M. K. Ahmed

Invariant relative orbits for satellite constellations: A second order theory

Working with the mean orbit elements, the secular drift of the longitude of the ascending node and the sum of the argument of perigee and mean anomaly are set equal between two neighboring orbits. By having both orbits drift at equal angular rates on the average, they will not separate over time due to the influence of the perturbative effects of the asphericity of the Earth, as is considered in this work. The problem is stated. The expressions for the time rate of change of the longitude of the ascending node and the sum of the argument of perigee and mean anomaly in terms of the Delaunay canonical elements are obtained. The expressions for the second order conditions that guarantee that the drift rates of two neighboring orbits are equal on the average are derived.

Analytical treatment of the relativistic and solar radiation pressure effects on an artificial satellite

Abstract A development of an analytical solution for the motion of a spherical Earth artificial satellite subjected to the combined effects of the post-Newtonian (PN) geopotential and direct solar radiation pressure (SRP) is presented. The equations of motion are derived in previous paper [A.A. El-Enna, Appl. Math. Comput. 149 (2004) 359–368]. Two Lie transformations are used to derive explicit results for the secular and periodic perturbations of the satellite orbits, retaining secular and periodic terms up to orders 4 and 3, respectively. The developments focussed on the joint effects of the relativistic and SRP terms. The existence of some resonance cases are discussed using the present long periodic terms. Moreover, these cases are investigated using the conditions of resonance.