Horizontal magnification of finite-sized celestial objects

Abstract

We investigate the magnification due to refraction of the apparent horizontal sizes of finite celestial bodies, such as the Sun or Moon. Two models are discussed and compared with the earlier works of Biot and Chauvenet. It is shown that the apparent horizontal size of the object varies with respect to its true horizontal size as a function of altitude or zenith distance, from a reduction of about 0.0276% at the zenith, to an amplification of about 0.0045% when the object appears just at the horizon (namely, when the true altitude γ is negative and related to the corresponding refraction R by γ=−R). It is also shown that the apparent horizontal size is equal to the true size when the true altitude γ is related to the corresponding refraction R by γ=−R/2. Thus, the total magnification (and reduction) range for differently sized objects is about 0.032%–0.033% and depends on the refraction.