Abstract
An analytic solution for theJ 2 perturbed equatorial orbit is obtained in terms of elliptic functions and integrals. The necessary equations for computing the position and velocity vectors, and the time are given in terms of known functions. The perturbed periapsis and apoapsis distances are determined from the roots of a characteristic cubic.
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References
Battin, R. H.: 1964,Astronautical Guidance, McGraw-Hill, New York.
Brouwer, D.: 1959,Astron. J. 64, (1274), 378–397.
Byrd, P. F. and Friedman, M. D.: 1971,Handbook of Elliptic Integrals for Engineers and Scientists, Springer-Verlag, New York.
Cohen, C. J. and Lyddane, R. H.: 1981,Celest. Mech. 25, 221.
Jezewski, D. J.: 1983,Celest. Mech. 30, 343 (this issue).
Lyddane, R. H.: 1963,Astron. J. 68, 555.
O'Mathuna, D.: 1970,Celest. Mech. 1, 467.
Ramnath, R.: 1973,Celest. Mech. 8, 85.
Sterne, T. E.: 1957,Astron. J. 63, (1255), 28–40.
Vinti, J. P.: 1961,J. Res. NBS 65B (Math. Phys.), 169.
Vinti, J. P.: 1962,J. Res. NBS 66B (Math. Phys.), 5.
Whittaker, E. T.: 1944,A Treatise on the Analytical Dynamics of Particles and Rigid Bodies, Cambridge University Press, 80 pp.
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Jezewski, D.J. An analytic solution for theJ 2 perturbed equatorial orbit. Celestial Mechanics 30, 363–371 (1983). https://doi.org/10.1007/BF01375506
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DOI: https://doi.org/10.1007/BF01375506