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Concept
Air mass (astronomy)
Summary
In astronomy, air mass or airmass is a measure of the amount of air along the line of sight when observing a star or other celestial source from below Earth's atmosphere . It is formulated as the integral of air density along the light ray.
As it penetrates the atmosphere, light is attenuated by scattering and absorption; the thicker atmosphere through which it passes, the greater the attenuation. Consequently, celestial bodies when nearer the horizon appear less bright than when nearer the zenith. This attenuation, known as atmospheric extinction, is described quantitatively by the Beer–Lambert law.
"Air mass" normally indicates relative air mass, the ratio of absolute air masses (as defined above) at oblique incidence relative to that at zenith. So, by definition, the relative air mass at the zenith is 1. Air mass increases as the angle between the source and the zenith increases, reaching a value of approximately 38 at the horizon. Air mass can be less than one at an elevation greater than sea level; however, most closed-form expressions for air mass do not include the effects of the observer's elevation, so adjustment must usually be accomplished by other means.
Tables of air mass have been published by numerous authors, including , , and .
The absolute air mass is defined as:
where is volumetric density of air. Thus is a type of oblique column density.
In the vertical direction, the absolute air mass at zenith is:
So is a type of vertical column density.
Finally, the relative air mass is:
Assuming air density is uniform allows removing it out of the integrals. The absolute air mass then simplifies to a product:
where is the average density and the arc length of the oblique and zenith light paths are:
In the corresponding simplified relative air mass, the average density cancels out in the fraction, leading to the ratio of path lengths:
Further simplifications are often made, assuming straight-line propagation (neglecting ray bending), as discussed below.
Official source
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