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    Re: refraction
    From: Paul Hirose
    Date: 2005 Aug 5, 12:56 -0700

    Marcel E. Tschudin wrote:
    > Yes, how do I get in this? Just trying to cover in a self-made program the
    > situation from an object at the horizon (over sea level) as seen from a
    > mountain or air craft.
    The problem is similar to a rise/set calculation, isn't it? That is, you
    want to know the altitude the object would have if refraction were
    turned off and you could see through the Earth. That equals dip of the
    horizon plus the total curvature due to refraction of the light from the
    object to the observer.
    Imagine a theodolite at the summit of say a 100 meter mountain
    overlooking the sea. A star is precisely on the horizon. Dip of the
    horizon at H meters high is about 1.75′√H, so in this example the
    telescope must be 17.5′ below horizontal to center the star and horizon
    in the crosshairs. That sets it parallel to the arriving light rays at
    the theodolite.
    However, it is not parallel to the rays at the distant point where
    they're tangent to the sea. To make it so, the scope has to be tilted
    down a little more, by the amount of refraction between the tangent
    point and the observer. According to the Explanatory Supplement to the
    Astronomical Almanac, it equals about .37′√H for H in meters, or 3.7′ in
    this example.
    Finally, you tilt the scope down still more to allow for the refraction
    between the tangent point and the celestial body. This is simply the
    horizontal refraction, about 34′ in standard conditions.
    You end up with the telescope 55′ below horizontal. It is now parallel
    to the rays from the star before they enter the atmosphere.
    The 1.75′√H and .37′√H terms can be combined, in which case the
    depression angle expression is -34′ - 2.12′√H.
    I don't think that will be accurate at great height, though. For
    example, the .37′√H term for refraction between horizon and observer can
    increase without bound. In reality, it should never exceed the
    horizontal refraction (34′).

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