Optimizing the observation schedule for tests of gravity in lunar laser ranging and similar experiments

Abstract

A worth function is constructed for any fitted parameter of the lunar laser ranging (LLR) model. It quantifies the reduction in the formal noise uncertainty of the parameter's estimated value which will result from an additional LLR observation made at a particular future time. This function is applied to optimizing the measurement of three effects in gravitational theory which are scrutinized by LLR - possible violation of the universality of gravitational free-fall rates (the so-called violation of the equivalence principle), geodetic precession of the local inertial frame and possible time variation of Newton's coupling parameter, G. An asymmetry in the present data distribution (more observations exist between quarter and full moon phase than between quarter and new moon phase) is found to strongly shape the worth function for the equivalence principle test, so that future observations on the new moon side of quarter moon are of much higher value. The worth function for the moon's synodic rate, a parameter central to determining both the geodetic precession of local inertial space and any time variation of Newton's G, is found to be quite variable through the synodic month and with those variations also differing significantly from one month to another. The lunar nodical rate is also important for determining the geodetic precession, helping to eliminate uncertainty due to a weakly known lunar quadrupole moment parameter. Its worth function is found to not only vary through the month and year, but also to vary noticeably by the hour during a typical observation session. Shaping the future LLR observation schedule to take advantage of these worth function variations can appreciably increase the rate of improvement in the measurement precisions for the scientific parameters from LLR. Applying the worth function a priori to optimize observation times in other future ranging experiments can significantly increase the sensitivity of the resulting data to model parameters of scientific interest, and properties of such optimal distributions are explored in an appendix.