Atmospheric drag effects on the motion of an artificial Earth satellite

Perturbative effects of atmospheric drag on the motion of an artificial Earth satellite are investigated in this paper. The atmosphere is considered to rotate with the same angular velocity as the Earth. The altitudes of the satellite are given with reference to the standard Earth-ellipsoid. The Lagrange planetary equations in Gaussian form are applied to determine the variations of the orbital elements. The atmospheric density at the satellite is regarded as a function of time. The density function is approximated by polynomials determined by the least-squares method. The coefficients are calculated from the finite set of ordinates corresponding to the density values computed by analytically evaluating the 1971 Jacchia density model. By use of the osculating orbital elements the position of the satellite is predicted. In this case it is assumed that the orbit of the satellite is perturbed by the variations of the Earth's gravitational field alone. The ratio of the rate of the Earth's rotation and the mean motion of the satellite is usually less than 1/10. This ratio and the eccentricity of the orbit are considered to be of the first order. In the expression of the magnitude of the relative velocity of the satellite with respect to the atmosphere, terms up to the third order are included.