Abstract
For Vinti's dynamical problem, there is proposed a new form of solution wherein all three coordinates are expressed in terms of one independent variable. The formulae for the three co-ordinates are clear generalizations of the corresponding formulae for the Kepler problem while the independent variable corresponds to the true anomaly. The solution is completed by the relation connecting the independent variable with time: the latter is a generalization of the well known Kepler time-angle relationship. From the form and method of solution the main qualitative features of the motion are readily derived.
Similar content being viewed by others
References
Aksenov, E. P., Gribenikov, E. A., and Demin, V. C.: 1964,Soviet Astron. 16, 164–174.
Brouwer, D. and Clemence, G. M.: 1962,Methods of Celestial Mechanics, Academic Press, New York.
Davis, H. T.: 1960,Introduction to Nonlinear Differential and Integral Equations, U.S. Govt. Printing Office, Washington, D.C.
Izsak, I. M.: 1960, ‘A Theory of Satellite Motion about an Oblate Planet’, Smithsonian Institute Astrophysical Observatory, Research in Space Science, Special Report No. 52.
O'Mathuna, D.: 1969, The Vinti Dynamical Problem and the Geopotential. NASA TR R-307, ERC, Cambridge, Mass.
Vinti, J. P.: 1959, ‘A New Method of Solution for Unretarded Satellite Orbits’,J. Res. NBS 63B;Math. Math. Phys. 2, 1965–116.
Vinti, J. P.: 1961, ‘Theory of an Accurate Intermediary Orbit for Satellite Astronomy,J. Res. NBS 65B;Math. Math. Phys. 3, 169–201.
Vinti, J. P.: 1963, ‘Zonal Harmonic Perturbations of an Accurate Reference Orbit of an Artificial Satellite’,J. Res. NBS 67B;Math. Math. Phys. 4, 191–222.
Vinti, J. P.: 1966a, ‘Invariant Properties of the Spheroidal Potential of an Oblate Planet and Inclusion of the Third Zonal Harmonic in an Accurate Reference Orbit of an Artificial Satellite’,J. Res. NBS 70B;Math. Math. Phys. 1, 1–16.
Vinti, J. P.: 1966b,Mathematische Methoden der Himmelsmechanik und Astrodynamik (ed. by E. Steifel), Bibliographisches Institut, Mannheim, Germany, pp. 97–111.
Whittaker, E. T.: 1944,Analytical Dynamics, 4th ed., Dover Publications, New York.
Whittaker, E. T. and Watson, G. N.: 1952,Modern Analysis, 4th ed., Camb. Univ. Press., Cambridge, England.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
O'Mathuna, D. Satellite prediction formulae for Vinti's model. Celestial Mechanics 1, 467–478 (1970). https://doi.org/10.1007/BF01231144
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01231144