John Pazmino
 NYSkies Astronomy Inc
 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 
    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 
    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.