What airmass is
Airmass is the amount of atmosphere light crosses on its way to you, relative to the amount straight overhead. At the zenith the airmass is 1. As an object sinks toward the horizon its light travels through more and more air, which dims it, reddens it and blurs it.
The formula
For altitudes above about 30°, the simple secant formula works well: X = 1 ÷ cos(zenith angle) = 1 ÷ sin(altitude). Close to the horizon it overestimates, because Earth’s atmosphere is curved. The calculator uses the Kasten and Young (1989) formula, accurate down to the horizon:
X = 1 ÷ (cos z + 0.50572 × (96.07995° − z)^−1.6364)
| Altitude | Airmass |
|---|---|
| 90° | 1.00 |
| 60° | 1.15 |
| 45° | 1.41 |
| 30° | 1.99 |
| 20° | 2.90 |
| 10° | 5.6 |
| 5° | 10.3 |
| 0° | about 38 |
Atmospheric extinction
Each airmass dims starlight by the extinction coefficient k, in magnitudes. In visible light k is about 0.15 at an excellent mountain site, 0.2 at a typical site and 0.3 or more in haze. Total extinction is k × X.
At 30° altitude with k = 0.2, a star loses about 0.4 magnitude, so only 69% of its light arrives; that is 0.2 magnitude more than at the zenith. Blue light is absorbed more than red, which is why the rising Moon looks orange.
Seeing
Atmospheric turbulence also grows with airmass. A common rule is that seeing scales roughly as X^0.6: 2″ of seeing at the zenith becomes about 3″ at 30° altitude. Planetary observers and astrophotographers therefore wait for targets to cross the meridian, when they are highest.
Practical rules
- Image targets above 30 to 40° when you can, ideally near the meridian.
- Shoot the lowest targets first if they are setting, or last if they are rising.
- Photometry corrects for extinction by measuring comparison stars at a similar airmass.
- Narrowband filters suffer less from extinction and light pollution near the horizon than broadband color.