Variation in Argument of Perigee for Near-Earth Satellite Orbits Perturbedby Earths Oblateness and Atmospheric Drag Interms of Ks Elements

Abstract

Analytical solutions with the KS element equations of motion due to the combined effect of zonal harmonics J2,J3 and J4 and drag by considering an analytical oblate diurnal exponential density model when density scale height varies with altitude is obtained using series expansion method. Terms up to third terms in e, eccentricity, c, a small parameter depending on the ellipticity of the atmosphere and second order terms in μ, gradient of the scale height altitude are considered. The KS element equations are numerically integrated (NUM) through a fixed step size fourth-order Runge-Kutta-Gill method having a very small step-size of half degree in the eccentric anomaly for comparing analytically integrated (ANAL) values. After 100 revolutions, decrease in argument of perigee, ω, at perigee height = 400 kilometer, e = 0.1 and inclination i = 20 and 80 degrees, are found to be 7.42 and 39.8 degrees. At i =80 degree, the percentage error = (ANAL - NUM) / NUM after 1 and 100 revolutions are 0.61 and 2.09.