The Gravitomagnetic Influence on Gyroscopes and on the Lunar Orbit

Abstract

Gravitomagnetism--a motional coupling of matter analogous to the Lorentz force in electromagnetism--has observable consequences for any scenario involving differing mass currents. Examples include gyroscopes located near a rotating massive body, and the interaction of two orbiting bodies. In the former case, the resulting precession of the gyroscope is often called ``frame dragging,'' and is the principal measurement sought by the Gravity Probe-B experiment. The latter case is realized in the earth-moon system, and the effect has in fact been confirmed via lunar laser ranging (LLR) to approximately 0.1% accuracy--better than the anticipated accuracy of the Gravity-Probe-B result. This paper shows the connnection between these seemingly disparate phenomena by employing the same gravitomagnetic term in the equation of motion to obtain both gyroscopic precession and modification of the lunar orbit. Since lunar ranging currently provides a part in a thousand fit to the gravitomagnetic contributions to the lunar orbit, this feature of post-Newtonian gravity is not adjustable to fit any anomalous result beyond the 0.1% level from Gravity Probe-B without disturbing the existing fit of theory to the 36 years of LLR data.