Sunrise and Sunset Times Near the Solstices
The period within a few weeks of the winter solstice in late December
is the darkest time of the year for northern latitudes. Not only does the
Sun traverse its lowest arc across the sky at this time, but in many places
the Sun sets before the end of a normal workday and rises after many people have
already started their daily routines. At latitude 40° north, earliest
sunset occurs around December 8 each year, and latest sunrise occurs around
January 5. The day with the least amount of daylight is the winter
solstice, the first day of winter, on or
about December 21. Why are not all these dates the same? The answer is
not trivial, but on this page we have tried to provide as simple an explanation
as possible. It has to do
with the fact that our clocks and the Sun do not keep the same kind of time.
Below are three explanations, with increasing detail. Choose the one that most
fits your level of interest!
By the way, a similar situation occurs at the summer solstice, for the same
basic reason, though the effect is not as extreme. Solstice occurs around
June 21, but at latitude 40° north the earliest sunrise occurs around
June 14 and the latest sunset occurs around June 28. The changing
times of sunrise and sunset are probably more noticeable in the winter months,
because sunrise and sunset occur when we are more likely to be paying
attention — when we're starting our day and during the evening rush hour.
Also, most of us don't like the short
period of daylight then and are looking forward to getting more of it.
Note: These explanations are written from a northern-hemisphere
perspective. The situation is similar in the southern hemisphere.
A Thumbnail Explanation
Our clocks do not keep Sun time. Time measured by the position of the Sun
in the sky is somewhat variable over the course of a year, but our clocks keep
a uniform approximation to Sun time with each day exactly 24 hours
long. One consequence of this is that sundials usually seem to be wrong; that
is, they do not keep clock time. The times of sunrise and sunset, measured by
the clock, are also affected by the difference between the two kinds of time.
Although the length of daylight is shortest on the winter solstice, around
December 21, the dates of earliest sunset and latest sunrise are, somewhat
surprisingly, not on this date. Why is that?
The reason can be traced to the fact that the
difference between Sun time and clock time is rapidly changing in December and
January. The Sun runs slow compared to clock time then, so the times of both
sunrise and sunset tend to be a bit late according to the clock, delayed
from one day to the next by up to a half minute. Consequently, the time of
sunset begins to shift later at an earlier date than we would
expect (so that the earliest sunset is in early December), and the time of
sunrise doesn't begin to shift earlier until a later date than we
would expect (so that the latest sunrise is in early January).
Expanding a Bit . . .
The changing position of the Sun in the sky over the course of a day is
mainly an effect of the Earth's rotation on its axis, which is quite uniform to
a small fraction of a second. However, where the Sun appears in the sky at any
given time is also affected by the position of the Earth in its orbit around the
Sun. For reasons explained
elsewhere, time kept by the Sun
is not uniform throughout the year. Some solar days (the interval between
the instants when the Sun is due south in the sky) are longer or
shorter than 24 hours by as much as a half minute. On the other hand, our
clocks keep civil time, with a uniform rate equal to the solar rate
averaged over the entire year, with each day exactly 24 hours long. Therefore,
even very carefully made sundials located in the middle of a time zone
do not keep clock time.
Regardless of what kind of time we use, the day with the shortest overall
length of daylight is always the winter solstice, on or about December 21, when
the Sun appears to move along its most southern track in our sky. If we kept
time by the Sun, and not mechanical or electrical clocks, the date of the
earliest sunset and the date of the latest sunrise would also be the date of the
winter solstice. This is what most people (even astronomers!) would expect: the
solstice, earliest sunset, and latest sunrise should "naturally" occur on the
But our clocks do not run on Sun time. In fact, actual solar days from mid
November to early February are each longer than 24 hours by anywhere from a few
seconds to a half minute. In other words, the Sun moves with what seems to be a
very slightly slower-than-average apparent westward daily motion in the sky
(measured with respect to our uniform clock time) during that part of the year.
