We describe an experiment to measure the mass of the Milky Way galaxy. The experiment is based on calculated light travel times along radial and azimuthal directions in the Kerr metric of the galactic centre. We show that the difference is proportional to the galactic mass. We apply the result to light travel times in a 10 cm Michelson-type interferometer located on Earth. The mass of the galactic centre is shown to contribute 10-6 to the flat space component of the metric. The result is also applicable to clock corrections in GPS navigation systems, to interpretations of the Michelson-Morley experiment and to the 'strong equivalence' principle. Experiments are proposed to measure the effects.
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