A noncanonical analytic solution to the J2 perturbed two-body problem

Details A noncanonical analytic solution to the J2 perturbed two-body problem A noncanonical analytic solution to the J2 perturbed two-body problem

Aug 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983cemec..30..343j&link_type=abstract

Celestial Mechanics (ISSN 0008-8714), vol. 30, Aug. 1983, p. 343-361.

Astronomy and Astrophysics

Astronomy

7

Artificial Satellites, Astrodynamics, Gravitational Effects, Orbital Mechanics, Satellite Perturbation, Two Body Problem, Angular Momentum, Differential Equations, Earth Orbits, Harmonic Oscillators, Position Errors, Velocity Errors

Scientific paper

The motion of a satellite subject to an inverse-square gravitational force of attraction and a perturbation due to the Earth's oblateness as the J2 term is analyzed, and a uniform, analytic solution correct to first-order in J2, is obtained using a noncanonical approach. The basis for the solution is the transformation and uncoupling of the differential equations for the model. The resulting solution is expressed in terms of elementary functions of the independent variable (the "true anomaly"), and is of a compact and simple form. Numerical results are comparable to existing solutions.

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