This tends to delay both sunrises and sunsets as measured by the clock. As a
result, the times of sunset start moving later before the date of the
solstice (that is, the date of earliest sunset occurs early) and the times of
sunrises do not start moving earlier until after the date of the solstice
(the date of latest sunrise occurs late). How much these two dates differ from
that of the winter solstice depends on your latitude; at 40° north latitude,
these dates are about two weeks from the solstice, earlier or later,
respectively. The range of these dates is wider at lower latitudes and narrower
at higher latitudes.
The Long Story
The Earth's seasons are caused by three factors:
- The Earth orbits the Sun once a year in a nearly circular orbit.
- The Earth's axis of rotation (the straight line through the center of the
Earth between the north and south poles) is not perpendicular to the plane of
the Earth's orbit. The Earth's axis is tilted by about 23.4° from the the
direction perpendiular to the orbital plane.
- The orientation of the Earth's axis in space remains nearly constant even
as the Earth revolves around the Sun. It always points in the general
direction of the star Polaris.
The result is that when the Earth is on one side of its orbit, the south pole
is tilted toward the Sun (by as much as 23.4°) and the southern hemisphere
experiences summer. Six months later, when the Earth is on the opposite side of
its orbit, the north pole is tilted toward the Sun (by as much as 23.4°) and the
northern hemisphere experiences summer.
What we see from our viewpoint in the Earth's northern hemisphere is that the Sun's
apparent daily track across the sky is much higher (that is, more northerly) in
summer, and lower (more southerly) in winter. From horizon to horizon, the Sun's
track is longer in summer and shorter in winter; so that in summer, sunrises are
much earlier and sunsets are much later than in winter. See,
for example, the graphic below, or this
the Sun's paths
through the sky at different times of the year.
The Sun's track across the sky is much shorter and lower in the winter than in
the summer. During the early fall, as the Sun moves lower in the southern sky,
sunrises get later, and sunsets earlier.
So we are used to the fact that the length of daylight is significantly longer
in summer than winter, and most of us know that the "longest day" (that is, the
day when the Sun is above the horizon the longest) is the summer solstice, around
June 21, when the Sun has reached its most northerly and longest track in our
sky; and the "shortest day" is the winter solstice, around December 21, when
the Sun has reached its most southerly and shortest track in our sky.
It would make sense, then, for the summer solstice to also be the date at which
sunrise is earliest and sunset is latest; and for the winter solstice to be the
date when sunrise is latest and sunset is earliest. However, that is not what
happens! Nature sometimes defies our expectations.
The local meridian is a great circle passing through the celestial poles and through the zenith of an observer's location on the planet. Image Credit:
Daniel V. Schroeder
And that is because we have not talked about one other factor in sunrise and
sunset times that is not at all obvious. It is that the Sun moves across the sky,
in its apparent daily track, at slightly different rates at different parts of the
year. Most of the Sun's east-to-west apparent motion in the sky is caused, of
course, by the rotation of the Earth, which is quite uniform (to milliseconds per
day). But a small part of the Sun's apparent daily motion depends
on the position of the Earth in its orbit around the Sun. This component of the
Sun's apparent motion varies by a small
amount over the course of a year due to the elliptical shape
of the Earth's orbit and to the tilt of the Earth's axis. The details of this
variation are explained in detail
but the overall effect is that the Sun's total
apparent angular rate as it moves across the sky varies by as much as 0.07% from
one part of the year to another. That doesn't seem like much, but it means that
the length of the solar day, measured by successive transits of the Sun across
(successive noons on a sundial),
can be as much as a half minute different from 24 hours, one way or the other.
Therefore, we effectively have two kinds of time. Time kept by the Sun's motion
in the sky (apparent solar time) is not a uniform kind of time, like that
kept by our clocks. Mechanical or electrical clocks run at a uniform rate, and
that rate has been set to correspond to the average rate of the Sun across
the sky over the course of the year. So our clock time (neglecting, of course,
daylight time shifts) is a form of what is called mean solar time. Every
day by our clocks has 24 hours exactly, but each day of apparent solar time can be
different from 24 hours by as much as a half minute. At some parts of the year,
the two kinds of time can accumulate a difference of as much as 16 minutes, which
is one reason why sundials hardly ever seem to be correct. We are comparing apples
and oranges: Sun time is not clock time.
