Lunar laser ranging and the equivalence principle signal

The fitting of 28 years of lunar laser ranging data for a possible range signal indicating an equivalence principle-violating difference in the gravitational acceleration rate of Earth and the Moon toward the Sun is performed and then examined, both analytically and by computer simulations. The EP-violating signal is synodic, being predominately proportional to $\cos D$ $(D$ is the synodic phase). Because LLR data do not uniformly sample the synodic month cycle, almost any hypothesis of a specific post-model synodic range signal responds strongly and with bias to the presence of most any other un-modeled synodic range effect. Since the physical and operational structure of the LLR experiment is of synodic periodicity, many of its modeling problems tend to be synodic: so we have created a synodic phase, bin-averaged presentation of the experiment’s post-fit range residuals. By this technique the entire structure of the synodic modeling inadequacies can be detected without preconceptions or hypotheses as to their particular form. A synodic post-model residual signal of characteristic size 1 cm is found in the data. An observation “worth” function has been found which quantifies the potency of each additional observation for reducing the rms noise uncertainty in the fit of the $\cos D$ amplitude. It strongly indicates that LLR observations should, for some time into the future, preferentially be made on the new moon side of the quarter moon phase.