Plot of the airmass calculations using the formulas discussed,

The airmass in astronomy quantifies the path length that the light from a celestial source must travel through the Earth's atmosphere to get to the observatory, relative to that for a source at the zenith. Image File history File links Download high-resolution version (1692x1188, 76 KB) I created this image using GNU Octave I, the creator of this work, hereby grant the permission to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1. ... Image File history File links Download high-resolution version (1692x1188, 76 KB) I created this image using GNU Octave I, the creator of this work, hereby grant the permission to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1. ... A giant Hubble mosaic of the Crab Nebula. ... Prism splitting light Light is electromagnetic radiation with a wavelength that is visible to the eye (visible light) or, in a technical or scientific context, electromagnetic radiation of any wavelength [citation needed]. The elementary particle that defines light is the photon. ... The term celestial refers to the sky and/or Heaven. ... Layers of Atmosphere (NOAA) Air redirects here. ... MolÄ—tai Astronomical Observatory An observatory is a location used for observing terrestrial and/or celestial events. ... The zenith, in astronomy, is the point in the sky which appears directly above the observer. ...

When the zenith distance is less than 60 degrees, a good approximation is given by assuming a plane parallel atmosphere. In this case, the airmass is simply the secant of the zenith distance, which is often denoted "sec(zen)". This formula for the airmass breaks down near the horizon where it becomes infinite. It has been suggested that this article or section be merged into Celestial coordinate system. ... A degree (in full, a degree of arc, arc degree, or arcdegree), usually symbolized °, is a measurement of plane angle, representing 1／360 of a full rotation. ... Secant is a term in mathematics. ... It has been suggested that this article or section be merged into Celestial coordinate system. ...

By definition, a source at the zenith has an airmass of 1. A source at a zenith distance of 60 degrees (i.e. at an altitude = 90 - zenith distance = 30 degrees) has an airmass of 2. The airmass at point directly above the horizon is given with a very good accuracy by where H is the scale height of the atmosphere and R the radius of the earth. The zenith, in astronomy, is the point in the sky which appears directly above the observer. ... It has been suggested that this article or section be merged into Celestial coordinate system. ... In astronomy and surveying, altitude (sometimes called elevation) is one of the two coordinates of the horizontal coordinate system, and refers to the vertical angle from the horizon. ... It has been suggested that this article or section be merged into Celestial coordinate system. ... To meet Wikipedias quality standards, this article or section may require cleanup. ...

In astronomy, a corrected formula is used for observations near the horizon:

where:

zen denotes the distance to the zenith or zenith angle.

This multiplies sec(zen) times a correction term which is usually very close to 1 (0.9988 in the zenith) and grows as the distance increases. Unfortunately this ends in an asymptotic behavior at 90 degrees where the airmass decreases very fast, making this expression unsuitable for observations at really small distances from the horizon. In astronomy, a celestial coordinate system is a coordinate system for mapping positions in the sky. ...

For observations even closer to the horizon, a second expression might be useful:

This formula works for degrees and most software do the calculations in radians, so you have to use radians for the term inside the cosine but leave the other term in degrees. In mathematics and physics, the radian is a unit of angle measure. ...

Note: In atmospheric science the above corrections to the secant formula are seldom used, since corrections for optical depth formulas take into account the vertical profile of atmospheric attenuators (see Thomason et al., "The effect of atmospheric attenuators with structured vertical distributions on air mass determination and Langley plot analyses", Journal of the Atmospheric Sciences 40, 1851-1854, 1983). Meteorology is the scientific study of the atmosphere that focuses on weather processes and forecasting. ... Optical depth is a measure of transparency, and is defined as the fraction of radiation that is scattered between a point and the observer. ...

External links

• A downloadable airmass calculator, written in C (the source code describes the theory in detail)