Sundials hardly ever give the same time as our clocks. Sun time (technically,
apparent solar time) is not the same as clock time (a type of mean solar
time). The difference affects not only the time kept by sundials, but also the
clock times of sunrise and sunset. Near both the winter and summer solstices, the
changing difference between the two kinds of time has more effect on the times of
sunrise and sunset than the slowly changing geometry of the Sun's track in the sky.
The two effects on sunrise and sunset time might be called, succinctly, the
"geometric effect", which is the variation in the length of the Sun's track across
the sky as a function of the season; and the "clock effect", caused by the fact
that the Sun keeps its own time, which on any given day may be somewhat different
from what our clocks say. Notice that the geometric effect tends to work
oppositely on sunrise and sunset times; for example, in the fall, when the length of
the Sun's track in the sky is getting shorter, sunrises get later and sunsets
earlier. On the other hand, the clock effect works the same way on all Sun
phenomena—if the Sun is "late" on a particular day (compared to the day
before), then sunrise, sun transit (sundial noon), and sunset will all be "late" by
the same amount. The technical name for the clock effect is the
Equation of Time.
During the early fall, the geometric effect dominates the change in rise and set
times; from one day to the next, the Sun is shifting ever more southward in the sky,
and at mid northern latitudes, the total length of daylight (sunset time minus
sunrise time) gets shorter by several minutes every day (see the
Duration of Daylight/Darkness
Table for One Year). For example, on October 15 at 40° north latitude,
the Sun is above the horizon for 2½ fewer minutes than on the previous day.
Based on that effect alone, we would expect sunrise to be later, and sunset earlier, by
1¼ minutes compared to the day before. The clock effect at this time of
year is a rather minor factor; considering the clock effect alone (which is the same
for all latitudes), the Sun is ¼ minute earlier in all of its phenomena
on October 15 than it was on October 14. So the geometric effect
dominates at this time of year in determining the times of rise and set.
As the fall progresses, though, several things change. For one thing, as we get
into November, the geometric effect becomes less of a factor in the day-to-day
changes. The Sun's southerly migration in the sky slows considerably as we get into
December. (It comes to a stop at the winter solstice, around December 21,
after which the Sun begins its slow march northward.) Also, around November 3,
the clock effect changes sign and the Sun begins to run later and later each day.
In fact, as the magnitude of the geometric effect is ramping down, the magnitude of
the clock effect is ramping up. On December 15, the Sun is above the horizon
for only ½ minute less than on the previous day, so sunrise will be
later, and sunset earlier, by only ¼ minute compared to December 14,
based on the geometric effect alone. But the clock effect shifts all Sun phenomena
about ½ minute later by our clocks on December 15 than on
December 14. So, adding the two effects together, the times of both
sunrise and sunset on December 15 are later than on December 14.
Evidently, we have already passed the date of earliest sunset, and the solstice has
not yet occurred. The date of earliest sunset, about December 8 at a latitude
of 40° north, is the date when the clock effect takes over from the geometric
effect in having the greater influence on the times of sunset.
The date of latest sunrise is determined by similar considerations. As we have
seen, in late December, both sunrise and sunset occur later each day. But after the
solstice, the geometric effect, considered alone, tends to shift sunrise earlier as
the Sun's daily track in the sky becomes more northerly and longer. But that effect
is weaker than the clock effect—at least, for a while. Eventually, the
geometric effect overcomes the clock effect's tendency to move all Sun phenomena
later each day. The date of latest sunrise is therefore the date, after the
solstice, when the geometric effect equals the clock effect in magnitude. That date
is about January 5 at a latitude of 40° north. After that, the geometric
effect takes over and the times of sunrise move consistently earlier.
Therefore, between the dates of earliest sunset and latest sunrise, the clock
effect dominates the geometric effect in determining the times of sunrise and sunset
for a given latitude.
