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
Dear Mr: Blateyron,
first of all, my congratulations for your SHADOWS
program I have downloaded in the last week; I have
installed it on my computer and I will send you soon
my remarks.
As far as the Equation of Time is concerned, the last
edition of the Explanatory Supplement to the Astronomical
Almanac reports (pag. 484) the following algorithm:
1) Using the Julian Date (JD) and the universal time (UT)
in hours, calculate the number of centuries from J2000
with the relation
T = (JD + UT / 24 - 2451545.0) / 36525.
2) Calculate the solar mean longitude corrected for aberration
L = 280°.460 + 36000°.770 T (remove multiples of 360°)
then the mean anomaly G
G = 357°.528 + 35999°.050 T ( " )
and finally the ecliptic longitude EL
EL = L + 1°.915 * sin G + 0°.020 * sin 2G
3) The equation of Time ET is given by
ET = - 1°.915 * sin G - 0°.020 * sin 2G +
+ 2°.466 * sin 2 EL - 0°.053 * sin 4 EL
I hope this algorithm is sufficient for your needs, so we will
have soon a new release of your excellent program.
Happy New Year!
Prof. Paolo GREGORIO
