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

Martin Lara and Jesús F. Palacián

Mathematical Problems in Engineering, 2009, vol. 2009, 1-18

Abstract:

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 connects the averaged and nonaveraged models. A fourth-order analytical theory is necessary for the accurate computation of quasi-periodic frozen orbits.

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:753653

DOI: 10.1155/2009/753653

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