Calculating the air mass

catphotomfit and catphotomtrn can optionally calculate the air mass from the observed zenith distance. They use subroutine SLA_AIRMAS in the SLA subroutine library (see SUN/67[32]) for this task. This routine is more than sufficiently accurate for the present purposes. The following notes are based on the documentation for SLA_AIRMAS in SUN/67.

The air mass is calculated using Hardie's[16] polynomial fit to Bemporad's data for the relative air mass, $X$, in units of thickness at the zenith as tabulated by Schoenberg[25]. This method is adequate for all normal needs as it is accurate to better than 0.1% up to $X = 6.8$ and better than 1% up to $X = 10$. Bemporad's tabulated values are unlikely to be trustworthy to such accuracy because of variations in density, pressure and other conditions in the atmosphere from those that he assumed. At zenith distances greater than about $87^{\circ}$ the air mass is held constant to avoid arithmetic overflows.