Applied Mathematics & Information Sciences

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Low-altitude Earth orbits provide important benefits for space missions. Among these benefits are the high-resolution images and resupply. In the present work, we studied the dynamics of Earth satellites that move in low orbits. The force model comprises the gravitational resonance 13:1, besides the Earth’s gravitational potential up to the second degree and order. In order to avoid the appearance of singularities, the quasi-Hamiltonian equations of motion are formulated in terms of non-singular universal variables instead of Delaunay variables. We integrated numerically the equations of motion and performed some numerical simulations. It is found that the variations in eccentricity and inclination are small. In addition, we studied the effect of gravitational resonance 13:1 on the dynamics using Lagrange planetary equations. It is found that the effect of the gravitational resonance 13:1 in low Earth orbits is about tens of meters.

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