NavList:

Ahoy, Bruce.

Others have already answered you, but I just wanted to add that tables for this were available in the very earliest works on "scientific" celestial navigation way back in the 18th century. That explains our rather quaint name for it, "dip short". Given the modern world's taste in technical language, if this were invented today, it would be known by some four-letter acronym... :)

You can find tables of "dip short" in most navigation manuals and textbooks, both modern and historical.

Any of the calculations for dip, dip short, distance off by angle above the horizon, etc. that we use in navigation have to include the correction for terrestrial refraction. It turns out that in every case of interest this is equivalent to increasing the radius of the Earth by about 17%. So if you want to generate your own tables, you can treat any of these as a simple geometry problem (in which there is no refraction and light travels in straight lines) and get results that match nearly all of the tables just by changing the radius of the Earth. This is good physics, by the way. It's fully justified by the behavior of refracted light. The percentage change varies with the temperature distribution of the lower atmosphere. For example, if there's a significant temperature inversion where the air gets warmer with altitude above the ground (not uncommon) that factor might be 200% or more instead of 17%. If the air is every dry, as in a desert, the air might cool faster with altitude than normal and then the factor might be only 5% or 10%. This variability in terrestrial refraction is one of the most fundamental limitations on the potential accuracy of any fixes. The dip should always be considered uncertain by a few tenths of a minute of arc even under seemingly normal weather circumstances. The tables are based on normal atmospheric conditions.

-FER

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