Lunar laser ranging (LLR) measures the round-trip travel time of short laser pulses that are reflected back to Earth from corner-cube (retroreflector) arrays on the Moon. The range data are used to perform a general phenomenological check on our understanding of gravity—the weakest of the fundamental forces of nature. They also enable the refinement of the constants in the parameterized post-Newtonian formulation of general relativity and the testing of other theories of gravitation. LLR has provided the most precise limits to date on the following properties of gravity:

• Weak equivalence principle differential (fractional) acceleration Δa/a < 1.4 × 10⁻¹³,

• Strong equivalence principle (self gravity) to <4.5 × 10⁻⁴,

• Time-rate-of-change of Newton’s gravitational constant to Ġ/G < 10⁻¹² per year,

• Gravitomagnetism (frame dragging) to 0.1 percent,

• Geodetic precession to 0.6 percent, and

• Inverse square law to <10⁻¹⁰ times the strength of gravity at 10⁸ m length scales.

The first placement of retroreflectors on the lunar surface was by the Apollo astronauts in 1969. Recently, the Apache Point Observatory Lunar Laser-ranging Operation (APOLLO) began achieving 1 mm precision on lunar range. Deployment of next-generation reflectors would allow range precision to approach the 0.1 mm level, a better than two orders-of-magnitude improvement over the data used to determine the limits on the gravitational properties listed above.

Placement of a single new array would be helpful, although by itself incapable of adequately constraining lunar rotational and tidal motions.

Placement of three total new arrays widely distributed near the limb would optimally benefit high-precision ranging. The distribution of such reflectors/transponders may naturally and economically be associated with the implementation of a geophysical network.

In addition to probing the predictions of gravitational physics, the rich LLR data set can be used for other scientific purposes. For example, by monitoring the physical reactions to known torques on the Moon, the properties of the lunar interior, such as the presence of a liquid core and the interaction between this core and the surrounding mantle, may be discerned. The LLR data series can also be used to study the orientation of Earth in space, which connects to climate monitoring, and geophysics. Solar system navigation also benefits from the LLR data series.

SOURCE: Adapted from T.W. Murphy, University of California, San Diego, “Lunar Reflectors for Tests of Relativity,” white paper for the committee, 2006.