Could you use reflectors, anchored to the moon, for long-base-line Gravity Wave detectors? What about satellites, or systems thereof, in Geo-Synchronous Orbit? (Or, given the success of detecting earth's precession, with Relativistic accuracy, w/ gyro-scopes, could 3 mutually-perpendicular gyro-scopes detect GWs -- i.e., would GWs affect transverse vs. longitudinal rotations differently??)

http://lisa.gsfc.nasa.gov/

"Could you use reflectors, anchored to the moon, for long-base-line Gravity Wave detectors?"

Yes, but where would you put the other end of the base line?

Earth's atmosphere pretty much rules it out.

So you would need a satellite in orbit round the moon to use as the "other end" You could do that, but the earth's gravitational field would make it difficult.

It's probably best to do what they already chose to do.

I also wonder if moon quakes would disturb the experiments.

Thanks for the clarifications. If I might impose -- if interferometry allows multiple radio dishes, to be "thralled" together, to mimic a (patchy) radar of much larger dimensions... can something similar be done, at optical wavelengths ? To wit, could a "farm" of "solar panels", as it were, be thralled together, to mimic large >1000m, multi-acre, mirrors ??

Yes, there's optical interferometry:

 

http://en.wikipedia.org/wiki/VLT

 

The trouble is that it's difficult to accurately combine light beams that are received a large distance apart.

1000m? No, not currently, AFAIK

 

http://en.wikipedia.org/wiki/Navy_Prototype_Optical_Interferometer

http://www2.lowell.edu/npoi/

 

The instrument shop in our basement did a lot of the work for this. When they weren't doing important machining, like atomic fountain parts.

Wow -- what about using existing sight-lines, to distant stars, in substitute for the legs of LISA; and, then, looking for "gravitational scintillation" effects, from passing gravity waves ??

All I'm saying is, "gravitational lensing" -- i.e., a transiting compact object makes observable "gravitational scintillations" in earth-bound light rays, by "warping" space-time; similarly, masses can also induce propagating "vibrations" in space-time, which would produce effects similar to grav. lensing, i.e., "grav. scintillation".