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 cosD (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 cosD 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.