The Earth’s Shadowing Effects in the Short-Periodic Perturbations of Satellite Orbits

Abstract

The authors investigate the short-periodic perturbations of the orbit of an artificial satellite, during one revolution of the satellite around the Earth, caused by the direct solar radiation pressure. Special interest is paid to the study of the influence of the Earth’s shadow, which is considered as a special mathematical function in the equations for the perturbations. The position of the satellite orbit according to the Sun is considered to be constant during one orbital period of the satellite, so the quasi-secular perturbations are obtained under those conditions too. Analytical formulae were found for computation of both quasi-secular and short-periodic terms in the perturbations of an arbitrary orbital element. A corresponding algorithm is used in the FORTRAN program for the IBM 360/65 computer. Practical application of this semi-analytical theory is shown for perturbations of semi-major axis and eccentricity of Echo 1, Echo 2 and Explorer 19 satellites. A comparison is made with the previous work neglecting the shadow, and quasisecular changes of eccentricity are compared directly with changes in the SAO Mean Elements. Satisfactory agreement with observations is obtained.