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

Martı́n Lara | Zendy; Jesús F. Palacián | Zendy

Open Access

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

Author(s) -

Martı́n Lara,

Jesús F. Palacián

Publication year - 2009

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2009/753653

Subject(s) - computation , perturbation theory (quantum mechanics) , periodic orbits , perturbation (astronomy) , first order , transformation (genetics) , order (exchange) , mathematics , celestial mechanics , mathematical analysis , physics , classical mechanics , algorithm , quantum mechanics , biochemistry , chemistry , finance , economics , gene

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

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