Air mass (astronomy)

The air mass (English Air mass , short AM ) is in astronomy a relative measure of the length of the path that the light of a celestial body travels through the earth's atmosphere to the ground or to the observing observatory . This light path influences the scattering and absorption of starlight and also its spectral composition.

In meteorology , the term air mass is used differently to describe homogeneous large areas of the troposphere .

geometry

The air mass is defined as the ratio of the respective path length based on the minimum length with perpendicular incidence of light: ${\ displaystyle l}$ ${\ displaystyle l_ {0}}$

{\ displaystyle \ mathrm {AM}: = {\ frac {l} {l_ {0}}} \ geq 1}

At a zenith angle ζ of 0, the light falls perpendicularly on the earth's surface and the path through the atmosphere is the shortest; the light passes exactly one air mass:

{\ displaystyle l = l_ {0} \ Rightarrow \ mathrm {AM} = 1}

Air mass as a function of the zenith angle

To estimate the angle-dependent air mass, one calculates with an atmosphere of constant density ; for the earth, this equivalent atmosphere has a layer thickness ( scale height ) of H = 8.5 km. Then with the earth's radius R:

{\ displaystyle \ mathrm {AM} (\ zeta) = {\ frac {{\ sqrt {(R + H) ^ {2} - (R \ cdot \ sin \ zeta) ^ {2}}} - R \ cdot \ cos \ zeta} {H}}}

For zenith angles ζ <60 ° the approximation applies:

{\ displaystyle \ mathrm {AM} (\ zeta <60 ^ {\ circ}) \ approx {\ frac {1} {\ cos \ zeta}} = \ sec \ zeta}

with sec for the secant .

Abbreviations:

AM0: radiation without attenuation by the atmosphere, i.e. H. without air in the light path
AM1: perpendicular incidence on the earth's surface
AM1.5: angle of incidence 48 ° related to the vertical.

At a zenith angle of 60 °, the light crosses 2 AM, at 80 ° almost 6 AM, and at 90 ° the path is geometrically extended to almost 40 AM.

If the air mass is defined alternatively via the elevation angle (angle of the incident radiation to the horizontal at the observation site), the result for an elevation angle> 30 °: ${\ displaystyle h = 90 ^ {\ circ} - \ zeta}$

{\ displaystyle \ Leftrightarrow \ mathrm {AM} (h> 30 ^ {\ circ}) \ approx {\ frac {1} {\ sin h}} = \ csc \, h}

with csc for the coscan .

Effects

In observational astronomy, the air mass is a measure of the effect of the zenith angle and allows a quick assessment of the achievable observation quality: in general, air masses greater than two are rarely observed; Most large telescopes have safety circuits that prevent observations at values above 2.5 to 3. The attenuation ( extinction ) of the light plays a lesser role here than the increasing differential refraction between blue and red light: near the horizon , a white star becomes a color spot that is blue at the top and red at the bottom.

With the air mass also increases air turbulence markedly - both the brightness variation ( scintillation ) and the focus ( Seeing ). At zenith angles above 80 ° (i.e. at elevation angles below 10 °), astronomical refraction extends the optical path additionally because the light beam in the atmosphere is more curved.

There is also a slight reddening of the starlight if the air contains a lot of aerosol : blue light is scattered more strongly than red light on the dust particles - an effect similar to the sunset .

Solar physics

The spectrum of solar radiation depends on the length of the path that light has to travel through the atmosphere. Corresponding spectra and radiation powers are assigned to the linear dimensions . A more oblique incidence of sunlight means a weakening of the radiation power and a change in the spectrum. In particular, the short-wave rays (UV and blue) are increasingly scattered and absorbed.

Various spectra and radiation powers were defined for comparative measurements :

AM = 0 is defined as the spectrum outside the atmosphere (extraterrestrial spectrum) in space, the radiation power there is 1367 W / m ² ( solar constant ).
AM = 1 is the spectrum of the sun rays falling perpendicularly on the earth's surface, ie the sun must be exactly in the zenith ; the rays then cover the shortest path to the surface of the earth.
For AM = 1.5 the zenith angle is about 48.2 °. With this spectrum the global irradiance is 1000 W / m²; For this reason, AM = 1.5 was introduced as the standard value for the measurement of solar modules ( photovoltaics ). The spectrum AM = 1.5 is recorded in the standard IEC 904-3 (1989) Part III. Assuming a typical sunshine duration of 1000 hours of sunshine per year, the average irradiance in Germany is 115 W / m².

For Berlin , the zenith angle is 76 ° at midday on the winter solstice ; and therefore AM = 4.13 applies here. For the summer solstice and at the highest point of the sun, the zenith angle is approx. 29 °, which corresponds to AM = 1.14.

swell

↑ NASA Earth Fact Sheet , specification "Scale height" in the section "Terrestrial Atmosphere"
↑ [1] NREL : The AM1.5 spectrum for download

[1] NASA Earth Fact Sheet , specification "Scale height" in the section "Terrestrial Atmosphere"

[2] [1] NREL : The AM1.5 spectrum for download