Abstract
The transformation of classical orbit element perturbations to perturbations in position and velocity in the radial, transverse and normal directions of the orbital frame is developed. The formulation is given for the case of mean anomaly perturbations as well as for eccentric and true anomaly perturbations. Approximate formulas are also developed for the case of nearly circular orbits and compared with those found in the literature.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Broucke, R.: 1970, ‘On the Matrizant of the Two-Body Problem’,Astr. & Astrophys. 6, 173.
Brouwer, D.: 1959, ‘Solution of the Problem of Artificial Satellite Theory without Drag’,Astron. J. 64, 378.
Brouwer, D. and Clemence, G.M.: 1961,Methods of Celestical Mechanics, Academic Press, New York.
Christodoulidis, D.C., Smith, D.E., Williamson, R.G. and Klosko, S.M.: 1988, ‘Observed Tidal Braking in the Earth/Moon/Sun System’,J. Geophys. Res. 93 (B6), 6216.
Engelis, T.L.: 1987,Radial Orbit Error Reduction and Sea Surface Topography Determination Using Satellite Altimetry, Report No. 377, Dept. of Geodetic Science and Surveying, The Ohio State University, Columbus, Ohio 43210.
Herrick, W.S.: 1971,Astrodynamics, Vol. II, Van Nostrand Reinhold, London.
Kaula, W.M.: 1966,Theory of Satellite Geodesy, Blaisdell, Waltham, Massachusetts.
Kaula, W.M.: 1983, ‘Inference of Variations in the Gravity Field from Satellite-to-Satellite Range-Rate’,J. Geophys. Res. 88 (B10), 8345.
Roy, A.E.: 1982,Orbital Motion, Adam Hilger, Bristol.
Rosborough, G. W.: 1986,Satellite Orbit Perturbations Due to the Geopotential, Report CSR-86-1, The University of Texas at Austin, Austin, Texas 78712.
Rosborough, G. W. and Tapley, B.D.: 1987, ‘Radial, Transverse and Normal Perturbations due to the Geopotential’,Celestial Mechanics 40, 409.
Sconzo, P.: 1963, ‘Explicit Expressions for the 36 Terms of the Jacobian Matrix Used in Orbit Computations’,Mem. Soc. Astron. Italiana 34 (2).
Smart, W.M.: 1953,Celestial Mechanics, Longmans, London.
Sterne, T.E.: 1960,An Introduction to Celestial Mechanics, Wiley Interscience, New York.
Tapley, B.D. and Rosborough, G.W.: 1985, ‘Geographically Correlated Orbit Errors and Its Effects on Satellite Altimetry’,J. Geophys. Res. 90 (C6), 11817.
Wagner, C.A.: 1987, ‘Geopotential Orbit Variations: Applications to Error Analysis’,J. Geophys. Res. 92 (B8), 8136.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Casotto, S. Position and velocity perturbations in the orbital frame in terms of classical element perturbations. Celestial Mech Dyn Astr 55, 209–221 (1993). https://doi.org/10.1007/BF00692510
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00692510