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The motion of artificial satellites is influenced by complex gravitational interactions, necessitating accurate predictive models for their trajectories. This work establishes a new set of differential equations using classical and generalized Sundman time transformations, enabling efficient short- and long-term motion predictions for satellites in Earth's gravitational field, validated through numerical results.
Abstract
In this paper, the classical and generalized Sundman time transformations are used to establish new generating set of differential equations of motion in terms of the Eulerian redundant parameters. The implementation of this set on digital computers for the commonly used independent variables is developed once and for all. Motion prediction algorithms based on these equations are developed in a recursive manner for the motions in the Earth's gravitational field with axial symmetry whatever the number of the zonal harmonic terms may be. Applications for the two types of short and long term predictions are considered for the perturbed motion in the Earth's gravitational field with axial symmetry with zonal harmonic terms up to J 36 . Numerical results proved the very high efficiency and flexibility of the developed equations.
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Sharaf, M.A., Awad, M.ES. & Najmuldeen, S.AS.A. Motion of artificial satellites in the set of Eulerian redundant parameters (III). Earth Moon Planet 56, 141–164 (1992). https://doi.org/10.1007/BF00056354
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DOI: https://doi.org/10.1007/BF00056354
