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Lovely - by the time you did this calculation you would have flown to Chile
Just a passing thought for those who must teach differential
geometry, either as part of a math class or a relativity class, or
just as an interesting feature of coordinate systems, which almost
all physics classes use.
This is a real-world example of what is known as a "coordinate
patch". The collection of all coordinate patches that cover a
manifold (space) is known as an "atlas". And we see that if one is
using lat-longs you are forced to use more than one coordinate patch
to cover the surface of a two sphere (or in our case a slightly
deformed two sphere.)