Numerical verification of analytic expressions for the perturbations due to an arbitrary zonal harmonic of the geopotential
- 45 Downloads
- 2 Citations
Abstract
Expressions are given for the first order node-to-node perturbations in the orbital elements of a satellite due to an arbitrary zonal harmonic of the geopotential. Accurate and efficient procedures for computing such perturbations are necessary for orbit determination methods which will fully utilize the highly accurate observations now available.
Comparison with a double precision numerical integration is made for an intermediate altitude satellite, TELSTAR I. (Second order perturbations due to the second harmonic, derived elsewhere, are included, as are the first order perturbations due to the zonals through fourteenth order.) Discrepancies in semi-major axis after 1 period are of the order of 0.1 mm. Discrepancies in timing are of the order of 0.03 msec. A detailed discussion of computational efficiency is included.
Keywords
Computational Efficiency Determination Method Orbital Element Orbit Determination Double PrecisionPreview
Unable to display preview. Download preview PDF.
References
- Claus, A. J.: 1968, private communication, September 3.Google Scholar
- Claus, A. J. and Lubowe, A. G.: 1963, ‘A High Accuracy Perturbation Method with Direct Application to Communication Satellite Orbit Prediction’,Astronaut. Acta 9, Fasc. 5–6, 275–301.Google Scholar
- Groves, G. V.: 1960, ‘Motion of a Satellite in the Earth's Gravitational Field,’Proc. Roy. Soc. A 254, 48–65.Google Scholar
- Kaula, W. M.: 1966,Theory of Satellite Geodesy, Blaisdell Publishing Company.Google Scholar
- Kozai, Y.: 1964, ‘New Determination of Zonal Harmonics Coefficients of the Earth's Gravitational Potential’, Smithsonian Astrophysical Observatory Report SAO 165, November 2.Google Scholar
- Lubowe, A. G.: 1964, ‘High Accuracy Orbit Prediction From Node to Node’Astronaut. Acta 10, Fasc. 3–4, 253–261.Google Scholar
- Peirce, B. O. and Foster, R. M.: 1956,A Short Table of Integrals, 4th ed., Ginn and Company.Google Scholar