Analytic models for a spherical satellite charging in sunlight at any spin rate
We present analytic models for the steady state potential distributions surrounding a spinning, dielectric-coated, spherical spacecraft charging in sunlight. The sun direction is assumed to lie in the satellite bellyband plane, perpendicular to the spin axes. The models are based on a multipole expansion of Laplacian potentials external to the spacecraft surface. The combination of monopole potentials along with the dipole or quadrupole contributions produce potential barriers which form at the satellite surface. These barriers can block escaping photoelectrons and lead to current balance, allowing sunlight charging to high negative levels. In a previous treatment, analytic models were limited to fast spin relative to differential charging rates so that the solutions had azimuthal symmetry around the spin axes. By introducing an associated Legendre term into the potential expansion, the azimuthal symmetry is removed, and the models can be developed to encompass any spin rate. The analysis turns up three functions of spin rate which are only known at the spin limits, but the characteristics of the charging of a rotating sphere can be explored using approximate forms which represent the basic trends. For finite spin, the sunlit side charges less (negatively) than the shade side which is in contrast to the fast spin case, where these two potentials are equal. Also, for finite spin, differential charging develops perpendicular to the sun and spin axis directions, due to the transverse motion. This transverse charging occurs at all finite spin rates, disappearing only at the zero and infinite spin limits. There is a correlated lag angle between the direction of maximum sheath radius and the sun line. Plots are given to illustrate the potential distributions representing barrier dominated sunlight charging of a spinning dielectric coated spherical satellite.