Post by Jerry Friedman Post by HVS
Ive been (non-obsessionally) monitoring the changes to the times of
sunrise and sunset since the solstice, and dont understand why the
changes to those times are asymmetrical.
On 21 December, the sunrise and sunset times for my location (51.2665
N/ 1.0924W) were 08:06 and 15:58. Today (14 January) theyre 08:02
and 16:23. So sunrise has become 4 minutes earlier in that time, while
sunset is 25 minutes later.
Checking for the other end of the year, the times for 21 June are 04:48
and 21:23, and for 14 July are 05:04 and 21:15 sunrise is 16
minutes later; sunset is 8 minutes earlier.
So how come the times of sunrise and sunset dont change at the same rate?
And why is the asymmetry more marked in December/January than in June/July?
tl;dr: It's because the Earth's orbit is an ellipse, not a circle, and
because the Earth's axis is tilted (causing the seasons).
When the Earth makes one exact rotation, the stars appear in the same
places in the sky, but the Sun does not. That's because the Earth has
moved in its orbit during that time. The Earth rotates in the same
direction as it moves in its orbit, counterclockwise as seen from the
north [*], so it has to rotate slightly farther for the Sun to be in the
same position in the sky. If we ignore the elliptical shape of the
Earth's orbit and the tilt of its axis, it has to go farther by 1/365
[**] of a day every day in order for the Sun to go around once in a
year. That's 24/365 of an hour, or 60*24/365 minutes, which is about 4
minutes. We define the /average/ time for the Sun to return to
approximately the same position as a day, so a day is about 4 minutes
longer than the rotation period of the Earth. In other words, the time
for one rotation, called the sidereal day because it's relative to the
stars, is about 23 hours and 56 minutes.
However, the Earth's orbit is an ellipse with the Sun off center, and
when the Earth is close to the Sun (it's closest about Jan. 4, whether
it feels close to the Sun then or not), it moves faster. So during that
time, the Earth has to rotate a little farther to bring the Sun into the
same position in the sky, and the interval between one noon and the next
is a little more than 24 hours. Thus sundials run slow, and in the
northern hemisphere sunsets get later faster than sunrises get earlier.
When the Earth is farther from the Sun (it's farthest around July 6),
the opposite happens.
Got that? Also, the Earth's axis is tilted with respect to the plane of
its orbit. Now if we could pretend the orbit is a circle again, the
apparent position of the Sun relative to the stars would move at the
same speed all year. However, at the solstices it's moving directly
east [***], making the difference between the 24-hour day and the
sidereal day more than 4 minutes and making sundials run slow. In
contrast, at the March equinox the Sun is moving northeast and at the
September equinox it's moving southeast, so it makes less progress east,
and the difference between the 24-hour day and the sidereal day is less
than 4 minutes; sundials run fast.
Those two effects combine to control the times of sunrise and sunset.
As Jan said, a good search term if you want to know more is "equation of
Do you deal with sundials in your work? This is the sort of thing
sundial experts know about. (ObVocab: Gnomonists.)
[*] Almost by definition. The Earth rotates counterclockwise as seen
from the north, so the Sun appears to us to move clockwise in the
northern hemisphere, so shadows move clockwise, and sundials are
numbered clockwise--and clock dials are numbered the same way as
[**] Closer to 1/365.25, you pedants, but I'm going to give the answer
to one significant figure.
[***] The solstices (solstitia) are when the sun is "standing still".
Standing still and moving directly east? The Sun at local noon is
always due north or south (or overhead, in the tropics, and kindly allow
me to ignore the Arctic and Antarctic). When the ancients looked at the
position of the Sun at noon, they didn't see the eastward motion (which
is defined only relative to the stars, seldom visible at noon). They
saw only that at the solstices, the noonday Sun reached its most
northern point and its most southern point, so it briefly stopped moving
(north or south) as it turned around.