Automation of the Cavendish Experiment to 'Weigh the Earth'

We describe a simple and inexpensive method for automating the data collection in the well-known Cavendish torsion balance experiment to determine the gravitational constant $G$. The method uses a linear array of phototransistors and requires no moving parts. Multiplexers and a data-acquisition device are used to sample the state of each phototransistor sequentially. If the sampled phototransistor is illuminated by the laser spot, the position and time are recorded to a data file. The recorded data does an excellent job of capturing the damped harmonic oscillations. The resulting data were analysed to extract an experimental value of $G$ that was within 5% of the accepted value.