicated evolution of the eccentricity in corresponding areas of the phase space and the space of parameters. Phase portraits contain fixed saddle points and separatrices that divide different types of oscillations of the eccentricity. In the unsimplified problem, separatrices break down, and specific stochastic motions arise. The aims of the present study are (1) evaluation of the accuracy of analytical approximation with the help of numerical integration using a sufficiently complete model of motion and (2) numerical investigation of stochastic motions and dimensions of stochastic zones in the region of broken separatrices for an adequate model of motion. For a balloon satellite with a semimajor axis of 2.15 Earth's radii and a windage of 30 cm²/g the dimensions of a stochastic zone in eccentricity and solar angle are 10^–5and 0.1°, respectively. The analytical approximation describes the orbit evolution in the right way, except for the cases of large eccentricities, e> 0.4, which corresponds to a pericenter height of less than 1400 km, where the atmospheric drag is already significant.