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The generalized F and G series for the satellite orbit propagation | ||
| Earth Observation and Geomatics Engineering | ||
| مقاله 1، دوره 1، شماره 2، اسفند 2017، صفحه 71-81 اصل مقاله (854.99 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22059/eoge.2017.235787.1008 | ||
| نویسنده | ||
| Mohammad Reza Seif* | ||
| Department of Civil Engineering, Imam Hossein University (IHU), Tehran, Iran | ||
| چکیده | ||
| In this paper, an advanced version of the Lagrange method, F and G series, is proposed for the many applications in the celestial mechanics and space science such as initial orbit determination and satellite orbit propagation. In this development, the Lagrange coefficients were developed from a gravitational field of an inhomogeneous attractive body to all the perturbing accelerations acting on an orbiter. The efficiency of the method is tested for the satellite orbit propagation. This assessment is based on the comparison between the Lagrange solution and the analytical one for Keplerian motion and numerically integrated orbit for non-Keplerian motion. The discrepancy at centimeter and sub-centimeter accuracy shows the performance of the developed algorithm for MEO and LEO satellites orbit propagation. The results of computational time showed that the Lagrange method is as time-consuming as the multi-step methods where it is faster than the single-step methods. Besides the CPU-time, the stability test of the Lagrange method shows that it is as stable as the single-step and is more stable than the multi-step methods at the equivalent orders. Therefore, the Lagrange method offers the advantages of the single- and multi-step methods. | ||
| کلیدواژهها | ||
| Lagrange coefficients؛ Satellite orbit propagation؛ F and G functions؛ LEO satellite؛ MEO satellites | ||
| مراجع | ||
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Bem, J., & Szczodrowska-Kozar, B. (1995). High order F and G power series for orbit determination. Astronomy and Astrophysics Supplement Series, 110, 411. Beutler, G. (2004). Methods of celestial mechanics volume ii: application to planetary system, geodynamics and satellite geodesy [M]: Berlin, Heidelberg: Springer-Verlag. Butcher, J. (1987). The Numerical Analysis of Ordinary Differential Equations: Runge–Kutta and General Linear Methods: John Wiley & Sons, Chichester, New York. Chapront-Touzé, M., & Chapront, J. (1983). The lunar ephemeris ELP 2000. Astronomy and Astrophysics, 124, 50-62. Curtis, H. D. (2005). Orbital mechanics for engineering students (Third edition. ed.). Dahlquist, G., & Björk, Å. (1974). Translated by N. Anderson. 1974. Numerical Methods: Prentice Hall, New Jersey. Dormand, J., & Prince, P. (1978). New Runge-Kutta algorithms for numerical simulation in dynamical astronomy. Celestial Mechanics, 18(3), 223-232. Escobal, P. R. (1965). Methods of orbit determination. New York: Wiley, 1965, 1. Feng, Y. (2001). An alternative orbit integration algorithm for gps-based precise leo autonomous navigation. GPS Solutions, 5(2), 1-11. Goodyear, W. H. (1965). Completely general closed-form solution for coordinates and partial derivative of the two-body problem. The Astronomical Journal, 70, 189. Hairer, E., & Wanner, G. (1991). Solving ordinary differential equations, vol. II: Springer Verlag, Berlin. Lemoine, F. G., Kenyon, S. C., Factor, J. K., Trimmer, R. G., Pavlis, N. K., Chinn, D. S., Torrence, M. H. (1998). The Development of the Joint NASA GSFC and the National Imagery and Mapping Agency(NIMA) Geopotential Model EGM 96. NASA(19980218814). Lin, L., & Xin, W. (2003). A method of orbit computation taking into account the earth's oblateness. Chinese Astronomy and Astrophysics, 27(3), 335-339. doi: http://dx.doi.org/10.1016/S0275-1062(03)90056-7 Taylor, C. J., & Kriegman, D. J. (1994). Minimization on the Lie group SO (3) and related manifolds. Yale University. McCarthy, D. D., & Petit, G. (2003). IERS conventions. Paper presented at the IAU Joint Discussion. Montenbruck, O. (1989). Practical ephemeris calculations (A. H. Armstrong, Trans.): Springer-verlag Heidelberg. Montenbruck, O. (1992). Numerical integration of orbital motion using Taylor series. Spaceflight mechanics 1992, 1217-1231. Montenbruck, O., & Gill, E. (2000). Satellite orbits: Springer. Pellegrini, E., Russell, R., & Vittaldev, V. (2014). F and G Taylor series solutions to the Stark and Kepler problems with Sundman transformations. Celestial Mechanics and Dynamical Astronomy, 118(4), 355-378. doi: 10.1007/s10569-014-9538-7 Picone, J., Hedin, A., Drob, D. P., & Aikin, A. (2002). NRLMSISE‐00 empirical model of the atmosphere: Statistical comparisons and scientific issues. Journal of Geophysical Research: Space Physics (1978–2012), 107(A12), SIA 15-11-SIA 15-16. Schaub, H., & Junkins, J. L. (2003). Analytical mechanics of space systems: Aiaa. Sconzo, P., LeSchack, A., & Tobey, R. (1965). Symbolic computation of F and G series by computer. The Astronomical Journal, 70, 269. Seeber, G. (2003). Satellite geodesy: foundations, methods, and applications: Walter de Gruyter. Shampine, L. F. (2005). Error estimation and control for ODEs. Journal of Scientific Computing, 25(1), 3-16. Shampine, L. F., & Reichelt, M. W. (1997). The matlab ode suite. SIAM journal on scientific computing, 18(1), 1-22. Sharifi, M. A., & Seif, M. R. (2011). Dynamic orbit propagation in a gravitational field of an inhomogeneous attractive body using the Lagrange coefficients. Advances in Space Research, 48(5), 904-913. doi: http://dx.doi.org/10.1016/j.asr.2011.04.021 Sharifi, M. A., Sneeuw, N., Seif, M. R., & Farzaneh, S. (2013). A semi-analytical formulation of the Earth's flattening on the satellite formation flying observables using the Lagrange coefficients. Paper presented at the Hotine-Marussi Symposium, Rome, Italy. Steffensen, J. F. (1956). On the restricted problem of three bodies. Mat.-fys. medd.; Bd 30. Tapley, B., Schutz, B., & Born, G. H. (2004). Statistical orbit determination: Academic Press. Taylor, C. J., & Kriegman, D. J. (1994). Minimization on the Lie group SO and related manifolds. Yale University. | ||
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