If the ratio of gravitational mass to inertial mass is not invariant, then there would be profound
consequences for gravitation. Such a violation of the equivalence principle (EP) would affect
how bodies move under the influence of gravity. The EP is not violated in general theory of
relativity, but violations are expected for many alternative theories of gravitation. Consequently,
tests of the EP are important to the search for a new theory of gravity.
The EP is considered in its two forms; the weak equivalence principle (WEP) is sensitive
to composition while the strong equivalence principle (SEP) considers possible sensitivity to
the gravitational energy of a body. The main sensitivity of the lunar orbit to the EP comes
from the acceleration of the Earth and Moon by the Sun. Any difference in those accelerations
due to a failure of the EP causes an anomalous term in the lunar range with the 29.53 d synodic
period. The amplitude would be proportional to the difference in the gravitational to inertial
mass ratios for Earth and Moon. Thus, LLR is sensitive to a failure of the EP due to either
the WEP or the SEP. In the case of the SEP, any violation of the EP can be related to a linear
combination of the parameterized post-Newtonian parameters β and γ