We present two novel methods, tested by LISA Pathfinder, to measure the gravitational constant $G$ for the first time in space. Experiment 1 uses electrostatic suspension forces to measure a change in acceleration of a test mass due to a displaced source mass. Experiment 2 measures a change in relative acceleration between two test masses due to a slowly varying fuel tank mass. Experiment 1 gave a value of $G=6.71\pm 0.42(\times {10}^{-11}){\mathrm{m}}^3{\mathrm{s}}^{-2}{\mathrm{kg}}^{-1}$ and experiment 2 gave $6.15\pm 0.35(\times {10}^{-11}){\mathrm{m}}^3{\mathrm{s}}^{-2}{\mathrm{kg}}^{-1}$, both consistent with each other to $1\sigma$ and with the CODATA 2014 recommended value of $6.67408\pm 0.00031(\times {10}^{-11}){\mathrm{m}}^3{\mathrm{s}}^{-2}{\mathrm{kg}}^{-1}$ to $2\sigma$. We outline several ideas to improve the results for a future experiment, and we suggest that a measurement in space would isolate many terrestrial issues that could be responsible for the inconsistencies between recent measurements.

• Received 25 July 2019

DOI:https://doi.org/10.1103/PhysRevD.100.062003