The analytic treatment of the atmospheric drag perturbation effect on the motion of a spacecraft in a low, near-circular orbit with arbitrary inclination energy and perigee location is presented. Due to the oblateness of the Earth it is assumed that the surfaces of constant density are spheroidal with the same flattening as the Earth. Furthermore, these constant density contours are assumed to form a bulge that lags behind the sun by about 2 h. Assuming an exponential decay law with radial distance from the Earth center for the air density ρ{variant}, a constant scale height and a uniform rotation rate for the atmosphere as well as a sinusoidal variation of ρ{variant} with angular distance ∅ between the spacecraft and the center of the diurnal bulge, a suitable expression for ρ{variant} is derived in terms of the true anomaly which is then converted to a function of time as measured from any arbitrarily selected initial epoch on the near-circular orbit. Analytic expressions for the air relative velocity vector and its magnitude are also obtained and the acceleration vector due to drag is formed, from which radial tangential and out-of-plane components are derived. These components are then used to drive the linearized Euler-Hill equations of motion yielding thereby in the rotating frame attached to a reference circular orbit the six position and velocity components of the state vector in closed form as a function of time. © 1990.
