On the possibility of measuring accurately the PPN parameters β and γ with laser-ranged satellites

To date, the most accurate value of the combination 2+2γ−β 3 of the PPN Eddington-Robertson-Schiff parameters β and γ has been obtained by measuring the perihelion shift of Mercury in the gravitational field of the Sun by means of the radar ranging technique. The accuracy level is less than 10. In this paper we explore the possibility of measuring 2+2γ−β 3 in the gravitational field of the Earth by analyzing the laser-ranged data of some existing SLR geodetic satellites. Different combinations of orbital residuals could be used: the accuracy depends on the considered combination and on various sources of systematic errors. At the present level of knowledge of most of them, the obtainable precision ranges from 10 to 10. For example, by using a suitable weighted sum of the orbital residuals of the perigee of LAGEOS II and the nodes of LAGEOS and LAGEOS II over a 8 years time span we expect a precision level of 6.69 · 10. By using the combined results of this measurement and of the Nordvedt parameter η it would be possible to measure the PPN parameter β independently of γ with an accuracy of 3.2 · 10 over 8 years. Such levels of precision could be sensibly improved in the near future when the new data on the terrestrial gravitational field from the CHAMP and GRACE missions will be available.