General relativity predicts that the frequency of a clock varies with height above the earth's surface according to Δν/ν0=gh/c2, where g is the local acceleration due to gravity and the height h is assumed to be small with respect to the radius of the earth (so that g can be treated as a constant). Thus a gamma ray emitted at height zero will be red-shifted relative to the absorption frequency of an absorber at height h by frequency Δν. This can be compensated for by the Doppler effect, by giving the absorber a downward velocity v. Find v as a function of the height of the absorber relative to the emitter. What is its numerical value for a height of 20 m? At a height of 20 m, how large is the gravitational red-shift compared with the linewidth of 57Co, Δϵ∼1.6×10−8 eV? (Now you know why this was a difficult experiment!). Find the vertical velocity (including the sign!) of the source relative to the absorber such that the first-order Doppler shift cancels out the gravitational shift. Estimate the degree of temperature stability required in order that the second-order (relativistic time-dilation) shift is not a significant source of error in this experiment. (Hint: for simplicity use the classical equipartition theorem to obtain the nuclear kinetic energy.)