On the possibility of measuring the Lense-Thirring effect with a LAGEOS-LAGEOS II-OPTIS mission

A space mission, OPTIS, has been proposed for testing the foundations of special relativity and post-Newtonian gravitation in the field of the Earth. The constraints posed on the original OPTIS orbital geometry would allow for a rather wide range of possibilities for the final OPTIS orbital parameters. This freedom could be exploited for further tests of post-Newtonian gravity. In this paper, we wish to preliminarily investigate if it would be possible to use the orbital data from OPTIS together with those from the existing geodetic passive laser-ranged LAGEOS and LAGEOS II satellites in order to perform precise measurements of the Lense-Thirring effect. With regard to this possibility, it is important to note that the drag-free technology which should be adopted for the OPTIS mission would yield a lifetime of many years for this satellite. It turns out that the best choice would probably be to adopt the same orbital configuration as the proposed LAGEOS-like LARES satellite and, for testing, select a linear combination including the nodes of LAGEOS, LAGEOS II and OPTIS and the perigee of OPTIS. The total systematic error should be of the order of 1%. The LARES orbital geometry should not be too much in conflict with the original specifications of the OPTIS mission. However, a compromise solution could also be adopted. A comparison with the new perspectives of measuring the Lense-Thirring effect with the existing laser-tracked satellites opened by the new gravity models from CHAMP and, especially, GRACE is made. It turns out that an OPTIS/LARES mission would still be of great significance because the obtainable accuracy would be better than that offered by a reanalysis of the currently existing satellites.