24946
Author: Melissa Y. Tong
Mentor: Riley Newman
Title: An Analysis of Systematic Error Sources in a Measurement of Newton's Gravitational
Constant G
Error contributions to a measurement of Newton’s gravitational constant G arising from mass
density inhomogeneity are analyzed. Using multipole formalism, the torque experienced by the
torsion pendulum used in the G measurement is modeled as a function of the density of the field
source masses. Density variation of the source masses is found by comparing the densities of copper
samples taken from the material from which the field source masses are cut. The densities of the
samples are found using a method similar to Archimedes’ by first weighing the sample in air and then
in a dense liquid (Fluorinert 77; density of 1.766 g/cm^3). To measure G to within a few ppm
uncertainty, the measurement of the density variation among the copper samples may have an
uncertainty of no more than about 20 ppm. Preliminary results indicate the uncertainty of the density
variation to be about 50 ppm. Data suggests that the dominant source of this uncertainty is the
uncertainty in the force differences of the samples in liquid. With technique refinements we hope to
reduce the uncertainty of the density variation to 20 ppm.