Abstract
We present four integration methods which exploit efficient numerical techniques for orbit propagation. The methods have been selected to compare the strategy of using first order differential equations, required by the use of regularization, to integrating the equations of motion directly so that second order integrators can be used.
All the methods have demonstrated high levels of orbital accuracy as well as very short integration times in astronomical simulations of long term dynamical evolution. We outline the bases of these techniques and illustrate their accuracy by comparing the orbital predictions with data from a GPS receiver on board a satellite in Sun synchronous LEO orbit.
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AARSETH, S. “Multiple Time Scales,” ed. J.U. BRACKBILL & B.I. COHEN, Academic Press, Orlando, 1985, pp. 377.
BELBRUNO, E. A., and MILLER, J. K. “Sun-Perturbed Earth-to-Moon Transfers with Ballistic Capture,” Journal of Guidance, Control and Dynamics, Vol. 16, 1993, pp. 770–775.
BULIRSCH, R., and STOER, J. “Numerical Treatment of Differential Equations by Extrapolation Methods,” Numerical Mathematics, Vol. 8, 1966, pp. 1–13.
GOLD, K., BERTIGER, W., YUNCK T., WU, S., MULLERSCHOEN, R., BORN, G., and LARSON, K. “A Study of Real Time Orbit Determination for the Extreme Ultra Violet Explorer,” Proceedings of the National Technical Meeting of the Institute of Navigation, San Diego, 1994, pp. 625–634.
GOLD, K., REICHERT, A., BORN., G., BERTIGER, W., WU, S., and YUNCK, T. “GPS Orbit Determination in the Presence of Selective Availability for the Extreme Ultra Violet Explorer,” Proceedings of ION GPS-94, Institute of Navigation, Salt Lake City, 1994, pp. 1191–1199.
HANSON, J. M., EVANS, M. J., and TURNER, R. E. “Designing Good Partial Coverage Satellite Constellations,” Journal of the Astronautical Sciences, Vol. 40, 1992, pp. 215–239.
KUSTAANHEIMO, P. “Die Spinordarstellung der energetischen Identitäten der Keplerbewegung,” In: E. Stiefel (ed.): Mathematische Methoden der Himmelsmechanik und Astronautik, 1964, pp. 333–340.
KUSTAANHEIMO, P., and STIEFEL, E. “Perturbation Theory of Kepler Motion Based on Spinor Regularization,” Journal Fur Reine und Angewandte Mathematik, Vol. 218, 1965, pp. 204–219.
LEVI-CIVITA, T. “Sur la régularisation du problème des trois corps,” Acta Mathematica, Vol. 42, 1920, pp. 99–144.
MARTŃ, P., and FERRÁNDIZ, J. M. “Behaviour of the SMF Method for the Numerical Integration of Satellite Orbits,” Celestial Mechanics and Dynamical Astronomy, Vol. 63, 1995, pp. 29–40.
PALACIOS, M., and CALVO, C. “Ideal Frames and Regularization in Numerical Orbit Computation,” Journal of the Astronautical Sciences, Vol. 44, 1996, pp. 63–77.
RAJESHWARI, P. S., PUROHIT, N., RAMANI, N., and GAMBHIR, R. D. “Simulation Algorithm for Availability Computation of a Communication Satellite Constellation,” Journal of Spacecraft Technology, Vol. 4, 1994, pp. 68–77.
ROWLANDS, D.D., McCARTHY, J. J., TORRENCE, M.H., and WILLIAMSON, R.G. “Multi-Rate Numerical Integration of Satellite Orbits for Increased Computational Efficiency,” Journal of the Astronautical Sciences, Vol. 43, 1995, pp. 89–100.
STIEFEL, E.L., and SCHEIFELE, G. Linear and Regular Celestial Mechanics, Springer, Berlin, 1971.
UNWIN, M., and SWEETING, M. “A Practical Demonstration of Low-Cost Autonomous Orbit Determination using GPS,” Proceedings of ION GPS-95, Institute of Navigation, Palm Springs, 1995, pp. 579–587.
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Palmer, P.L., Aarseth, S.J., Mikkola, S. et al. High Precision Integration Methods for Orbit Propagation. J of Astronaut Sci 46, 329–342 (1998). https://doi.org/10.1007/BF03546385
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DOI: https://doi.org/10.1007/BF03546385