Sunrise Sunset

On February 6, an inquisitive reader of this column, whom we will call
Dorothy, sent me an email: “I have a question for you. This year I have been
keeping track of the times of sunrise and sunset. I have been surprised that the
morning daylight isn’t increasing as much as the evening light. I took the times
from the weather report on TV. On December 22 the sunrise was at 7:58 am and
sunset was at 4:55 pm. On February 5, sunrise was at 7:39 am and sunset was at
5:45 pm. Am I right in figuring that means 50 more minutes of light in the
evening, but only 19 more minutes in the morning? I had expected that it would
be about the same increase both times. My question is why doesn’t it increase
the same morning and evening?”
I sent her an email saying that I’d wondered about that too, and that would
try to find an answer. (Translation: I was basically clueless!)
On March 6, Dorothy sent another email. “I have still been charting the
sunrise and sunset times. For the past 30 days the sunrise has gained 42
minutes while sunset has gained only 39 minutes of light. I am guessing that by
summer the total gain will be equal when it again begins losing minutes of light.
It will be interesting to see.”
Again, she got no explanation from me. I was still in the dark about the sun.
On April 12, Dorothy sent another email. “I notice now that morning light is
increasing faster than the evening one so the total is getting more even. I sure
don’t understand how it works though.”

Okay, Dorothy, let’s see if I can take a stab at answering your question.
First of all, the reason for our seasons is the 23.5 degree tilt of the earth’s
axis. In the summer, the Northern Hemisphere is tilting toward the sun. In the
winter, the Northern Hemisphere is tilting away from the sun. Winter solstice
occurs when the earth’s axis is most tilted away from the sun. It is the shortest
sun-lit day of the year for us in the Northern Hemisphere. It occurs on or about
December 21. From that day on, the Northern Hemisphere gets more and more
minutes of sunlight. From our point of view on the earth we see the path of the
sun, instead of being in the southern part of the sky, begin to creep northward.
Sunset and sunrise times change in such as way as to give us more sunlight every
day. The summer solstice occurs in June when the earth’s axis is most inclined
toward the sun. It is the longest sun-lit day of the year. We discussed this in the
March 27 issue of the Standard Journal.
Second big idea: There are two ways to define when one day has passed.
See the figure below, taken from the Millennium Mathematics Project, University of
Cambridge web site:

The figure shows the earth (in blue) at position 1 at noon at some place on
the earth. The earth then makes one complete rotation, shown as position 2.
Ordinarily, we would think that one complete rotation of the earth about its axis
should equal one day, right? But if we want to go from noon on day 1 to noon the
next day, the sun (yellow at the center of the figure) should be directly overhead
each time. However, because the earth has been traveling through space in its
orbit at the same time it’s rotating about its axis, it will take a little more rotation
for the sun to be directly overhead. This happens at position 3 on the figure.
Confusing? Try this analogy. Imagine you’ve taken a child named Johnny to
an amusement park. On one ride, kids sit on a large ball that is attached to a track.
The ball (and Johnny) moves slowly around an oblong track at the same time the
ball rotates. You stand in the middle and take Johnny’s picture when he’s directly
facing you at position 1 in the figure.
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When Johnny is at position 2, he calls out, “Take my picture! Take my
picture!”
You say, “No, Johnny, I’m not going to take your picture until you’re directly
facing me.”
Because Johnny is both rotating and moving along a track, before you take
the second picture, you have to wait until Johnny is at position 3, when he’s facing
you again. Replace you by the sun and Johnny by someone looking at the sun at
noon on two different days, and you’ve got the idea of what this is all about.
In astronomy, the time it takes to go from position 1 to position 3 is called a
solar day. The time it takes to go from position 1 to position 2 is called a sidereal
day.
This extra time to go from position 2 to position 3, on average, is about four
minutes. According to the Cal Tech outreach web site, “This little difference in
time would cause no concern if it were always the same, but it is not!”
Now we have to add one more complication: The earth moves in an elliptical
orbit. (An ellipse looks like a circle that someone has sat on.)
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As shown in the figure, on January 3, the Earth is the closest to the sun.
This position is called the perihelion of its orbit. On July 4, the Earth is the farthest
away from the sun. This is called the aphelion.
Back to you and Johnny again. Suppose that the ride that Johnny is on
speeds up along the track some of the time and slows down at other times. This
happens with the earth too. And that affects the length of the solar day.
According to the New Scientist web site: “The asymmetry in the rates of
change of sunrise and sunset times arises from the nature of the Earth’s orbit
around the sun, and is caused by variations in the length of the solar day, the time
between solar noons on successive days, throughout the year. Sunrise and
sunset are essentially symmetric about solar noon, but solar noon is not always
clock noon.”
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“The Earth speeds up as it approaches the perihelion of its elliptical orbit,
the point of closest approach to the sun, and slows down as it approaches the
aphelion. The increased speed at the perihelion, together with the shorter distance
to the sun, means the angle swept out by the Earth about the sun every day is
greater near the perihelion than near the aphelion. So more rotation is needed to
complete a solar day near the perihelion, causing the solar day to lengthen.”
That is what introduces the lack of symmetry between the changes in
sunrise and sunset as noticed by Dorothy. There’s much more that could be said,
but we’ll leave that for another day.
Thanks for the question, Dorothy! It’s been fun to try to fin d an answer.
Weyland welcomes your comments. He can be reached at
jack.weyland@gmail.com