The N-Dipole Problem and the Rings of Saturn

Abstract

N-magnetic dipoles each located on a star-member of an n-body star system, are assumed to move with their carrier stars and control the motions of charged grains in their vicinity. The case N=5, in a special configuration, where four dipoles perform rigid rotation about the fifth, while all have magnetic moments parallel to the angular velocity vector, is used as a test case to show that the "spaces of trapping" found to exist in the two and three dipole problems, receive a form similar to the rings of Saturn and that pairs of "spaces of trapping" are separated by gaps similar to the Cassini division- The effect of gravity of a rotating planet within which the five dipoles, of internal "dynamo" origin exist and corrotate are taken into account. In the Appendix a model called N-D (N-Dipole) equivalent to the Z3 model for Saturn is given.