Short-Term Orbit Prediction with J2 and Mean Orbital Elements
ABSTRACT
An analytical theory for calculating perturbations of the orbital elements of a satellite due to J2 to accuracy up to fourth power in eccentricity is developed. It is observed that there is significant improvement in all the orbital elements with the present theory over second-order theory. The theory is used for computing the mean orbital elements, which are found to be more accurate than provided by Bhatnagar and taqvi’s theory (up to second power in eccentricity). Mean elements have a large number of practical applications.
An analytical theory for calculating perturbations of the orbital elements of a satellite due to J2 to accuracy up to fourth power in eccentricity is developed. It is observed that there is significant improvement in all the orbital elements with the present theory over second-order theory. The theory is used for computing the mean orbital elements, which are found to be more accurate than provided by Bhatnagar and taqvi’s theory (up to second power in eccentricity). Mean elements have a large number of practical applications.
KEYWORDS
Perturbation Due to J2, Mean Orbital Elements, Short-Periodic Terms, Osculating Orbital Elements, Fourth Power in Eccentricit
Perturbation Due to J2, Mean Orbital Elements, Short-Periodic Terms, Osculating Orbital Elements, Fourth Power in Eccentricit
Cite this paper
nullS. Gupta, M. Raj and R. Sharma, "Short-Term Orbit Prediction with J2 and Mean Orbital Elements," International Journal of Astronomy and Astrophysics, Vol. 1 No. 3, 2011, pp. 135-146. doi: 10.4236/ijaa.2011.13018.
nullS. Gupta, M. Raj and R. Sharma, "Short-Term Orbit Prediction with J2 and Mean Orbital Elements," International Journal of Astronomy and Astrophysics, Vol. 1 No. 3, 2011, pp. 135-146. doi: 10.4236/ijaa.2011.13018.
References
[1] [1] Y. Kozai, “The Motion of a Close Earth Satellite,” Astronomical Journal, Vol. 64, 1959, pp. 367-377. [2] D. Brouwer, “Solution of the Problem of Artificial Satellite Theory without Drag,” Astronomical Journal, Vol. 64, 1959, pp. 378-396. doi:10.1086/107958 [3] G. A. Chebotarev, “Motion of an Artificial Satellite in an Orbit of Small Eccentricity,” AIAA Journal, Vol. 2, No. 1, 1964. [4] A.mDepritq and A. Rom, “The Main Problem of Satellite Theory for Small Eccentricities,” Celestial Mechanics, Vol. 2, No. 4, 1970, pp. 166-206. [5] K. Aksnes, “A Second-Order Artificial Satellite Theory Based on an Intermediate Orbit,” The Astronomical Journal, Vol. 75, No. 9, 1970: pp. 1066-1076. doi:10.1086/111061 [6] J. J. F. Liu, “Satellite Motion about an Oblate Earth,” AIAA Journal, Vol. 12, 1974, pp. 1511-1516. [7] H. Kinoshita, “Third-Order Solution of an Artificial Satellite Theory,” SAO Special Report #379, 1977. [8] K. B. Bhatnagar and Z. A. Taqvi, “Perturbations of the Elements of Near-Circular Earth Satellite Orbits,” Proceedings of the Indian National Science Academy, Vol. 43, No. 6, 1977, pp. 432-451. [9] R. H. Gooding, “A Second-Order Satellite Orbit Theory, with Compact Results in Cylindrical Coordinates,” Philosophical Transactions of the Royal Society, Vol. 299, No. 1451, 1981, pp. 425-474. [10] R. K. Sharma, “On Mean Orbital Elements Computation for Near-Earth Orbits,” Indian Journal of Pure and Applied Mathematics, Vol. 21, No. 5, 1990, pp. 468-474. [11] R. H. Gooding, “On the Generation of Satellite Position (and Velocity) by a Mixed Analytical-Numerical Procedure,” Advances in Space Research, Vol. 1, No. 6, 1981, pp. 83-93. doi:10.1016/0273-1177(81)90010-7 [12] Macsyma, Inc., “Mascsyma User’s Guide,” Macsyma, Inc., Boston, 1992 [13] E. L. Stiefel and G. Scheifele, “Linear and Regular Celestial Mechanics,” Springer-Verlag, Berlin, 1971. [14] R. K. Sharma and J. R. Xavier, “Long Term Orbit Computations with KS Uniformly Regular Canonical Elements with Oblateness,” Earth, Moon and Planets, Vol. 42, No. 2, 1988, pp. 163-178. doi:10.1007/BF00054544
[1] [1] Y. Kozai, “The Motion of a Close Earth Satellite,” Astronomical Journal, Vol. 64, 1959, pp. 367-377. [2] D. Brouwer, “Solution of the Problem of Artificial Satellite Theory without Drag,” Astronomical Journal, Vol. 64, 1959, pp. 378-396. doi:10.1086/107958 [3] G. A. Chebotarev, “Motion of an Artificial Satellite in an Orbit of Small Eccentricity,” AIAA Journal, Vol. 2, No. 1, 1964. [4] A.mDepritq and A. Rom, “The Main Problem of Satellite Theory for Small Eccentricities,” Celestial Mechanics, Vol. 2, No. 4, 1970, pp. 166-206. [5] K. Aksnes, “A Second-Order Artificial Satellite Theory Based on an Intermediate Orbit,” The Astronomical Journal, Vol. 75, No. 9, 1970: pp. 1066-1076. doi:10.1086/111061 [6] J. J. F. Liu, “Satellite Motion about an Oblate Earth,” AIAA Journal, Vol. 12, 1974, pp. 1511-1516. [7] H. Kinoshita, “Third-Order Solution of an Artificial Satellite Theory,” SAO Special Report #379, 1977. [8] K. B. Bhatnagar and Z. A. Taqvi, “Perturbations of the Elements of Near-Circular Earth Satellite Orbits,” Proceedings of the Indian National Science Academy, Vol. 43, No. 6, 1977, pp. 432-451. [9] R. H. Gooding, “A Second-Order Satellite Orbit Theory, with Compact Results in Cylindrical Coordinates,” Philosophical Transactions of the Royal Society, Vol. 299, No. 1451, 1981, pp. 425-474. [10] R. K. Sharma, “On Mean Orbital Elements Computation for Near-Earth Orbits,” Indian Journal of Pure and Applied Mathematics, Vol. 21, No. 5, 1990, pp. 468-474. [11] R. H. Gooding, “On the Generation of Satellite Position (and Velocity) by a Mixed Analytical-Numerical Procedure,” Advances in Space Research, Vol. 1, No. 6, 1981, pp. 83-93. doi:10.1016/0273-1177(81)90010-7 [12] Macsyma, Inc., “Mascsyma User’s Guide,” Macsyma, Inc., Boston, 1992 [13] E. L. Stiefel and G. Scheifele, “Linear and Regular Celestial Mechanics,” Springer-Verlag, Berlin, 1971. [14] R. K. Sharma and J. R. Xavier, “Long Term Orbit Computations with KS Uniformly Regular Canonical Elements with Oblateness,” Earth, Moon and Planets, Vol. 42, No. 2, 1988, pp. 163-178. doi:10.1007/BF00054544