Testing various facets of the equivalence principle using lunar laser ranging

Abstract

More than 42 years of lunar laser ranging provides an excellent basis for the determination of various parameters of the Earth-Moon system and for tests related to gravitational physics. In this paper, we focus on tests of the equivalence principle with the Earth and Moon as test bodies in the gravitational field of the Sun as well as a test of a possible violation of the equivalence principle as a result of the coupling of the galactic dark matter with the ordinary matter of the Earth and the Moon. Tests were carried out for three different data sets with observations from 1969 to 2011, 1986 to 2011, and one set with data only from the Apache Point Observatory. No significant deviation from the predictions of general relativity was found within the reached accuracy of 3.6 × 10 −4 for the Nordtvedt parameter η and 1.6 × 10 −13 for the mass ratio (m g /m i) EM of gravitational and inertial masses between the Earth and the Moon.

Relevance of the weak equivalence principle and experiments to test it: Lessons from the past and improvements expected in space

“…The gravitational effect of the Sun on bodies with different mass-energy content has been tested also with LLR experiments. Using more than 45 years of laser ranging data to retroreflectors on the surface of the Moon scientists have shown no violation for Earth and Moon towards the Sun to about 10 −13 [3,4]. (The composition of the Moon is similar to that of the Earth's mantle and different from the Ni-Fe rich core).…”

“…Since self gravitation is a very small fraction of the total mass-energy even for celestial bodies, tests of whether it obeys WEP are much less precise. LLR has reached a few parts in 10 4 [4]. Tests of UFF for gravity are performed also in strong field with pulsarwhite dwarfs binary [32] and recently with the triple pulsar data for which a result to 3 · 10 −8 is reported [33].…”

“…A completely different technique, Lunar Laser Ranging (LLR), tests the WEP for the Earth and Moon as bodies of different composition falling in the field of the Sun. Such tests have reached a precision similar to the torsion balance [3,4] and a 10-fold improvement requires not only mm-level laser ranging, but also a matching improvement of the physical model which describes the Earth-Moon system [5].…”

Dilaton, screening of the cosmological constant and IR-driven inflation

“…3 Current observational bound [59][60][61][62][63] for the time-dependence of the Newton constant 8πG = M −2 P is small and is of the order of |Ġ/G| ∼ 10 −11 − 10 −14 year −1 .…”

Evolution of the fine-structure constant in runaway dilaton models

“…Current solar system tests of the equivalence principle (see Refs 4,5,6) and recent measurements by Planck (Refs. 7,8) constrain the dilaton parameters as…”