An evacuated drop tower gives a free-fall height of
PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Relativity & Gravitation · The equivalence principle and gravity as geometry
Relativity and Gravitation, Ch Experimental foundations: free fall, Lorentz invariance and clock tests
Problem
An evacuated drop tower gives a free-fall height of h=110m. Two spheres of different composition are released together at the top, and the difference in their arrival positions at the bottom can be measured optically to 1.0×10−9m. Take g=9.81ms−2, constant over the tower, and c=2.998×108ms−1.
((a)) Estimate the smallest Eötvös parameter η a single drop could reveal, and compare it with the satellite bound ∣η∣≲3×10−15.
((b)) Estimate the fractional difference in rate between two identical clocks at the bottom and the top of the same tower, to first order in gh/c2.
((c)) If gamma rays were sent from the bottom of this tower to the top, estimate the speed with which the source would have to be moved to compensate the gravitational shift by a first-order Doppler shift.