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Hi Brad,

All your mentioned equations are approximations. It really depends on
the accuracy one wants to achieve and whether this accuracy is really
necessary or not. If one wants really to be exact, it is in this
context actually not the radius of the earth which is of interest,
it's rather the earth's radius of curvature at the location of the
observer. Because the earth's shape is approximately an ellipsoid this
radius of curvature depends on latitude and also on the azimuth,
except at the poles. If you do not require this accuracy you can use
any other less accurate mean earth radius which in the context of
calculating dip are likely to be completely sufficient.

Regarding the pressure and temperature dependency of refraction here
some further explanations: The scaling factor (P/1010)/(T/283) adjusts
the refactivity property of air, n, and as a consequence of it also
the refraction resulting from it. However, the cause for light rays
being bend in the atmosphere are temperature-GRADIENTS. The parameter
k is introduced to describe in a simplified model the bended ray for
terrestrial refraction and dip. From observations one obtained then
typical values for it.

Marcel

   

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