Dear friends,
I've followed with much interest the several
messages arrived in last days on EoT calculation.
I've nothing to add to what the authors have written but I will
note that the long calculation described not always are useful
if we wont only design a sundial.
The Sun's Right Ascension(RA) and Declination(D) and the EoT infact
change their values non only hourly in a day but also in the same
hour and in the same day ( Calendar's date) in different years.
This because of the Equinoce's precession and of the existence of the
February 29 in the leap years ( for example the RA can change in
the same hour of the same day in different years as far as 0.60
degree )
Given that a sundial is generally fixed and daily or annual
corrections are non allowed, it's necessary to use (in the
calculations) for every date average values of RA, D ( and EoT).
In such a way the sundial will mark always an imprecise time but
this time will be more exact of the one marked by a sundial
designed with the values( of RA, D, EoT) exactly calculated in a
given year.
For this reason, and to speed up the work, I have developed the
average values of AR,D and EoT in Fourier series with time measured
in days from the beginning of the year.
I've calculated, with great accuracy ,the values in all the days of
the year for 32 consecutive years (1990-2021) and after I've found
the average values for each day.
Later on I've developed AR, D, and EoT in Fourier series with 20
harmonics.
I've used the Jeffrey Sax's programs distributed by Willmann-Bell
and based on Astronomical Algorithms by J. Meeus -1991 .
With a PC 386 the calculation took 40 minutes.
Given that the coefficients extinguish quickly in my programs I use
only the first 6 terms with errors less then 0.11d. in RA, 0.06d.
in D and 0.1 min in EoT
EoT= E0+E1*cos(wt+F1) + E2*cos(2wt+F2) +.. + E6*cos(6wt+F6)
where t is in days from the beginning of the year ( for 1/1 t=1)
w=2*3.141592653/Tropical_year_in days
The values of the coefficients are :
E0=0.01822 min E1=7.36332 min F1=86.37 degree
E2=9.9205 F2=110.35
E3=0.31794 F3=106.81
E4=0.21958 F4=130.06
E5=0.01470 F5=124.90
E6=0.00661 F6=149.45
With my best wishes for an Happy New Year
Gianni Ferrari
