On the gravitomagnetic effects on the orbits of two counter–orbiting satellites

The effects of the general relativistic gravitomagnetic force on the orbits of a couple of counter–orbiting test particles, denoted as + and –, respectively, in the gravitational field of a central rotating mass are investigated. Based on the fact that, for identical orbital configurations, the secular Lense–Thirring rates of the nodes Ω are the same, contrary to the secular rates of the perigees ω which are equal and opposite, two different, new observables for a couple of new, counter–orbiting satellites in the gravitational field of the Earth are proposed and preliminary error budgets are presented. As a complementary consequence, also the gravitoelectric Einstein perigee precession could be measured by suitably combining the data of one of the two new satellites and of LAGEOS and LAGEOS II.