jeffrey.kissel@LIGO.ORG - posted 17:04, Thursday 21 August 2014 - last comment - 21:50, Thursday 21 August 2014(13542)
Fun with H1 EX BRS -- Sensitivity to Gravity Gradient Change
J. Kissel, K. Venkateswara, R. Schofield, S. Karki Robert didn't believe that we can use our change in gravity gradient to damp the rung-up 8.8 [mHz] oscillations in the BRS, so we performed a demonstrative test in his presence. With Krishna himself as our test mass, he (1) Waited for the balance to come to an equilibrium position, (2) Moved in next to the North (+X) side of the sensor and squatted there. His approach created a bit of torque noise, but more importantly created a change in local gravity, changing the equilibrium position of the balance up because his squatted C.o.M. is slightly higher than the beam. (3) Stood up, increasing his center of mass much higher. This causes little-to-no tilt/torque and again changes the local gravity gradient shifting the DC equilibrium position of the oscillation to shift up. (4) Squatted back down, restoring his center of mass to the original location. Again there is a quick bit of torque noise as he squats, but one can see the DC equilibrium position has shifted back (roughly) to it's original location. All of these changes in C.o.M. served to excite the 8.8 [mHz] mode, which is why you see the amplitude of motion increase at each change. The first attachment is the time series of the tilt readout, and the second is pictures of the two positions.
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K. Venkateswara For the skeptical, here's a rough order of magnitude calculation of the deflection: The angular stiffness of the flexures = kappa = I*(w_0)^2 = 0.59*(2*pi*8.8e-3)^2 = 1.8e-3 N m. The torque on the balance due to me standing a distance of ~2 m is Tau = (G * M1 * M2/R^2) * Lever arm * sin(angle) ~ 6.7e-11 * 2 * 70/2^2 * 0.4 * sin(arctan(0.5/2)) which gives torque Tau ~ 2.3e-10 N m The angular deflection is simply Tau/kappa ~ 0.1 microrad (=100 counts), which is roughly what we saw.