Abstract
The equations of motion of the planar three-body problem split into two parts, called an external part and an internal part. When the third mass approaches zero, the first part tends to the equations of the Kepler motion of the primaries and the second part to the equations of motion of the restricted problem.
We discuss the Hill stability from these equations of motion and the energy integral. In particular, the Jacobi integral for the circular restricted problem is seen as an infinitesimal-mass-order term of the Sundman function in this context.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Marchal, C. and Bozis, G: 1982, ‘Hill Stability and Distance Curves for the General Three-Body Problem’, Celest. Mech., 26, 311–333.
Milani, A. and Nobili, A.M.: 1983, ‘On Topological Stability in the General Three-Body Problem’, Celest. Mech, 31, 213–240.
Szebehely, V.: 1967, Theory of Orbits, Academic Press, New York.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Nakamura, T., Yoshida, J. Hill stability of the planar three-body problem: General and restricted cases. Celestial Mech Dyn Astr 54, 255–260 (1992). https://doi.org/10.1007/BF00049560
Issue Date:
DOI: https://doi.org/10.1007/BF00049560