By the longest solar day I mean the longest time from one solar noon to the next. And similarly for shortest. My google-fu seems not up to the question although I found one site that claims December days are generally longest. By dividing the time between earliest and latest solar noon (a difference of about a half hour) I conjecture it is on or near Dec. 23. And I assume the shortest is similarly in late June. By the way, the answer will be the same everywhere on earth except at the poles (where there is no meridional passage).
You have just asked for the definition of a solstice.
I believe you’re measuring solar time (as you said) so that, rather than using our usual definition of a mean solar day having 86,400 seconds (adjusted from time to time with a leap second), you are wanting the maximum time difference from the sun passing directly over your local zenith, to the next day when that happens again (about 24 hours).
When the Earth is close to its perihelion, the sun would appear to be moving the fastest, which should require the Earth to rotate a bit more to “move the sun” back over that zenith line. But a whole half and hour difference between max and min solar day? That seems a lot.
Or are you instead talking about the longest duration the sun appears in the sky, based on the season? (also ref. gnoitall’s ninja post)
I am definitely talking about the longest time from one solar noon to the next. This is always around 24 hours, but not exactly that. And from what I can glean the earliest solar noon (in Montreal) was 11:37 (12:37 DST) on Nov. 2 and the latest was 12:08 on Feb. 11. The actual times will vary with where you are in your time zone (we are about 1 1/2 degrees east of the center of the zone) but the variance ought to be the same. If this has anything to do with the equinox, that is coincidental.
Note btw that the greatest altitude of the sun does not occur at the instant of meridian transit. Anyhow a glance at the table in Mathematical Astronomy Morsels shows that the longest true solar day occurs near the December solstice, approximately 24 hours and 30 seconds. (His table for 1998 has the longest day on December 22, and the shortest day on September 16, but I need a sec to recalculate for 2024…)
It’s not a coincidence; the Equation of Time is definitely affected by the obliquity of the ecliptic.
I’m not sure why it would be at the solstice, instead of at the perihelion point, which is a few weeks later.
The orbital eccentricity is not the only factor determining the length of the day.
I wonder if @Hari_Seldon is actually asking about the absolute length of a solar day (notionally 86,400 seconds). Because there is a degree of variability, caused by the fact that Earth’s orbit is eccentric rather than perfectly circular, as well as the Earth’s polar tilt.
If I’m guessing correctly what @Hari_Seldon is asking about, the apparent solar day (how long the Sun takes to appear directly overhead a particular meridian two times in a row, essentially “local noon to local noon”) does vary by ± 30 seconds or less.
Table from that Wikipedia article:
Length of apparent solar day (1998)
| Date | Duration in mean solar time |
|---|---|
| February 11 | 24 hours |
| March 26 | 24 hours − 18.1 seconds |
| May 14 | 24 hours |
| June 19 | 24 hours + 13.1 seconds |
| July 25/26 | 24 hours |
| September 16 | 24 hours − 21.3 seconds |
| November 2/2 | 24 hours |
| December 22 | 24 hours + 29.9 seconds |
So there is some regular variability in the absolute length of a solar day.
I thought that he was quite clear that that’s what he was asking about.
I’m glad you understood that at first. Some of us are distracted and it takes a little while for the rest of the thought process to percolate across the brain through all the traffic.
That is exactly what I wanted to know. Somehow google did not point to that Wiki article. I was right about Feb. 11 and Nov. 2, but I did not know there were other 24 hour days. I guess that is what the analemma is all about.
I am getting roughly similar dates and durations in 2024 but maybe someone wants to whip out an Astronomical Almanac and check? Note also that which noon-to-noon interval represents a certain date depends on your longitude! (So, you can just write a script that takes your location and, for each day, prints out the exact time the Sun crosses your meridian.)
Roughly speaking it looks like a certain sum of two sine waves; the 24-hour days will occur at extreme values (maxima and minima), and long/short days at extreme values of the derivative.
For example, if I did not screw this up, the almanac says noon in Chicago occurs (rounding to the nearest second) on 11:49:40 on December 22, 2024, and again at 11:50:10 on December 23, giving a day of 24h + 29.9 seconds, but the preceding and following days round to 24h + 29.8 seconds.
Similarly, the shortest day of 24h − 21.5 seconds occurs between 11:45:21 on 16th September and 11:44:59 on 17th September, the previous day being a few milliseconds longer.
Nice to see this solar day variation is more on the order of +/- 30 seconds, rather than minutes, which (as I said upthread) seemed a bit long.
But to explain the +/- 30 minutes at different times of the year, another term mentioned upthread, equation of time, is definitely worth a look.
I greatly appreciate this, as I think it nicely explains why my analemma has width in a second dimension (the fat parts of the figure 8) rather then just a one dimensional line
Could you please elaborate? How does one read the “fat” analemma?
When you look at an analemma, the northern loop is skinnier than the southern loop. I wonder what it looked like 700 years ago when the perihelion coincided with the winter solstice. I’m presuming it was symmetrical. What will it look like in 5000 years when perihelion coincides with the vernal equinox?
I guess that makes it symmetric with respect to reflection about the vertical axis?
The two lobes (northern and southern loops) will be the same size? That is a different symmetry.
My take on the 30min difference between longest and shortest, is that its the cumulative affects of each day being a few seconds longer (or shorter) than the previous ones.
Looking at the analemma on a globe they include a scale that shows “Clock ahead of sun” and “Clock behind sun” measured in minutes
