Satellite non-gravitational orbital perturbations and the detection of the gravitomagnetic clock effect

The general relativistic gravitomagnetic clock effect consists of the fact that two massive test bodies orbiting a central spinning mass in its equatorial plane along two identical circular trajectories, but in opposite directions, take different times in describing a full revolution with respect to an asymptotically inertial observer. In the field of the Earth such time shift amounts to 10(-7) s. Detecting it by means of a space-based mission with artificial satellites is a very demanding task because there are severe constraints on the precision with which the radial and azimuthal positions of a satellite must be known: deltar similar to 10(-2) cm and delta phi similar to 10(-2) milliarcseconds (mas) per revolution. In this paper we assess whether the systematic errors induced by various non-gravitational perturbations allow one to meet such stringent requirements. A pair of identical, passive laser-ranged satellites of LAGEOS type with their spins aligned with the Earth's is considered. It turns out that all the non-vanishing non-gravitational perturbations induce systematic errors in r and phi within the required constraints for a reasonable assumption of the mismodelling in some parameters for satellites and the Earth and/or by using dense satellites with small area-to-mass ratio. However, the error in the Earth's GM is by far the largest source of uncertainty in the azimuthal location which is affected at a level of 1.2 mas/revolution.