Astronomy and Astrophysics – Astronomy
Scientific paper
Jul 2001
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2001mnras.324.1109b&link_type=abstract
Monthly Notices of the Royal Astronomical Society, Volume 324, Issue 4, pp. 1109-1116.
Astronomy and Astrophysics
Astronomy
12
Celestial Mechanics, Comets: General, Solar System: General
Scientific paper
In this paper the effect of the Galactic tidal field on a Sun-comet pair will be considered when the comet is situated in the Oort cloud and planetary perturbations can be neglected. First, two averaged models were created, one of which can be solved analytically in terms of Jacobi elliptic functions. In the latter system, switching between libration and circulation of the argument of perihelion is prohibited. The non-averaged equations of motion are integrated numerically in order to determine the regions of the (e,i) phase space in which chaotic orbits can be found, and an effort is made to explain why the chaotic orbits manifest in these regions only. It is evident that for moderate values of semimajor axis, a~50000au, chaotic orbits are found for (e<0.15, 40°<=i<=140°) as determined by integrating the evolution of the comet over a period of 104 orbits. These regions of chaos increase in size with increasing semimajor axis. The typical e-folding times for these orbits range from around 600Myr to 1Gyr and thus are of little practical interest, as the time-scales for chaos arising from passing stars are much shorter. As a result of Galactic rotation, the chaotic regions in (e,i) phase space are not symmetric for prograde and retrograde orbits.
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