The reason the dates of earliest sunset and latest sunrise depend on latitude is
that the geometric effect is a greater factor at high latitudes. There, the length
of the Sun's track across the sky varies more throughout the year. The clock effect
is the same for all latitudes. So at higher latitudes, the dates of earliest sunset
and latest sunrise are closer to the solstice; i.e., closer to when we expect them
to be, based on the geometry of the Sun's seasonal motion. At the equator, there is
no geometric effect at all—the Sun's daily track above the horizon is always
exactly half a circle. The clock effect completely determines when sunrise and
sunset occur there. Earliest sunset occurs around November 2 and latest
sunrise occurs around February 11. But the total variation in sunrise or
sunset times at the equator, over the year, amounts to only about a half hour.
Returning to the middle northern latitudes, sunrise and sunset times near the
summer solstice are influenced by the geometric and clock effects in the same way as
those near the winter solstice. However, the magnitude of the clock effect is not
as large in June as in December. The date of earliest sunrise occurs before the
solstice and the date of latest sunset occurs after.
Getting Technical . . .
The geometric effect mentioned above is a function of the Sun's declination,
the term that astronomers use for the angle that the center of the Sun makes with the
plane of the Earth's equator, as viewed by a fictitious observer at the center of the
Earth. As the Earth orbits the Sun, the Sun's declination goes from +23.4° at
the summer solstice to −23.4° at the winter solstice, and back again, passing
through declination zero (that is, through the equatorial plane) at the two
equinoxes. On the surface of the Earth, the length of time that the center of the Sun
is above the horizon at any given latitude, in hours, is given approximately by
ts = 2/15 arccos (–tan φ tan δ)
where φ is the latitude and δ is the Sun's declination. It is
assumed that the value of the arccos function is given in degrees. This formula
works only for latitudes between the arctic and antarctic circles. The time
ts changes over the course of a year as the Sun's declination
δ changes. This simple formula neglects (1) atmospheric refraction at the
horizon, (2) the small variation in the Sun's apparent rate of east-west motion
across the sky due to the "clock effect", and (3) the small changes in the Sun's
declination that occur during most days. In particular, it's worth noting here that
sunrise and sunset are defined to occur when the top of the Sun (its upper limb)
appears to be on the horizon, with atmospheric refraction taken into account, so the
time between sunrise and sunset is always greater than ts by at
least a few minutes.
As mentioned above, astronomers call the clock effect the
Equation of Time, which is the
difference between apparent solar time and mean solar time. Civil time—what our
clocks read—is a form of mean solar time on the local time zone's
defining meridian (each time zone is based on a meridian with a longitude evenly
divisible by 15°). Officially, civil time is an integral number of hours offset from
Coordinated Universal Time, abbreviated UTC.
The hour offset depends on the time zone and whether daylight time is in effect. UTC is the
successor to Greenwich Mean Time and is synchronized worldwide to very high precision.
The dates of earliest sunset and latest sunrise are the dates before and after the
winter solstice when, at a given latitude, the magnitude of half the daily change in
ts equals the magnitude of the daily change of the Equation of Time.
Half the daily change in ts is used because the geometric (or
declination) effect is divided equally between sunrise and sunset. On the other hand,
the change in the Equation of Time shifts the timing of all Sun phenomena by its full
Approximate formulas for the Sun's declination and the Equation of Time are given
on our page about computing
Solar Coordinates. A table listing both the Sun's declination and the
Equation of Time, for each day of the year, is printed in the annual booklet
The values in the table change from year to year but not by much. You can get the same
information online, for a range of specific dates,
(be sure to select Apparent Geocentric Right Ascension and Declination for the Sun). If
you use this data to make a graph of the Sun's declination as the y-axis and the
Equation of Time as the x-axis, you obtain a figure-8 curve for the year called the
The analemma is the pattern of Sun images that you would obtain if, using a fixed
camera and a multiple exposure setting, you recorded the Sun at noon clock time on
every day of the year that it was clear; see, for example