# Air mass coefficient

Air mass is the length of an optical path that light from an observed object travels through the Earth’s atmosphere. Along this path, the light is attenuated by scattering and absorption. The greater is the air mass, the greater is the attenuation. This is illustrated in Figure 1, objects near the horizon appear less bright than when they are at the zenith.

Air mass. $z$ – zenith angle of the object. By definition, the air mass coefficient is equal to 1 at zenith ($z=0$).

The air mass coefficient X is the air mass relative to that at the zenith. So, its value is 1 when the object is at zenith, and increases as the zenith angle z grows, reaching approximately 38 at the horizon.

Versions 1.2.21 and older

In versions 1.2.21 and older, the air mass coefficient X was computed using the approximation published by Hardie in 1962 (see [hardie62]). This gives usable results for zenith angles up to about 85 degrees. For greater zenith angles, the program returned a negative value, to indicate that air mass cannot be computed.

Versions 1.2.22 and newer

Since version 1.2.22, the air mass coefficient X is computed using the approximation published by Pickering in 2002 (see [pickering02]). The formula (1) works well even for zenith angles up to 90 degrees. The program stores a negative value to indicate a situation when an object is below a horizon.

(1)X = \frac{1} { \sin (h + {244}/(165+47 h^{1.1}) ) }

where h is apparent altitude (90^\circ - z) in degrees.