Varying Alpha: New Constraints from Seasonal Variations
  We analyse the constraints obtained from new atomic clock data on the possible time variation of the fine structure `constant' and the electron-proton mass ratio and show how they are strengthened when the seasonal variation of Sun's gravitational field at the Earth's surface is taken into account. We compare these bounds with those obtainable from tests of the Weak Equivalence Principle and high-redshift observations of quasar absorption spectra consistent with time variations in the fine structure constant. 
John D. Barrow, Douglas J. Shaw