Abstract
The motion of a satellite subject to an inverse-square gravitational force of attraction and a perturbation due to the Earth's oblateness as theJ 2 term is analyzed, and a uniform, analytic solution correct to first-order inJ 2, 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.
Similar content being viewed by others
References
Bond, V. R.: 1974,Celest. Mech. 10, 303.
Bond, V. R.: 1979, ‘An Analytical Singularity-Free Solution to theJ 2 Perturbation Problem’, NASA TM 58221.
Brouwer, D.: 1959,Astron. J. 64, No. 1274, 378–397.
Engles, R. C. and Junkins, J. L.: 1981,Celest. Mech. 24, 3.
Junkins, J. L. Kraige, L. G. Engels, R. C., and Ziems, L.: 1980, ‘Regularized Integration of Gravity Perturbed Trajectories’, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, Contract No. N60921-78-C-A214.
Kaplan, M. H.: 1976,Modern Spacecraft Dynamics and Control, John Wiley, New York, Chapter 8.
Lyddane, R. H.: 1963,Astron. J. 68, 555.
Mittleman, Don and Jezewski, Don: 1982,Celest. Mech. 28, 401.
Scheifele, G.: 1970,Celest. Mech. 2, 296–310.
Scheifele, G. and Graf, O.: 1974, ‘Analytical Satellite Theories Based on a New Set of Canonical Elements’,AIAA Paper 74-838.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Jezewski, D.J. A noncanonical analytic solution to theJ 2 perturbed two-body problem. Celestial Mechanics 30, 343–361 (1983). https://doi.org/10.1007/BF01375505
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01375505