LOPSIDED SUNRISES?
-----------------
John Pazmino
NYSkies Astronomy Inc
nyskies@nyskies.org
www.nyskies.org
2000 July 1 initial
2006 July 9 current
Fellow astronomer Lee Baltin is also a member of the American
Littoral Society. On 21 June 2000 that club held a 'solstice hike' on
Sandy Hook, NJ. At the event a fellow hiker posed to Lee the following
problem.
Why are the sunrise and sunset times so unsymmetrical? The change
month-by-month in the hour of sunrise should be the same, numericly,
as the change in the hour of sunset.
But the hours are not changing in such neat synchronism!
Lee checked the allegation with a couple planetarium programs and
found that, yes, the sunrise-sunset hours are not at all symmetrical
relative to midday or noon. He could not figure out why.
Then he called me. Yep, Lee's figures are correct by programs I
checked them with. But, ah-HA!, there is a very simple -- but commonly
overlooked -- explanation. The sunrise-sunset hour should be
equidistant from the midday hour, which is when the Sun crosses the
observer's local meridian. Which is to say, it takes just as long
between sunrise and noon as it does from noon to sunset. This neglects
the minute motion of the Sun in the ecliptic in the course of a day.
Yet it is exactly the accumulation of such small displacements over
days and weeks that causes the entire deviation.
The hours cited in almanacs are mean solar time, the time shown by a
good quartz clock, and not true solar time, as shown by a sundial. By
mean time the Sun does not cross the meridian at noon, but a few minutes
before or after. Many sundials have a plaque listing the addition or
subtraction to bring the dial reading to mean time.
This erraticism of the Sun is the combination of two motions. First,
in the northern winter the Earth is a bit closer to the Sun. It moves
thru a larger arc each day in its orbit and the Sun trudges thru a
larger arc than average thru the stars.
The opposite happens in northern summer. The Earth, farther from the
Sun, moves thru a smaller arc and so does the Sun.
Second, the Sun runs in the ecliptic circle, inclined 23-1/2 degrees
to the equator. Near the equinoxes some of the Sun's eastward motion
is displaces north or south. Near the solstices almost all the Sun's
displacement is eastward.
These two effects are consolidated into a single offset, the 'equation
of time'. This is the addition or subtraction noted on the sundial plaque.
I built the table here from the computer program Dance of the Planets.
Other programs may differ by a minute or two on a given date.
Each cell in the table has five lines. The first is the data from
Dance. The second is the increment of the sunrise and sunset from the
instant cell to the next cell. This ignores the equation of time. The
increment, the shift, cell to cell is of unequal size. This causes the
unsymmetrical migration of the sunrise and sunset hour thru the
seasons.
The third is the interval from sunrise to noon and from noon to sunset.
The equation of time is again ignored so that noon, 12:00, is that shown
by a sundial. The intervals are unequal so that depending on the date the
forenoon lasts longer or shorter than the afternoon.
The fourth is the sunrise-sunset increment with the equation of time
included. The shifts are now just about equal. The residual difference
is mostly due to roundings and in the calculations.
The fifth, last, line is the interval from sunrise to noon and from
noon to sunset, also with the equation of time included. Noon is now
that shown by a clock. The intervals are more equal, to the extent of
roundings in the calculations.
I took strict 30 day intervals; the months do not line up.
date rise EqT set | date rise EqT set
------ ----- ---- ----- | ------ ----- ---- -----
01 Jan 07:22 +02m 16:42 | 29 Jun 04:31 +03m 19:34
wo/EqT -12m +33m | wo/EqT +23m -26m
-/+noon 4:38 4:42 | -/+noon 7:29 7:34
w/EqT -22m +23m | w/EqT +21m -22m
-/+noon 4:40 4:40 | -/+noon 7:32 7:31
---------------------------+---------------------------
31 Jan 07:10 +13m 17:15 | 29 Jul 04:54 +05m 19:17
wo/EqT -38m +36m | wo/EqT +29m -40m
-/+noon 4:50 5:15 | -/+noon 7:06 7:17
w/EqT -37m +37n | w/EqT +34m -35m
-/+noon 5:03 5:02 | -/+noon 7:11 7:12
---------------------------+---------------------------
01 Mar 06:32 +12m 17:51 | 28 Aug 05:23 +00m 18:37
wo/EqT -48m +32m | wo/EqT +29m -50m
-/+noon 5:28 5:51 | -/+noon 6:37 6:37
w/EqT -39m +41m | w/EqT +39m -40m
-/+noon 5:37 5:39 | -/+noon 6:37 6:37
---------------------------+---------------------------
31 Mar 05:44 +03m 18:23 | 27 Sep 05:52 -10m 17:47
wo/EqT -45m +31m | wo/EqT +32m -46m
-/+noon 6:16 6:23 | -/+noon 6:08 5:47
w/EqT -38m +38m | w/EqT +39m -39m
-/+noon 6:19 6:20 | -/+noon 5:58 5:57
---------------------------+---------------------------
30 Apr 04:59 -04m 18:54 | 27 Oct 06:24 -17m 17:01
wo/EqT -28m +00m -30m | wo/EqT +34m +03m -27m
-/+noon 7:01 6:54 | -/+noon 5:36 5:01
w/EqT -28m -30m | w/EqT +31m -30m
-/+noon 6:57 6:58 | -/+noon 5:19 5:18
---------------------------+---------------------------
30 May 04:31 -04m 19:22 | 26 Nov 06:58 -14m 16:34
wo/EqT -00m +12m | wo/EqT +23m +05m
-/+noon 7:29 7:22 | -/+noon 5:02 4:34
w/EqT -07m +05m | w/EqT +09m -09m
-/+noon 7:25 7:26 | -/+noon 4:48 4:48
---------------------------+---------------------------
29 Jun 04:31 +03m 19:34 | 26 Dec 07:21 +00n 16:39
From the foregoing figures the gross lopsidedness of the sunrise
and sunset times comes from the equation of time. In ordinary stargazing
we ignore it, either because we use mean (clock) time or the hour is
really not critical. Here is one of those cases in home astronomy where
an underappreciated feature of the Sun's behavior can whack us in the neck.