Abstract
An analytic model for third-body perturbations and for the second zonal harmonic of the central body's gravitational field is presented. A simplified version of this model applied to the Earth-Moon-Sun system indicates the existence of high-altitude and highly-inclined orbits with their apsides in the equator plane, for which the apsidal as well as the nodal motion ceases. For special positions of the node, secular changes of eccentricity and inclination disappear too (“balanced” orbits). For an ascending node at vernal equinox, the inclination of balanced orbits is 94.56°, for a node at autumnal equinox 85.44°, independent of the eccentricity of the orbit. For a node perpendicular to the equinox, there exist circular balanced orbits at 90° inclination. By slightly adjusting the initial inclination as suggested by the simplified model, orbits can be found — calculated by the full model or by different methods — that show only minor variations in eccentricity, inclination, argument of perigee, and longitude of the ascending node for 105 revolutions and more. Orbits near the unstable equilibria at 94.56° and 85.44° inclination show very long periodic librations and oscillations between retrogade and prograde motion.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Allan, R.R. and Cook, G.E.: 1964,Proc. R. Soc. Lond. A 280, 97–109.
Cook, G.E.: 1962,Geophys. J. R. Astr. Soc. 6, 271–291.
Hough, M.E.: 1981,Celest. Mech. 25, 111–136.
Hughes, S.: 1980,Proc. R. Soc. Lond. A 372, 243–264.
King-Hele, D.G.: 1958,Proc. R. Soc. Lond. A 247, 49–72.
Kozai, Y.: 1959, ‘The Earth's Gravitational Potential Derived from the Motion of Satellite 1958 Beta Two’,Smithsonian Inst. Astrophys. Observ. Spec. Rep. 22, 03/1959, 1–6.
Lidov, M.L.: 1961,Planet. Space Sci. 9, 719–759.
Lidov, M.L.: 1962, ‘On the Approximated Analysis of the Orbit Evolution of Artificial Satellites’, inDynamics of Satellites, pp. 168–179.
Lorell, J.: 1965,J. Astronaut. Sci. 12, 142–152.
Meeus, J.: 1980, ‘Astronomical Formulae for Calculators’,Monografieën over Astronomie en Astrofysica 4.
Montenbruck, O.: 1984, ‘Grundlagen der Ephemeridenrechnung’,Sterne und Weltraum Taschenbuch 10.
Orlov, A.A.: 1954,Tr. Gos. Astron. Inst. Mosk. Gos. Univ. 24, 139–153.
Roy, A.E.: 1969,Astrophysics and Space Science 4, 375–386.
Shapiro, I.I.: 1962, ‘The Prediction of Satellite Orbits’, in M. Roy (ed.),Dynamics of Satellites, pp. 257–312.
Solari G. and Viola R.: 1992, ‘M-HEO: The Optimal Satellite System for the Most Highly-Populated Regions of the Northern Hemisphere’,ESA Bull. 70, 05/1992, 81–88.
Stumpff, K. and Weiss, E.H.: 1968a, ‘A Fast Method of Orbit Computation’,NASA TN D-4470, 04/1968, 37 p.
Stumpff, K. and Weiss, E.H.: 1968b, ‘Application of an N-body Reference Orbit’,The J. Astronaut. Sci. XV, No. 5, pp. 257–261.
Stumpff, K.: 1974, ‘Himmelsmechanik’,Vol. III, Chap. XXXI, Sect. 258, pp. 322–327.
Wolfram, S.: 1988, ‘Mathematica: A System for Doing Mathematics by Computer’, 2nd ed.
Author information
Authors and Affiliations
Additional information
Retired from IBM Vienna Software Development Laboratory.
Rights and permissions
About this article
Cite this article
Kudielka, V. Balanced earth satellite orbits. Celestial Mech Dyn Astr 60, 455–470 (1994). https://doi.org/10.1007/BF00692028
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00692028