Effect of Geomagnetic Field on Motion of Passive Conductive Satellites

In this paper we analyze theoretically the effect of geomagnetic field on rotation of passive conductive satellites of a spherical shape such as Russian-Australian satellite WESTPAC or Russian satellite Larets. The main cause of this effect is the generation of eddy currents and satellite magnetic moment, which interact with the Earth’s magnetic field. The analytical solutions have been derived for orbital and intrinsic magnetic moments of satellite, which result from a translatory motion of an Earth-orbiting satellite and from a satellite spin around axes passing through its center of mass. An arbitrary relation between skin layer depth and satellite radius is assumed. Both a torque acting on satellite in geomagnetic field and the changes in its angular velocity are derived. The satellite orbiting the Earth in a circular orbit with an arbitrary tilt of the orbital plane is studied having regard to rotation of the vector of geomagnetic dipole moment. A characteristic time it takes for the angular velocity of the satellite to decrease exponentially is estimated. Peculiarities of residual irregular vibrations of the satellite angular velocity are examined.