Gravitational perturbations of equatorial orbits

Computational algorithm to solve two–body problem using power series in geocentric system

“…So, it has many applications in scientific researches, where N ≥ 2, where the problem is solved for N = 2 because it can be reduced to perturbed two-body problem or the perturbed Kepler problem, which is a system of ordinary differential equations that describe the motion of two particles moving under their mutual gravitational attraction force. Some considerable work on the solution of the Kepler problem are studied in [1][2][3][4][5][6][7][8].…”

Prediction of Satellite Motion under the Effects of the Earth’s Gravity, Drag Force and Solar Radiation Pressure in terms of the KS-regularized Variables

“…One of such transformation, known as the KS-transformation, is due to Kustaa-neimo and Stiefel, who regularized the non-linear Kepler motion and reduced it to linear differential equations of a harmonic oscillator of constant frequency. Reference [29] further developed the application of the KS-transformation to problems of perturbed motion, producing a perturbational equations version ( [1] ; [3] ; [4] ; [13] ; [14] ; [15] ; [20] ; [21] ; [23] ; [28] ; [30]; [31]; [32] ; and [33]).…”

Geomagnetic Attitude Control of Satellites Using Generalized Multiple Scales

“…This refinement, i.e. the principle of subminimal simplification was developed by Ramnath [6,9] and has been applied succesfully by Ramnath [10]. It will find its application in our analysis later on.…”

“…where B 10 and 030 are constants to be determined from the initial conditions. In the above equation, k*(t) = k 3 (t) -k, 3 …”