Abatement of thermal noise due to internal damping in 2D oscillators with rapidly rotating test masses

Mechanical oscillators can be sensitive to very small forces. Low frequency effects are up-converted to higher frequency by rotating the oscillator. We show that for 2-dimensional oscillators rotating at frequency much higher than the signal the thermal noise force due to internal losses and competing with it is abated as the square root of the rotation frequency. We also show that rotation at frequency much higher than the natural one is possible if the oscillator has 2 degrees of freedom, and describe how this property applies also to torsion balances. In addition, in the 2D oscillator the signal is up-converted above resonance without being attenuated as in the 1D case, thus relaxing requirements on the read out. This work indicates that proof masses weakly coupled in 2D and rapidly rotating can play a major role in very small force physics experiments.

Gravitomagnetic influence on gyroscopes and on the lunar orbit

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 to approximately 0.1% accuracy--better than the anticipated accuracy of the Gravity-Probe-B result. This Letter shows the connection 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.