Hank,
some years ago also I have obtained the Fourier approximation of the EOT
from its MEAN values on a 48 year period (from 2000 to 2047) ( I published
it in 2000)
The coefficients that I have found are practically equal to those found by
you and precisely:
t = 2 * pi * (j - 1) / 365.2421897
EOT = 0 +
+ 7.3656 * Cos(t + 1.5113) _
+ 9.9158 * Cos(2 * t + 1.9574) _
+ 0.3060 * Cos(3 * t + 1.8347) _
+ 0.2027 * Cos(4 * t + 2.3213)_
Where j = N-1 and N = number of the day in the year (32 for February the
1st)
I have also calculated the difference ( true exact value - mean value from
formula ) in every day of the perod (17532 days) and I have found a maximum
error less than 18 sec.
The values (exact) of the EOT changes from one year to the other as in the
follwing example.
EOT calculated on December 25 at noon in Greenwich :
DAY Time Eq.
DEC 25 2003 Th - 6.90 sec
DEC 25 2004 Sa +16.74
DEC 25 2005 Su + 8.64
DEC 25 2006 Mo + 1.68
DEC 25 2007 Tu - 5.82
DEC 25 2008 Th +15.72
DEC 25 2009 Fr + 9.00
DEC 25 2010 Sa + 0.84
The mean value = 6.54 sec. On December 26 the mean value = 36.2 sec
Because of these changes of the EOT from one year to the other it is wrong,
in my
opinion, to use values very precise in calculating sundials. They may be
useful to find the exact istant of the noon in a given day, etc.
A regard
Gianni Ferrari
P.S. - The EOT is non changed from the atmospheric refraction
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