Cosmic acceleration of Earth and the Moon by dark matter

In order to test the hypothesis that the gravitational interaction between our Galaxy's dark matter and the ordinary matter in Earth and the Moon might not fulfill the equivalence principle (universality of free fall), we consider the pertinent perturbation of the lunar orbit -- a sidereal month period range oscillation resulting from a spatially fixed polarization of the orbit. Lunar laser ranging (LLR) data can measure this sidereal perturbation to an accuracy equal to or better than its existing measurement of the synodic month period range oscillation amplitude (+/- 3 cm) which has been used for testing whether Earth and the Moon accelerate at equal rates toward the Sun. Because of the slow precession rate of the Moon's perigree (8.9 yr period), the lunar orbit is particularly sensitive to a cosmic acceleration; the LLR fit of the orbit places an upper limit of 10(exp -13) cm/sq. s for any cosmic differential acceleration between Earth (Fe) and the Moon (silicates). This is 10(exp -5) of the total galactic acceleration of the solar system, of which, it has been suggested, a large portion is produced by dark matter.