However, the method of simple differences introduce a 12 hour phase
error so we would be better off producing the differential dEOT/dt. As
the fourier approximation is linear this can be done with high school
calculus. I've included the differential function below. Luckily this
produces the same numerical result (to two dec. places) as before
except the date is now 23.0UTC Dec (as expected from the phase argument).
Beware! The derivative of an approximating function need not be the
approximation of the derivative of the real function.
Besides, we must take into account that all algorithms to calculate the
EoT aren't very robust and are only accurate for
a more or less narrow span of time. No algorithm would be able to
calculate the EoT on the day when Ramses II was
born, for instance.
And finally, if John or somebody else wants to work in the range of 10
sec they'll have then to take into account other
difficult to calculate factors like the atmospheric reffraction (the
formulae we know are all rough approximations).
Best regards,
Anselmo Perez Serrada
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