Hi all,
I thought I might as well throw a little something into the EOT calculation
brew by expanding on Prof. Gregorio's contribution. The following series of
calculations, in addition to finding the EOT, will find the sun's
declination, semidiameter and, by iteration, sunrise and sunset for any
latitude and longitude.
What follows is not mine except for the correction I note in all capital
letters. I got this from the U.S. Naval Observatory:
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JD = Julian Date UT = Universal Time (hrs)
T <- (JD + UT/24 - 2451545.0)/36525. Number of centuries from J2000.
L <- 280.460 + 36000.770 * T Solar mean longitude, in degrees
(remove multiples of 360 degrees from it.)
G <- 357.528 + 35999.050 * T Mean anomaly, degrees
M <- L + 1.915 * sin (G) + 0.020 * sin (2*G) Ecliptic long., degrees
e <- 23.4393 - 0.01300 * T Obliquity of ecliptic, degrees
E <- -1.915 * sin (G) - 0.020 * sin(2*G) + 2.466*sin(2*M) - 0.053 *
sin(4*M)
Equation of time
GHA <- 15*UT -180 + E Greenwich hour angle, degrees
sin (DEC) <- sin (e) * sin (M) Declination of Sun
SD <- 0.267 / ( 1 - 0.017 * cos (G) ) Semidiameter of Sun, degrees
Define sunrise as the time when the apparent altitude (H) of the upper
limb of the Sun will be -50 arc minutes (34' for refraction + 16' for
semidiameter). Twilights are found for H = -6 degrees (civil), -12 degrees
(nautical), and -18 degrees (astronomical). Correct for height of the
observer if not at sea level.
Obtain the time of rise/set, (UT) by iterating the equation
UT = UTo - (GHA + LON +/- t ) <-- THIS IS NOT CORRECT
THE CORRECT EQUATION SHOULD BE
UT = UTo - (GHA + LON +/- t ) / 15
with initial guess UTo = 12, using + for rise, - for set and t defined by:
cos t = (sin H - sin LAT sin DEC ) / (cos DEC cos LAT)
replacing UTo by UT until their difference becomes small.
Convert UT to local timezone, applying Daylight Savings time if in effect.
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Back to me again!! Regarding the iteration mentioned above. It is not very
clear the way it was written but it is possible to figure out. I found it
took about three iterations for the difference between UT and UTo to become
small.
Maybe one of you with a wiser head can think of a way to word the
instructions above more clearly regarding the iteration process. I can give
one clue however, the new value for UT must be carried back to the top of
all the equations and run through again as well as replacing the initial
guess of 12.
Happy dialling!!!
Charles Gann
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* http://www.geocities.com/athens/1012 *
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