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

The general relativistic gravitomagnetic clock effect consists in 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: δr ∼ 10−2 cm and δφ ∼ 10−2 milliarcseconds per revolution. In this paper we assess if the systematic errors induced by various non-gravitational perturbations allow to meet such stringent requirements. A couple of identical, passive laser-ranged satellites of LAGEOS type with their spins aligned with the Earth’s one is considered. It turns out that all the non vanishing non-gravitational perturbations induce systematic errors in r and φ within the required constraints for a reasonable assumption of the mismodeling in some satellite’s and Earth’s parameters 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 milliarcseconds per revolution.