Lunar Laser Ranging: Relativistic Model and Tests of Gravitational Physics

Astronomy and Astrophysics – Astronomy

Scientific paper

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Scientific paper

The analysis of precise laser ranges, times of flight between observatories on the Earth and retroreflecting arrays on the Moon, both requires a precise relativistic model and has tests of gravitational physics as a goal. The relativistic equations of motion of the Moon and planets are integrated numerically with respect to the solar system center of mass. The resulting ephemeris is a realization using a solar system barycentric (SSB) celestial reference frame. To calculate the range it is necessary to transform time between the SSB, the centers of the Earth and Moon, and the ranging site on the Earth's surface. One must also apply relativistic space corrections to the geocentric ranging station positions and the Moon-centered reflecting site positions. The observed time of flight uses a clock at the ranging station and the computed time of flight, from transmit to bounce to receive times, must be compatible. Range is further modified by the gravitational time delay. These various manifestations of relativity offer opportunities for tests. The integrations of the equations of motion give sensitivity to PPN β and γ, geodetic precession of the lunar orbit, any violation of the equivalence principle, and any variation dG/dt of the gravitational constant. Gravitational time delay gives additional sensitivity to PPN γ. The strong equivalence principle is also sensitive to PPN β and γ giving strong sensitivity to β. Using lunar laser ranging data, the equivalence principle uncertainty for Mg/Mi is 1.3x10-13, the resulting β uncertainty is 0.00011, geodetic precession is verified to 0.4%, and (dG/dt)/G is tested to 3x10-13 /yr. Analysis of increasing spans of high accuracy data should improve upon these tests of gravitational physics.

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