Stability of inner planetary systems

  • Victor Szebehely
Original Papers
Received:

Abstract

The model of the planar restricted problem of three bodies is used to evaluate the stability of the inner planets of planetary systems with arbitrary mass ratios. A quantitative measure of stability is introduced by finding the difference between the critical value of the Jacobian constant (at which bifurcation may occur) and the value of the Jacobian constant that corresponds to planetary type orbits. Hill's definition of stability is used according to which inner planetary orbits are stable if they are bounded in a region enclosing only the larger primary. For small values of the massparameter (μ<10−3) the maximum value of the dimensionless radius of the orbit for Hill-stability is given by 1−2.4 µ1/3.

Keywords

Quantitative Measure Mathematical Method Planetary System Type Orbit Restricted Problem 
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Zusammenfassung

Die Stabilität von inneren Planetensystemen mit beliebigen Massenverhältnissen wird am Modell des ebenen restringierten Dreikörperproblems untersucht. Aufgrund der Differenz zwischen dem kritischen Wert der Jacobi-Konstanten (wo Bifurkation eintreten kann) und dem einer Planetenbahn entsprechenden Wert wird ein quantitatives Stabilitätsmass eingeführt. Dabei wird die Hillsche Stabilitätsdefinition verwendet, d.h. eine innere Planetenbahn heisst stabil, wenn sie ein nur den grösseren Zentralkörper enthaltendes Gebiet nicht verlassen kann. Für klein Werte des Massenparameters (μ<10−3) beträgt der maximale (dimensionslose) Radius einer Hill-stabilen Planetenbahn 1−2.4 µ1/3.

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References

  1. R. Broucke, Jet Propulsion Laboratory Technical Report 32-1168 (1968).Google Scholar
  2. J. Hadjidemetriou, Celestial Mechanics12, 255 (1975).Google Scholar
  3. G. Hill, Am. J. Math.1, 5, 129, 245 (1878).Google Scholar
  4. V. Szebehely,Theory of Orbits, Academic Press, New York (1967).Google Scholar
  5. V. Szebehely andR. McKenzie, Astron. J.82, 303 (1977).Google Scholar
  6. V. Szebehely andK. Zare, Astron. and Astroph.58, 145 (1977).Google Scholar

Copyright information

© Birkhäuser Verlag 1979

Authors and Affiliations

  • Victor Szebehely
    • 1
  1. 1.Dept of Aerospace Eng. and Eng. MechanicsThe University of Texas at AustinUSA

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