Seminari di gruppo IV

Earth-moon Lagrangian points as a test bed for general relativity and effective field theories of gravity

by Emmanuele Battista (Napoli)



In the space surrounding two bodies that orbit about their mutual mass center there are five points where a third body will remain in equilibrium under the gravitational attraction of the other two bodies. These points are called Lagrangian points in honor of Joseph Lagrange, who discovered them in 1772 while studying the restricted problem formed by the Sun-Jupiter system. We first evaluate the location of all Lagrangian points in the Earth-Moon system within the framework of general relativity. For the points L4 and L5, the corrections of coordinates are of order a few millimeters and describe a tiny departure from the equilateral triangle. After that we will analyze the position of Lagrangian points in a scheme involving quantum corrections to Einstein gravity, rather than to Newtonian gravity. Within this framework, for the Lagrangian points of stable equilibrium, we find quantum corrections of order 2 mm, whereas for Lagrangian points of unstable equilibrium we find quantum corrections below a millimeter. In the latter case, for the point L1, general relativity corrects Newtonian theory by 7.61 m, comparable, as an order of magnitude, with the lunar geodesic precession of about 3 m per orbit. The latter is a cumulative effect accurately measured at the centimeter level through the lunar laser ranging positioning technique. Thus, it is possible to study a new laser ranging test of general relativity to measure the 7.61 m correction to the L1 Lagrangian point, an observable never used before in the Earth-Moon system. This will then be the basis to consider an experiment to study deviations of effective field theories of gravity from general relativity in the Earth-Moon system.