Astronomy and Astrophysics – Astrophysics
Scientific paper
Mar 1976
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976ap%26ss..40..201h&link_type=abstract
Astrophysics and Space Science, vol. 40, Mar. 1976, p. 201-224.
Astronomy and Astrophysics
Astrophysics
20
Dynamic Stability, Numerical Stability, Solar Orbits, Three Body Problem, Equations Of Motion, Orbit Calculation, Planetary Systems, Solar System
Scientific paper
Several families of periodic orbits are presented for the general three-body problem in the case where the masses of two bodies are small, but not negligible, in comparison with the mass of the third body. These families are considered as representing a planetary system in which the body with the large mass is the star and the other bodies are two planets or comets. An example is given which closely describes the sun-Jupiter-Saturn system, a system that is known to be almost periodic in rotating coordinates. A stability analysis shows that planetary systems in which the two planets have relatively small masses and eccentricities are stable, while those in which the planets have relatively large masses and eccentricities are unstable. A connection is established between the present families of orbits and the orbits of the restricted three-body problem.
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