We study the effects of a non-singular gravitational potential on satellite orbits by deriving the corresponding time rates of change of its orbital elements. This is achieved by expanding the non-singular potential into power series up to second order. This series contains three terms, the first been the Newtonian potential and the other two, here R1 (first order term) and R2 (second order term), express deviations of the singular potential from the Newtonian. These deviations from the Newtonian potential are taken as disturbing potential terms in the Lagrange planetary equations that provide the time rates of change of the orbital elements of a satellite in a non-singular gravitational field. We split these effects into secular, low and high frequency components and we evaluate them numerically using the low Earth orbiting mission Gravity Recovery and Climate Experiment (GRACE). We show that the secular effect of the secondorder disturbing term R2 on the perigee and the mean anomaly are 4 .307 ? 10−9/a, and −2 .533 ? 10−15/a, respectively. These effects are far too small and most likely cannot easily be observed with today?s technology. Numerical evaluation of the low and high frequency effects of the disturbing term R2 on low Earth orbiters like GRACE are very small and undetectable by current observational means
In this paper we calculate the effect of atmospheric dust on the orbital elements of a satellite. Dust storms that originate in the Martian surface may evolve into global storms in the atmosphere that can last for months and can affect low orbiter and lander missions. We model the dust as a velocitysquare depended drag force acting on a satellite and we derive an appropriate disturbing function that accounts for the effect of dust on the orbit, using Lagrangean formulation. A first-order perturbation solution of Lagrange's planetary equations of motion indicates that for a local dust storm cloud that has a possible density of 8.323?e10-10 kg m-3 at an altitude of 100 km affects the orbital semimajor axis of a 1000kg satellite up -0.142 m day-1. Regional dust storms of the same density may affect the semimajor axis up to of -0.418 meters per day. Other orbital elements are also affected but to a lesser extend.