Celletti A., Chessa A. , Hadjidemetriou J., Valsecchi G.B.
A systematic study of the stability of symmetric periodic orbits in the planar,
circular, restricted three-body problem
(964K, Postcript)
ABSTRACT. We investigate symmetric periodic orbits in the framework of the
planar, circular, restricted, three-body problem. Having fixed the
mass of the primary equal to that of Jupiter, we determine the
linear stability of a number of periodic orbits for different
values of the eccentricity. A systematic study of internal
resonances, with frequency $p/q$ with $2\leq p\leq 9$,
$1\leq q\leq 5$ and $4/3\leq p/q\leq 5$, offers an overall picture
of the stability character of inner orbits. For each resonance we
compute the stability of the two possible periodic orbits. A
similar analysis is performed for some external periodic orbits.
Furthermore, we let the mass of the primary vary and we study the
linear stability of the main resonances as a function of the
eccentricity and of the mass of the primary. These results lead
to interesting conclusions about the stability of exosolar
planetary systems. In particular, we study the stability of
Earth-like planets in the planetary systems HD168746, GI86,
47UMa,b and HD10697.