Satellite motion in a non-singular gravitational potential

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. I. Haranas ( ) · S. Pagiatakis Dept. of Physics and Astronomy, York University, 4700 Keele Street, Toronto, ON M3J 1P3, Canada e-mail: [email protected] S. Pagiatakis Dept. of Earth and Space Science and Engineering, York University, 4700 Keele Street, Toronto, ON M3J 1P3, Canada e-mail: [email protected]