Department or Program


Primary Wellesley Thesis Advisor

James Battat


Lunar Laser Ranging (LLR) measures the transit time of a laser pulse from an observatory on Earth to corner cube retroreflectors on the Moon, installed by Apollo astronauts and Russian rovers. A transit time measurement with 7 ps precision gives the Earth-Moon distance with millimeter precision. Successive measurements indicate the evolution of this distance and can constrain theories of gravitation. These theories include General Relativity (GR), which remains incompatible with Quantum Mechanics. This project presents simulations of the Earth-Moon-Sun system in Python that focus solely on the physics of gravitation and provide a means of comparing the evolution of the Earth-Moon distance for different gravitational frameworks. The comparisons thus far have focused on violations of the Strong Equivalence Principle (SEP) using a quasi-Newtonian formulation of gravitation. The comparisons between the Newtonian and quasi-Newtonian frameworks take two approaches. The first involves subtracting simulated Newtonian Earth-Moon distances from simulated SEP violation Earth-Moon distances and analyzing the results using a Fourier transform, which identifies periodic signals. The Fourier spectrum revealed an SEP violation signal as well as three other signals related to the Sun's perturbation of the Earth-Moon system and the eccentricity of the lunar orbit. However, this method is not ideal because the rate of precession of the lunar orbit depends on the degree of SEP violation, or lack thereof. The more optimal, second approach consists of fitting SEP violation simulated data with a Newtonian model. The post-fit residuals should be dominated by the SEP violation signal. The results were varied: the SEP violation signal dominated some of the post-fit residuals, while in some fits with different initial conditions, the other periodic signals persisted. The reasons for this inconsistency remain unclear. Because of correlations between parameters, the model was able to absorb some of the SEP violation signal by adjusting parameters like the initial velocities and positions of the objects. However, all fits failed to fully mask the SEP violation, indicating that LLR is sensitive to an SEP violation. Future work may focus on optimizing the fit and increasing its accuracy, and on undertaking similar comparisons for GR and alternative theories.