Some properties of a two-body system under the influence of the Galactic tidal field

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 similar to 50 000 au, chaotic orbits are found for (e < 0.15, 40 degrees less than or equal to i less than or equal to 140 degrees) as determined by integrating the evolution of the comet over a period of 10(4) orbits. These regions of chaos increase in size with increasing semimajor axis. The typical e-folding times for these orbits range from around 600 Myr to 1 Gyr 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.