Gravity Probe B (GPB) is a huge project of NASA and Standford university, in which a satellite carrying four ultra-sensitive gyroscopes were put into orbit around Earth. The idea was to test two of Einstein's General Theory of Relativity (GR) effects: the geodetic effect and inertial frame dragging.
The geodetic effect represents the effect that the curvature of spacetime have on a spinning, moving body, as predicted by GR. The geodetic effect is relatively large and should not have posed any problems for GPB to detect.
Inertial frame dragging is a GR prediction that the rotation of an object would alter space and time, dragging a nearby object out of position compared to the predictions of Newtonian physics. The predicted effect is incredibly small — about one part in a few trillion, according to Wikipedia.
Although the Wikipedia article on the geodetic effect states that it has been confirmed to the 1% level, there is evidence that the best value that they obtained are not in agreement with Einstein's GR! This NASA/Stanford slide: http://colloquia.physics.cornell.edu/11-12-2007/cornellpres_files/v3_sli...
is showing that to a 1 sigma error confidence level the results for the geodetic precession are inconsistent with GR.
There were two unexpected sources of error affecting the gyros that almost ruined the whole effort, but the project scientists are confident that they can filter out the errors and reveal the true data. They are still struggling with the geodetic effect, never mind the very much smaller frame dragging effect.
So what if this whole effort turns out one big waste of money, with no clear result?
SL: Your Aerospace Watchdog