Satellite motion in a non-singular gravitational potential |
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Authors: | Ioannis Haranas Spiros Pagiatakis |
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Institution: | (1) Sternberg Astronomical Institute of Moscow State University, Universitetsky Pr. 13, Moscow, 119899, Russia |
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Abstract: | 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 R
1 (first order term) and R
2 (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 second-order disturbing term R
2 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 R
2 on low Earth orbiters like GRACE are very small and undetectable by current observational means. |
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