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Relativistic and quantum gravity corrections to Lagrangian points for the Sun-Earth, Sun-Jupiter, and Earth-Moon systems.

Emmanuele Battista
Human Research & Performance
Delivered As: 
Abstract Text: 

Motivated by modern developments in the context of effective field
theories of gravity and by the recent advances in aerospace engineering
and (lunar) laser ranging techniques, quantum and general relativity
corrections on the position of Lagrangian points of the Sun-Earth,
Sun-Jupiter, and Earth-Moon systems are evaluated.
In particular, Einstein theory corrects by 7.61 meters the location of the
Lagrangian point L1 in the Earth-Moon system. This theoretical prediction
turns out to be testable in light of modern advances in lunar
laser-ranging techniques mentioned before, but several perturbations, of
and non-gravitational nature, may (slightly) modify such a prediction.
Thus, if one wants to test also the tiny (of order a few millimeters)
corrections provided by effective field theories of gravity, it is
necessary to perform a theoretical investigation of all conceivable
perturbations of the Earth-Moon-satellite system, starting from the
aforementioned effect involving the Earth-Moon libration point L1. For
this reason the
n-body problem in general relativity is analyzed in order to check the
behavior of a small planetoid subjected to the gravitational attraction
produced by the Sun, the Earth, the Moon, and Jupiter. The Levi-Civita
Lagrangian, which brilliantly describes under which assumptions the
Newtonian result according to which the dimensions of celestial bodies can
be ignored also in the context of general relativity in the weak-gravity
regime, is employed. The
trajectories of the planetoid in various situations are shown and some
comments are reported about the reliability of the model we are proposing.

Emily Law, Eddie Arevalo, Bach Bui, George Chang, Richard Kim, Shan Malhotra, Syed Sadaqathullah, Quoc Vu
SSERVI Identifier: 

Recognizing that science and human exploration are mutually enabling, NASA created the Solar System Exploration Research Virtual Institute (SSERVI) to address basic and applied scientific questions fundamental to understanding the Moon, Near Earth Asteroids, the Martian moons Phobos and Deimos, and the near space environments of these target bodies. As a virtual institute, SSERVI funds investigators at a broad range of domestic institutions, bringing them together along with international partners via virtual technology to enable new scientific efforts."