Hi,
I have translated the spreadsheet formulae into a (Scilab) script to see
easier what is going on there. I could not find the EoT equation in
Meeus. Anyway I would prefer the representation at the end of the
script. It is as precise as its three variables are. No numerical
constants the pedigree of which is often doubtful!
//Meeus, Jean. Astronomical Algorithms, 2nd ed. with corrections as of 2009
//Meeus p. 163-164. all angles in degrees
clear, mode(0), clc(), lines(0)//Scilab's prelude
//Input
Date=[2016,10,26,21,0,0];//Y,M,D,h,m,s (UT)) //MICA: EOT=16.123 min
SolDec=-12.807° RA=211.63°
// Calculations
Date0=[2000,1,1,0,0,0];//reference date
T=(datenum(Date)-datenum(Date0))/36525;//time in Julian centuries
eps0=23.4393-0.013*T//excentricity of the Earth's orbit
L=36000.77*T+280.46//mean longitude of the sun referred to the mean eqinox
of the date
G=35999.05*T+357.528//mean anomaly of the sun
Lred=modulo(L,360)//L shifted to the interval 0...360°
Gred=modulo(G,360)//G shifted to the interval 0...360°
lambda=Lred+1.915*sind(Gred)+0.02*sind(2*Gred)//Sun's true longitude
SolDec=asind(sind(eps0)*sind(lambda))//Sun's declination
//Source ?
EoT=-1.915*sind(G)-0.02*sind(2*G)+2.466*sind(2*lambda)-0.053*sind(4*lambda)
EoTminutes=4*EoT
//https://de.wikipedia.org/wiki/Zeitgleichung#Resultat
EoT=atand((tand(L)-tand(lambda)*cosd(eps0))/(1+tand(L)*tand(lambda)*cosd(eps0)))
Regards, Helmut
------------------------------------------------------
Am 27.10.2016 04:57, schrieb Roger Bailey:
Hi Helmut,
Thanks for this feedback. When you send something out, you never know
how it was received without such feedback.
Date formats are difficult with Excel. What works on my version, 2003
Canada, obviously does not work on yours. Helmut Sonderegger did a lot
of debugging to make the original spreadsheet international but
copy/paste often does not carry forward the format. The format I used
for column A was date and time. Only date was exposed. Column E needed
to read the A format as a number and calculate the time from the 2000
epoch. They need to be in the same format. I cannot solve this from
here as the format works for me with my version of Excel. In Europe
and even the US the formats are different. Different versions of Excel
do not communicate. The math works which is why non spreadsheet
options are sometimes better. But I was answering a question specific
to a free spreadsheet calculation, which I provided.
Regards, Roger Bailey
*From:* Helmut Haase <mailto:[email protected]>
*Sent:* Wednesday, October 26, 2016 12:07 PM
*To:* Roger Bailey <mailto:[email protected]> ; [email protected]
<mailto:[email protected]>
*Subject:* Re: Solar Declination
Hi Roger,
I had to change the date format in colum A and in the formula of colum
E. Maybe this is of concern for others too.
It is a matter of taste of course to use a spreadsheet for this
calculation. I would prefer and recommend a free numerical software
like Scilab e.g.. Meeus's algorithm would appear readable and edits
are easy to make.
Regards, Helmut Haase
-----------------------------------------
Am 26.10.2016 19:05, schrieb Roger Bailey:
Hi Dan,
The advice you have received from Gian and others is excellent. I use
his "Sol et Umbra" android app in a smartphone and tablet. It is a
great app.
But you asked for a spreadsheet. Attached is one implementation of
Meeus's simplified solar coordinate calculation. Helmut Sonderegger
developed this and added it to my spreadsheet for calculating
analemmatic sundials. I have copied it into several other
spreadsheets whenever I needed declination and the equation of
time. This is a reduced version small enough to get through the SML
size filter. Input the start date and time into cell A7. Change the
increment from 1 day to whatever in cell A8. Copy row 8 and paste it
in below for as many rows as you wish. Copy the spreadsheet into
other spreadsheets using solar coordinates but be aware of the
absolute address to the degree to radian conversion in row 1
I answered this question about a year ago for Jack Aubert. he was
interested in the rate of change of declination near the equinox and
solstice. I sent him a full implementation of that included
calculating and plotting the time of sunrise near the winter
solstice. The copy to the SML was filtered out but I will forward his
note and my reply with the original spreadsheet.
To answer this question I needed to review Meeus's Astronomical
Algorithms, specifically Chapter 25 Solar Coordinates pg
163-170. This great reference book is now available as a free
download. Just Google Meeus Astronomical Algorithms free. Is this an
example of fair use, a single copy of a library copy or a copyright
violation? I don't know but I was glad to find it. meeus discusses
the accuracy of the simple calculation compared to the more rigorous
version. For sundials the simple version is fine.
Regards, Roger Bailey
*From:* Dan-George Uza <mailto:[email protected]>
*Sent:* Tuesday, October 25, 2016 9:38 AM
*To:* [email protected] <mailto:[email protected]>
*Subject:* Solar Declination
Hello,
Can you provide a free accurate spreadsheet for the calculation of
daily solar declination across a leap year as well as non-leap year?
Thanks,
Dan Uza
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