Noon-Midnight Red Shift

A terrestrial atomic clock at noon can be some ${10}^{\mathrm{g}}$ cm nearer the sun than an antipodal clock at midnight. The difference in gravitational potential due to the sun corresponds to a difference of time rates corresponding to a red shift $\frac{\Delta \nu }{\nu }=8\mathrm{}\times {10}^{-13\mathrm{}}$. But this red shift is almost exactly cancelled by a violet shift arising from the relativistic Doppler effect, so that the resultant shift is essentially zero. If the earth shielded or focussed the solar gravitational field, the gravitational contribution to the red shift would be altered and one might expect a resultant shift. But the motional contribution to the shift is also altered and, except for unrealistically large shielding or focussing, the resultant shift would still be zero.