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A note on lower bounds for relative equilibria in the main problem of artificial satellite theory. (English) Zbl 1162.70327
Summary: In the analytical approach to the main problem in satellite theory, the consideration of the physical parameters imposes a lower bound for normalized Hamiltonian. We show that there is no elliptic frozen orbits, at critical inclination, when we consider small values of H, the third component of the angular momentum. The argument used suggests that it might be applied also to more realistic zonal and tesseral models. Moreover, for almost polar orbits, when \(H\) may be taken as another small parameter, a different approach that will simplify the ephemerides generators is proposed.

MSC:
70M20 Orbital mechanics
70F15 Celestial mechanics
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