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

Abstract

The general relativistic gravitomagnetic clock effectconsists of the fact that two massive test bodies orbitinga central spinning mass in its equatorial plane along twoidentical circular trajectories, but in oppositedirections, take different times in describing a fullrevolution with respect to an asymptotically inertialobserver. In the field of the Earth such time shiftamounts to 10-7 s. Detecting it by means of aspace-based mission with artificial satellites is a verydemanding task because there are severe constraints onthe precision with which the radial and azimuthalpositions of a satellite must be known: δr~10-2 cm and δφ~10-2 milliarcseconds (mas) per revolution. In thispaper we assess whether the systematic errors induced byvarious non-gravitational perturbations allow one to meetsuch stringent requirements. A pair of identical,passive laser-ranged satellites of LAGEOS type with theirspins aligned with the Earth's is considered. Itturns out that all the non-vanishing non-gravitationalperturbations induce systematic errors in r and φ within the required constraints for a reasonableassumption of the mismodelling in someparameters for satellites and the Earth and/or by usingdense satellites with small area-to-mass ratio. However,the error in the Earth's GM is by far the largestsource of uncertainty in the azimuthal location which isaffected at a level of 1.2 mas/revolution.