Depth of the atmosphere at the horizon?

[michaelmorris]

I'm putting together a short talk on 'Seeing' for my local astro soc. There is one fact (amongst many) I don't seem to be able to find out and I don't have the maths skill to work it out.

I know that if I look straight up at the zenith at a star I am looking through about 100km of atmosphere. If I were to look out over the sea to a star on the horizon, how much atmosphere would I be looking through?

[acey]

You can get this from Pythagoras theorem. Sorry I can't upload a diagram, but draw two concentric circles (one for the Earth and one for its atmosphere), draw a vertical line from centre to surface of Earth, and a horizontal one starting from the same point on the Earth's surface and extending to the edge of the atmosphere, indicating the line of sight of an observer looking to the horizon. From where this line meets the edge of the atmosphere, draw a third straight line to the centre of the Earth - the hypoteneuse of a right-angled triangle. If x is the unknown thickness of atmosphere as seen on horizon, and R is the radius of the Earth, then the hyptoneuse has length R+100 (assuming your stated value of 100km) and the other two sides have lengths x and R. Then it's:

x² + R² = (R+100)² (where 2 means superscript, ie squared),

from which I get a figure of about 1130km.

Good luck with your talk!

Andrew

[Merlin66]

Not to get to sophisticated, but refraction near the horizon causes us to "see a bit round the bend". In photometry this is calculated in terms of "Air Mass".

and is 35 arc minutes at the horizon ie the object appears 35 arc minutes above where it actual is. The calcs show the air mass at 5 degrees ( zenith angle 85 degrees) is 10.2 times that above the zenith.

So if your 100Km is used this also gives about 1020Km of atmosphere we are looking through near the horizon.

[acey]

Just found an article here:

http://www.skyandtelescope.com/howto/visualobserving/19712459.html

which asserts that the atmosphere seen along horizon is "forty air masses". I'm guessing this is a misprint. The article contains a link to a paper:

http://www.cfa.harvard.edu/icq/ICQExtinct.html

which looks interesting though I haven't read through it yet.

Andrew

[michaelmorris]

Thanks guys, very helpful.