: Does anybody know if NASA has done, or plans, any gravity related experiments in earth orbit. Also are any gravity experiments being done on any of the deep space probes?

There have been such experiments, in hindsight one that is not an intentional experiment but turned out to be a great one was global positioning satellites. In Order to be as accurate as the are they must compensate for relativistic effects such as general relativistic gravitational time dilation and special relativistic relative simultaneity. LISA will be another good one. Given that the thing works, it will detect gravitational waves.