A doubly averaging method for third body perturbations in planet equator coordinates

Details A doubly averaging method for third body perturbations in planet equator coordinates A doubly averaging method for third body perturbations in planet equator coordinates

Aug 1992

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992asdy.conf.2223h&link_type=abstract

IN: Astrodynamics 1991; Proceedings of the AAS/AIAA Astrodynamics Conference, Durango, CO, Aug. 19-22, 1991. Pt. 3 (A92-43251 18

Astronomy and Astrophysics

Astronomy

Eccentricity, Gravitational Fields, High Altitude Environments, Orbit Perturbation, Orbital Elements, Average, Coordinate Transformations, Earth Orbital Environments, Equations Of Motion, Numerical Integration

Scientific paper

The first order doubly averaged potential due to third-body gravity is derived in any arbitrary coordinates. The equations of motion are nonsingular at zero eccentricity. The derivation uses a recursive method which allows easy expansion to higher order terms. Instead of using analytical quadrature to obtain the doubly averaged potential, the method presented in this paper simply eliminates the mean anomaly of the perturbed and perturbing bodies by inspection of the recursive formulation. The derivatives of the orbital elements can be numerically integrated rapidly. When a planet equator coordinate system is used, they can be added directly to the derivatives due to gravity harmonics without any coordinate transformation. The method is applied to various high altitude missions. The results are compared with a high precision numerical integration method and are found to provide excellent agreement.

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