Three-body orbital stability criteria for circular retrograde orbits

Details Three-body orbital stability criteria for circular retrograde orbits Three-body orbital stability criteria for circular retrograde orbits

Jan 1994

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994mnras.266...25d&link_type=abstract

Monthly Notices of the Royal Astronomical Society, vol. 266, p. 25

Astronomy and Astrophysics

Astronomy

13

Circular Orbits, Three Body Problem, Celestial Mechanics, Stellar Systems, Stellar Orbits, Systems Stability, Astronomical Models

Scientific paper

Previous investigations of the stability of hierarchical three-body retrograde systems moving on circular orbits by various authors have led to conflicting results and conclusions. The problem is reexamined, and the new numerical results indicate that these retrograde systems are more stable than their prograde counterparts with the same mass combinations. Although this result is similar to that of Harrington (1972-1977), there is no quantitative agreement between the actual values, except for the equal-mass case where there is complete agreement. The analytical (c-squared)H method which provides a sufficient condition for stability is found to be a poor indicator of orbital stability in this case, unlike the situation found for comparable prograde systems by Donnison and Mikulskis (1992). It is found that a functional form similar to that used by Black (1982) to fit prograde systems gives reasonable first approximations to the new results. The boundaries of stability are also examined for the inner-planet, outer-planet, and satellite mass combinations.

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