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Numerical integration of relativistic equations of motion for Earth satellites

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Abstract

The equations of motion proposed by Brumberg for an artificial satellite around the Earth (Celest Mech Dyn Astron 88:209, 2004), in which the relativistic effects due to the Earth’s oblatness and the gravitational action caused by a third body are added to those perturbations considered in the International Earth Rotation and Reference System Service (2003) convention, are here integrated numerically. To compute the solution of the time-dependent Langrangian system for a gravitational satellite–Earth–Sun model we consider a six-order partitioned Runge–Kutta integrator, whose coefficients satisfy the condition of symplecticity. A comparison with the classical Adams–Basforth–Moulton method allows to verify the good-performance of the partitioned Runge–Kutta method both in the description of the evolution of the satellite energy and in the efficiency of the method when applied to a long-term integration.

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  1. Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Valladolid, 47005, Valladolid, Spain

    A. San Miguel

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  1. A. San Miguel
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Correspondence to A. San Miguel.

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San Miguel, A. Numerical integration of relativistic equations of motion for Earth satellites. Celest Mech Dyn Astr 103, 17–30 (2009). https://doi.org/10.1007/s10569-008-9162-5

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  • DOI: https://doi.org/10.1007/s10569-008-9162-5

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