On the coupling of lunisolar resonances for Earth satellite orbits

Astronomy and Astrophysics – Astronomy

Scientific paper

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Artificial Satellites, Lunisolar Perturbations, Resonances, Analytical Methods

Scientific paper

The resonance C1 occurs when the longitude of the perigee measured from the equinox becomes a slow angle in the doubly averaged equations of motion. This resonance is one of the `critical inclination' family with I ~ 46°. For prograde Earth satellite orbits, up to five critical points can be identified. Only simple pitchfork bifurcations occur for the single resonance C1. A two degrees of freedom system is studied to check how a coupling of two lunisolar resonances affects the results furnished by the analysis of an isolated resonance case. In the system with two critical angles (g+h and h,+2 λsolar, seven types of critical points have been identified. The critical points arise and change their stability through 11 bifurcations. If the initial conditions are selected close to the critical points, the system becomes chaotic as shown in Poincaré maps.

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