Computer solutions of magnetopause shapes

Computer solutions are presented for the magnetopause shape of a configuration with axial symmetry. Surface currents flowing on a magnetopause cancel the magnetic field outside the magnetopause. The general expression for the magnetic vector potential of the surface currents may be expanded via Legendre polynomials. Michel (1977) has shown that the summed variable (h) of the generating function for the Legendre polynomials may be introduced into the vector potential equation. When the correct expression for the shape of a magnetopause is inserted into the integrand, the integral is independent of h. A computer program has been developed to check this independence for various parameterized solutions for a magnetopause and thus determine an approximate solution. The equations have been developed for the case of a solar wind interacting with a dipole magnetic field. The magnetic axis is aligned with the solar wind flow, so this problem has azimuthal symmetry. This configuration is called the Uranus problem. If Uranus had an intrinsic dipole magnetic field with axis aligned with its rotation axis, one pole would point approximately into the solar wind flow every forty two years