Families of frozen orbits of lunar artificial satellites

Approximation of artificial satellites' preliminary orbits: The efficiency challenge

In this paper the problem of the determination of the preliminary orbit of a celestial body is studied. We compare the results obtained by the classical Gauss’s method with those obtained by some higher-order iterative methods for solving nonlinear equations. The original problem of the determination of the preliminary orbits was posed by means of a nonlinear equation. We modify this equation i...

Orbital phasing of satellites on circular orbits

Asymptotic Analysis of Displaced Lunar Orbits

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Horseshoe Periodic Orbits for Saturn Coorbital Satellites

We consider the motion of coorbital satellites in the framework of the Restricted Three Body problem for We show a mechanism to generate horsehoe periodic orbits and we compute some families of horseshoe periodic orbits when vary ing the Jacobian constant We conclude that there exist stable horseshoe periodic orbits which t with the motion of Saturn coorbital satellites Janus and Epimetheus

Hill Problem Analytical Theory to the Order Four: Application to the Computation of Frozen Orbits around Planetary Satellites

Frozen orbits of the Hill problem are determined in the double-averaged problem, where short and long-period terms are removed by means of Lie transforms. Due to the perturbation method we use, the initial conditions of corresponding quasi-periodic solutions in the nonaveraged problem are computed straightforwardly. Moreover, the method provides the explicit equations of the transformation that...