airmass

Airmass is a term used in astronomy to describe the relative path length through Earth’s atmosphere that light from a celestial object must traverse to reach an observer. It is a dimensionless quantity, defined as the path length through the atmosphere relative to the path length when the object is at the zenith (directly overhead). The airmass increases with the object's zenith angle and thus with how far the object is from the zenith.

In the simplest approximation, known as the plane-parallel model, the airmass X is roughly secant of the zenith angle z: X ≈ sec z. This holds reasonably well for objects near the zenith but becomes inaccurate at larger zenith angles because the atmosphere is curved and its density profile changes with height. To obtain more accurate values over the whole sky, several empirical formulas are used. A common one is the Kasten and Young expression: X = 1 / (cos z + 0.50572 (96.07995 − z)^−1.6364), where z is the zenith angle in degrees and X is defined up to z = 90 degrees.

Airmass also depends on atmospheric conditions and wavelength. The amount of light extinction caused by the atmosphere is approximately proportional to X, often written as Aλ ≈ kλ X, where kλ is the extinction coefficient at a given wavelength. Photometric corrections use this relation, with observed magnitudes related to intrinsic magnitudes by m = m0 + kλ X. Near the horizon, large airmass values amplify extinction and refraction, affecting brightness, color, and position.

Applications of airmass include planning observations to minimize atmospheric effects, correcting photometric data for extinction, and estimating transparency. Many calculators provide X as a function of time and object coordinates to aid observers in selecting optimal observing windows.