  We propose to measure the rate \Rd\ for muon capture on the deuteron to
better than 1.5% precision. This process is the simplest weak interaction
process on a nucleus that can both be calculated and measured to a high degree
of precision. The measurement will provide a benchmark result, far more precise
than any current experimental information on weak interaction processes in the
two-nucleon system. Moreover, it can impact our understanding of fundamental
reactions of astrophysical interest, like solar pp fusion and the $\nu+d$
reactions observed by the Sudbury Neutrino Observatory. Recent effective field
theory calculations have demonstrated, that all these reactions are related by
one axial two-body current term, parameterized by a single low-energy constant.
Muon capture on the deuteron is a clean and accurate way to determine this
constant. Once it is known, the above mentioned astrophysical, as well as other
important two-nucleon reactions, will be determined in a model independent way
at the same precision as the measured muon capture reaction.
