François BLATEYRON wrote:
>
> Hi dear gnomonists...
>
> Can someone help me with the calculation of the equation of time ?
>
> I use the following equation:
>
> E = 460 sin M - 592 sin 2 (w+M)
> in seconds
>
> where M is (360/365.25)(t-t0) with t0 the instant of perihelion crossing
> and w the perihelion longitude.
>
> The curve obtained with this curve has the good shape but is a little
> shifted. The maximum is the 21 of feb instead of the 11 of feb. The zero
> crossings are on 22-april; 30-june and 6-sept instead of 16-april; 15-june
> and 2-sept.
>
> I can't find what is wrong... Is it t0 (3 january 1950) ? is it w ?
> For w, I use :
>
> w = 101°13'15" + 6189".T
> with T the number of days ( from the 1 january 1900 at 0h ) divided by
> 365.25.
>
> I would appreciate any help or results to compare. Thanks a lot.
>
> Francois Blateyron
> (and I wish everybody a happy new year with a lot of sunny days...)
>
> E-mail : [EMAIL PROTECTED]
> WWW : http://www.fc-net.fr/~frb/welcome.html
Francois,
The factor 6189" change in 'w' in one year is very high.
See also the remark of Roger Sinnot.
To compute the equation of time as well the suns declination out of a
daynumber in a given year I use a formala for that year.
This formula for 1998, a year between 2 leap years, is :
Fomulae to compute the equation of time and the suns declination out of
a daynumber:
L = DAYNR*360/365.2422 - 80.535132 DEGREES
EQUATION = - 107.0605*SIN( L) - 428.6697*COS( L)
+ 596.1009*SIN(2L) - 2.0898*COS(2L)
+ 4.4173*SIN(3L) + 19.2776*COS(3L)
+ 12.7338*SIN(4L) SECONDS (of time)
LAMBDA = L + 0.4277*SIN( L) + 1.8664*COS( L)
+ 0.0180*SIN(2L) + 0.0087*COS(2L) DEGREES
EPSILON = 23.43954 DEGREES
DECLINATION = ARCSIN(SIN LAMBDA * SIN EPSILON) DEGREES
Strictly these formulae are for 1998 and for 12.00 UT, but for sundials
you can use them during a long time.
See also 'Cousins', page 236, for such a fomula for the year 1931.
In my sundial program I use a procedure to compute this formula for a
certain year.
I learned this methode from one of the members of "De Zonnewijzerkring"
(the Dutch Sundial Society).
He also calculated the errors of this methode.
The error in the equation of time is about + or - 3 seconds.
For sundials this is very accurate.
To Paolo Gregorio I have the question if it is known what the errors are
with the formula given in your message?
Happy new year to all,
Fer J. de Vries, Netherlands.
