Contatto di riferimento: Barbara Simoni
Partecipanti: Dr. Giampiero Esposito
Abstract: The three-body problem has been investigated, among others, by Lagrange, Poincare, Szebehely, Brumberg, leading to the discovery of Trojan satellites of Jupiter, the role of chaos in modern science, the Apollo missions and an application of the equations of the N-body problem in general relativity.
We here 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, first discovered by Krefetz in the sixties. After that, we study a theory involving quantum corrections to Einstein gravity, rather than to Newtonian gravity.
By virtue of the effective-gravity correction to the long-distance form of the potential among two masses, all terms involving the ratio between the gravitational radius of the primary and its separation from the planetoid get modified. Within this framework, for the Lagrangian points of stable equilibrium, we find quantum corrections of order two millimeters, whereas for Lagrangian points of unstable equilibrium we find quantum correction below a millimeter.
In the latter case, for the point L1, general relativity corrects Newtonian theory by 7.61 meters, comparable, as an order of magnitude, with the lunar geodesic precession of about 3 meters 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 conceive a new, first-generation laser ranging test of general relativity, by measuring the 7.61-meter correction to the L1 Lagrangian point, an observable never used before in the Sun-Earth-Moon system.
Performing such an experiment requires controlling the propulsion to precisely reach L1, an instrumental accuracy comparable to the measurement of the lunar geodesic precession, understanding systematic effects resulting from thermal radiation and multi-body gravitational perturbations. This will be the basis to consider a second-generation experiment, indeed much more difficult, to set experimental constraints on deviations of effective field theories of gravity from general relativity in the Sun-Earth-Moon system.