A measure of the height of atmosphere through which an observation is being made. For a plane parallel atmosphere,
where
is the latitude,
is the declination, and HA is the hour angle.For an exponential spherical atmosphere
at a radius R from the center and scale height H,the optical path (ignoring atmospheric refraction ) is
(Young 1976). Dropping the
term in the numerato and the 
term in the denominator gives
Using Gradshteyn and Ryzhik (1965, p. 315) then gives
where erfc function is the complementary error function. An approximation for moderately large
is
(Young 1976), which gives
for the Earth. A correction for atmospheric refraction can be obtained by taking
(1)
where
is the latitude, is the declination, and HA is the hour angle.For an exponential spherical atmosphere(2)
at a radius R from the center and scale height H,the optical path (ignoring atmospheric refraction ) is
(3)
(Young 1976). Dropping the
term in the numerato and the term in the denominator gives (4)
Using Gradshteyn and Ryzhik (1965, p. 315) then gives
(5)
(6)
where erfc function is the complementary error function. An approximation for moderately large
(7)
is
(8)
(Young 1976), which gives
(9)
for the Earth. A correction for atmospheric refraction can be obtained by taking
(10)
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