ELi on EARTH: Perihelion Delays East Lansing’s Sunrise

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Monday, January 4, 2016, 1:57 am
Aron Sousa

The work of Johannes Kepler (shown above) explains the delays in East Lansing’s sunrise this winter.

There will be some interesting happenings in East Lansing’s sky this week. Saturn and Venus will appear very close together, and there will be a minor meteor shower, but it will be too cloudy in East Lansing to witness any of that. What you might expect to witness, even with clouds, would be earlier sunrises, since we passed the winter solstice on December 21. But in fact, sunrise is not coming any earlier yet, even though the days are getting longer. This is because of something astronomers call the perihelion.

The earth orbits the sun in an ellipse, with the sun at one foci of the ellipse, following Kepler’s First Law of Planetary Motion. Picture the earth’s orbit as an oval with the sun off-center, nearer to one of the narrow ends of the oval. Because of this arrangement, there are times of the year when the earth is slightly closer to the sun than others.

Somewhere between January 2 and 5 each year, the earth and sun are at the their closest, and this nearness is called the perihelion. Aphelion, when the earth and sun are farthest apart, occurs between July 3 and 6. The fact that the earth’s perihelion is falling right now, within two weeks of December solstice, and that the aphelion is within two weeks of the June solstice is a coincidence. It doesn’t have to be this way. But it does mean that just when it is our darkest time of year, sunrise is also not coming earlier, because we are at the perihelion.

The perihelion has an effect on the timing of our sunrise because of Kepler’s Second Law of Planetary Motion. That law describes that a line from a planet to a star sweeps out an equal area of space for a given time anywhere in its orbit. The implication of the second law is that the earth moves faster at perihelion (when it is close to the sun) and a little slower at aphelion (when it is farther from the sun). This happens because of the gravitational pull of the sun speeding the earth up when it is closer to the sun, and is the same reason an ice skater spins faster with her arms held in compared to with her arms straight out.

As Eli on Earth has previously covered, the sun rises on earth when our part of the earth rotates enough for us to see the sun over the horizon. Because the earth is tilted (on its axis) as it orbits around the sun, the time you will see sunrise or sunset depends on where the earth is in its yearly orbit (how close or far we are from a solstice) and how far north or south you are on the earth (East Lansing compared to, say, the North Pole).

The perihelion has a subtler effect on the time you will see sunset or sunrise. During a full day, the earth completes part of its orbit around the sun, and the earth has to rotate a little bit extra for those of us in East Lansing to see the sun. Around the perihelion (now), the earth is moving faster than it does at other times of the year, and that increases the distance the earth has to rotate for the sun to come up over our horizon.

This effect is enough to delay the sunrise near the perihelion. (The effect is smaller near the aphelion, when the earth is not moving as fast.) So the sunrise is delayed around perihelion. Even though our days are getting longer since the winter solstice, we are gaining daylight at the end of the day, not yet the beginning of the day. Soon, we’ll be gaining daylight on both ends of the day.

In the summer, it would seem that the sunset should get earlier and earlier after the summer solstice, but the distance traveled by the earth along its orbit in a day is enough to keep the sunset at the same time for a couple of weeks. Since the earth is traveling slower at aphelion, the sunset does not get earlier. (On Mars, which is in a more elliptical orbit, the effect would be greater, although you won’t learn that from The Martian.)

In summary, this winter, the time of sunrise has actually gotten slightly later in the two weeks since the solstice, and this June after the summer solstice, the sunsets will be at the same time for about two weeks.

To see a video about how all this works, click here.



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