I don’t know. It just might not be perceivable in systems as minor as our solar system. Perhaps on much larger scales, a time delay can be detected.
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From nasa.gov:
Satellite observations of Black Holes confirm frame-dragging effect 80 years after prediction
The next time you feel like you’re barely dragging along, blame relativity. You’ll be stretching the point, but it appears that Einstein was right: space and time get pulled out of shape near a rotating body.
Einstein predicted the effect, called ``frame dragging,’’ 80 years ago. Like many other aspects of Einstein’s famous theories of relativity, it’s so subtle that no conventional method could measure it.
Using recent observations by X-ray astronomy satellites, including NASA’s Rossi X-ray Timing Explorer, a team of astronomers is announcing that they see evidence of frame dragging in disks of gas swirling around a black hole. The discovery will be announced today at a meeting of the High Energy Astrophysics Division of the American Astronomical Society in Estes Park, Colo., by Dr. Wei Cui of the Massachusetts Institute of Technology, and his colleagues, Dr. Nan Zhang, working at NASA’s Marshall Space Flight Center, and Dr. Wan Chen of the University of Maryland in College Park.
Frame dragging is one of the last frontiers in relativity. More familiar and already proven are the conversion of mass into energy (as seen in atomic bombs and stars) and back, the Lorentz transformations that make objects near the speed of light grow thinner and heavier and stretch time, and the warping of space by gravity (as seen when light is bent by a massive object).
Einstein also predicted that the rotation of an object would alter space and time, dragging a nearby object out of position compared to predictions by the simpler math of Sir Isaac Newton.
The effect is incredibly small, about one part in a few trillion, which means that you have to look at something very massive, or build an instrument that is incredibly sensitive and put it in orbit.
http://science.nasa.gov/science-news/science-at-nasa/1997/ast06nov97_1/
The Laser Interferometer Gravitational-Wave Observatory (LIGO) is a facility dedicated to the detection of cosmic gravitational waves and the harnessing of these waves for scientific research. It consists of two widely separated installations within the United States, operated in unison as a single observatory. When it reaches maturity, this observatory will be open for use by the national community and will become part of a planned worldwide network of gravitational-wave observatories.
LIGO is being designed and constructed by a team of scientists from the California Institute of Technology and the Massachusetts Institute of Technology. LIGO is funded by the National Science Foundation (NSF). Construction of the facilities was completed in 1999. Initial operation of the detectors is scheduled for 2001 and the first data run is scheduled for 2003.
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General relativity describes gravity as a manifestation of the curvature of space-time. This description has been tested and proved correct in the solar system, where gravity is weak and changes slowly due to the orbital motions of planets and their satellites. LIGO will permit scientists to test this description for rapidly changing, dynamical gravity (the space-time ripples of the gravitational waves), and also for the extremely strong, dynamical gravity of two black holes as they collide.
More specifically, LIGO has the possibility to: