Latest and earliest sunrise and sunset

The day of the June solstice is  the longest day, with sunrise and sunset furthest apart; and the day of the December solstice is the shortest, with smallest interval between sunrise and sunset.  That is for /earth’s northern hemisphere; for the southern, the other way around.

Yet there is a sense in which this does not seem so.

For latitude 40° north, earliest sunrise and latest sunset occur not on June 21 but on June 14 (4:31 AM) and June 27 (7:33 PM).  And earliest sunset and latest sunrise occur on Dec. 7 (4:35 PM) and Jan. 5 (7:22 AM).

The calendar dates can vary by a day because of leap years.  The times are local Sun times, not the time as smoothed across time zones or distorted for the summer months.  But for any clock setting the differences would be the same.

The dates and times vary strongly with latitude on Earth.  With higher latitudes, the difference between the summer and winter times gets greater, but the dates when the extremes are reached get closer to the dates of the solstices.  For example, at 60° north, the times differ by two or three hours from 6 AM and 6 PM, but the dates when these extremes are reached are only between 2 and 6 days away fromthe solstice dates.  With lower latitudes, the difference between the summer and winter times gets smaller, but the dates when these slight extremes are reached get further from the dates of the solstices.  On the equator, sunrise and sunset times stray by only a few minutes from 6 AM and 6 PM; but the dates when these slight extremes are reached are Feb. 10 and 12 (latest sunrise and sunset) and Nov 2 and 4 (earliest sunrise and sunset).

Times of sunrise and sunset for various latitude.  The knobs on the curves are at the dates when they reach extremes:  earliest (leftward) or latest (rightward).  These extreme moments get closer to the solstices at higher latitudes.  The curves for the equator (latitude 0) oscillates only slightly,, but with more than one “earliest” and “latest” because they are so sensitive to the variation of Earth’s speed in its orbit.

Most people in urban cultures are oblivious of sunrise and aware of sunset.  So the latest-sunset day seems to be the longest day, and the earliest-sunset day seems the shortest.  Days seem to keep lengthening (only by seconds) from the June 21 solstice to the June 27 latest sunset, though they are really already shortening.  In this way, June 27 seems the peak of summer.

And days seem to start lengthening (very slightly at first) from the earliest sunset, Dec. 7, though they are really still shortening till the solstice.

In this way Dec. 7 seems the shortest day – the turning-point, from which we can look forward to spring.  Winter seems already half over – a cheerful thought, even though the coldest weather is probably yet to come!  So Howard Wilk of Philadelphia (latitude 40°) proposed a holiday called Seculus for the earliest-sunset day or, better, the next day, when people could theoretically time sunset as coming a few seconds later.  Or it might be called Hope Day.  The trouble is that it varies slightly from year to year because of leap-days (it is sometimes Dec. 8) and is a different day for other latitudes.

Why do earliest sunrise and latest sunset not coincide with the longest day, nor latest sunrise and earliest sunset with the shortest?  They do, if we measure hours from true solar midnight and noon.  But our clocks use mean solar time, as if noons were a fixed distance apart; which they are not, because of the difference of actual from mean solar time.