  Responding to calls from the National Science Foundation (NSF) for new
proposals to measure the gravitational constant $G$, we offer an interesting
experiment in deep space employing the classic gravity train mechanism. Our
setup requires three bodies: a larger layered solid sphere with a cylindrical
hole through its center, a much smaller retroreflector which will undergo
harmonic motion within the hole and a host spacecraft with laser ranging
capabilities to measure round trip light-times to the retroreflector but
ultimately separated a significant distance away from the sphere-retroreflector
apparatus. Measurements of the period of oscillation of the retroreflector in
terms of host spacecraft clock time using existing technology could give
determinations of $G$ nearly three orders of magnitude more accurate than
current measurements here on Earth. However, significant engineering advances
in the release mechanism of the apparatus from the host spacecraft will likely
be necessary. Issues with regard to the stability of the system are briefly
addressed.
