Hill stability of the planar three-body problem - General and restricted cases

Details Hill stability of the planar three-body problem - General and restricted cases Hill stability of the planar three-body problem - General and restricted cases

Mar 1992

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992cemda..54..255n&link_type=abstract

Celestial Mechanics and Dynamical Astronomy (ISSN 0923-2958), vol. 54, no. 1-3, p. 255-260.

Astronomy and Astrophysics

Astronomy

1

Circular Orbits, Coordinate Transformations, Three Body Problem, Celestial Mechanics, Equations Of Motion, Jacobi Integral, Motion Stability

Scientific paper

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.

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