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In my
message of yesterday I didn't want in any way to claim the priority or the
paternity of the Fourier series for declination and for EoT . It
would be as to claim the priority of the invention of the warm water" , as we say here :-) In
fact many series of sines and cosines were invented to make faster the
astronomic calculations, before the diffusion of the calculators as can be found
in texts of mathematical astronomy of the end of the XIXth and of the first half the XXth
century.
With
my note I want only to explain the method used for the calculation and the
values of the errors.
I am sorry if, certainly owing to my bad knowledge of the English language, I have been misunderstood. Always because of the difficulty to make clear the things
in a different language from one's mother one, I fear to have been not very clear on
the errors of the results. Two
types of error can be defined:
1 -
difference between the mean value calculated with the series and the mean value
calculated exactly on a given period of years. The maximum value of this error
is around 3-4 ' (as
2 -
difference between the mean value calculated with the series on a given day
(f.i. on March 23) and the exact value on a given date (f.i. on March 23, 2004). In this case the error can arrive
to 15'.
Since
the exact value is necessary when we want to find the azimuth of a wall (with
some methods), it is not advisable
to use the results of the development in series to find the declination of the
Sun in these cases.
From
calculations we have also that it is a good rule to use mean values
calculated at 12.00h (local time) on a period of time around equal to that
in which we supposed that the clock will stay in operation.
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