Dear all,
When I got into the discussion about the EoT I mentioned my method by
using formulae for a given year.
Those formulae also calculates the declination of the sun, because in
gnomonics I often need both values.
But I didn't mention how the formulae themself are calculated.
In this mail I will point out the procedure for this.
I learned this method from a member of 'De Zonnewijzerkring' some 15
years ago.
Mean longitude of the sun:
L = 279.696678 + 0.9856473354 d + 0.00002267 ( d*d / 100000000 ) degrees
Mean longitude of perigee:
w = 281.220844 + 0.0000470684 d + 0.0000339 ( d*d / 100000000 ) degrees.
Exentricity of earth's orbit:
e = 0.01675104 - 0.000011444 d - 0.0000000094 ( d*d / 100000000 )
degrees
Obliquity:
eps = 23.452294 - 0.0035626 ( d / 10000 ) degrees
d is number of days since 0 january 1900 12:00 UT ( formaly : Efemirid
time)
Calculate variable y = tan( eps/2) * tan(eps/2)
The formula for the EoT :
E = ( -2 e cosw - 2 e y cosw ) sinL
+ ( 2 e sinw - 2 e y sinw ) cosL
+ ( y - 1.25 e e cos2w ) sin2L
+ ( 1.25 e e sin2w ) cos2L
+ ( 2 e y cosw ) sin3L
- ( 2 e y sinw ) cos3L
- ( 0.5 y y ) sin4L ..... RADIANS
Astronomical longitue:
La = L + ( 2 e cosw ) sinL
- ( 2 e sinw ) cosL
+ ( 1.25 e e cos2w ) sin2L
- ( 1.25 e e sin2w ) cos2L..... degrees.
By assuming the parts in ( ) stay constant during a year we get a
year-formula with enough accuracy for our aims.
decl = arcsin ( sinLa * sin eps ) degrees.
Converting radians into seconds of time is
multiplying with 24 * 3600 / ( 2 * pi )
In 1994 I compared the results of this method with the results of the
basicprogram, that was distributed by NASS with Compendium vol 1.
number 1.
I discovered no difference in the output of the procedures, both for
the EoT and for the sun's declination.
The procedure of NASS, I think, is based on what is written in the book
Astronomical Algorithms by Jean Meeus, but I am not sure.
Is this the same procedure as used in the program DIALIST, distributed
by NASS?
( In his book Jean Meeus describes an even more accurate procedure. )
In general :
I need the values for EoT and declination for 2 main reasons.
The first is to calculate the sun's azimuth or the time when the sun is
due south or north to find out the declination of any plane I want to
use as a sundial.
I need rather accurate values for this problem.
The second reason is to calculate several lines on a sundial.
For this problem I don't need the values with the same accuracy because
a dial isn't such an accurate instrument for all the years.
See also the message of Gianni Ferrari ( 31 dec 1996)
And in gnomonics it is even usual to assume the values being constant
during one day.
But I have already a rather accurate procedure, so I use it for the
second problem as well.
I myself always choose the values of a year in the middle of 2 leap
years, par example 1998.
In another e-mail I sent a picture of 2 EoT curves, for 1902 and 2098.
Some asked me how I made that picture.
The picture is made by a program that I wrote some years ago.
The program writes the points in an own format to disk, the same format
as I use in ZONWVLAK and so on.
I convert that file into *.DXF, import it into Autocad, give the lines
color, scale the drawing and I add text.
Then the drawing is placed on the clipboard and imported into the
shareware program Painshop Pro version 4.
Then finaly I make a GIF picture of it.
It is rather complecated, but it works well.
The GIF picture is as an attechment added to the e-mail.
I use Netscape version 3 and Windows 95.
Fer de Vries.
