# What are the exact causes that differences in sunrises are shorter around june and december but long in march and september?

The changes of the sunrise and sunset times not expire regularly in a straight line but according to a sinusoid. Around the solstice (summer solstice on June 21st and winter solstice on December 21), the day length changes the least. The difference in sunrise and sunset in the days around the solstice is only a few tens of seconds per day.

At equinox (March 20 and September 23), the length of day and night on earth is everywhere the same. The difference in day length from day to day around the equinox is changing rapidly. The difference in the length of day can rise around the time of equinox to 3 minutes per day.

This asymmetrical lengthening and shortening of the days is because the "middle" of the day, every day a little shifts. This has to do with the fact that the earth does not describe a exact circle orbit around the sun, but an elliptical orbit. Because the Earth's axis at an angle to the orbit around the sun takes the shorter and longer are the days asymmetrical.

As for the elliptical orbit, I understand that, for example,the sun is the farthest from the earth in the summer (on northern hemispere). Because of the (second) law of areas of Kepler is the speed of the earth there the slowest. In itself, I understand then that at that time the difference in day length also is shorter. That is during June 21 (summer solstice).

But so is apparently also on the winter solstice on 21 December. Precisely at that time the earth is closest to the Sun (perihelion) so the earth has a higher speed. But because of the higher rate would you expect the day lengthening/shortening would therefore be greater. However, it appears not to be so. How is that possible?

So the question in short terms:

sunrise in june on the 21 at 5:30 and 22 at 5:31 etc sunrise in march on the 21 at 7:30 and 22 at 7:33 So the difference is in june one minute and in march it is 3 minutes. And the question is what causes that the difference is bigger in march then in june. See http://www.timeanddate.com/sun/france/paris for a bigger disquisition

• Do you have any sources for your claims on the rate of changing daylight during perihelion? – Dean Jul 3 '16 at 16:22
• Well actionally it is a little bit just an example to explain the difference which can occur. So those dates and times are not of an exact place. But just take this site timeanddate.com/sun/france/paris and switsh from march to june and you will see the same pattern – Marijn Jul 3 '16 at 20:13
• Also have a look at the analemma. The altitude of the sun changes through the year, and the rate of change is highest at the equinoxes and less at the solstices. (This is just a different way of saying what James has said in his answer.) – Andy Jul 4 '16 at 15:28
• but what causes the rate of change to be the highest at the equinoxes? – Marijn Jul 4 '16 at 15:42
• I find the geometry very difficult to explain in words, but think about a periodic function, like a sine wave: The curve is steepest (and moves fast) at two points, and is stationary (moving slow) at its maximum and minimum. The Sun's projection onto Earth's sky follows a similar rule. (Don't know if it's exactly a sine curve though.) – Andy Jul 4 '16 at 15:58

## 4 Answers

If I understand you correctly, you ask why does the length of the day not change much around the winter solstice.

There is no mystery here: The rate of change of day length has (almost) nothing to do with the elliptical orbit of the Earth.

In autumn the days get shorter; the rate of change of day length is negative. In spring the days get longer; the rate of change is positive. At midwinter solstice the rate of change of day length is zero: The length of the day doesn't change. Exactly the same is true in midsummer. Mathematicians would say that the "day length function" is stationary on those dates.

This has nothing to do with the elliptical orbit. Every smooth function is stationary at its maxima and minima. The reason is not astronomical but mathematical.

Note that the Earth is furthest from the sun (and therefore moving slowest) on July 4th.

• I think the OP has clarified their question. Reading the added paragraph, it seems to me that question is "Why is the change in day length less in June and December than in March and September?" If I'm right I'll stick by my answer. If they clarify further I'll delete. – James K Jul 3 '16 at 20:23
• ah, OP is asking about the difference three months apart. {TBC, I thought OP was asking about a difference 6 months apart.} TBC then, isn't the answer simply "sine waves are steep at the two middles and flat at the two tops". – Fattie Jul 3 '16 at 20:28
• Exactly, nothing to do with ellipses/Kepler's second law at all. – James K Jul 3 '16 at 20:30

The next aphelion is July 4 at UT 16:24. Next perihelion Jan 4, 2017. Depending on latitude, the length of daylight varies over a year. Since the Earth's spin is NOT locked to its rotation, where the Sun is in the sky on the same date for consecutive years will not be the same. I am unable to find a table of day lengths to the second, so I can neither confirm nor deny the accuracy of your vague claim - that is since you didn't provide specific evidence, nor cite any source, I am left with little to work with. You noted that the date of maximum axial tilt is NOT the date of apses? Given two non-linear factors, I'm surprised you expect the result to be exactly symmetrical. You also need to be careful writing about differences of differences. There is a better language for that than English: it's called mathematics.

Because of an apparent language barrier, I'm not sure if the question is about the cause of the seasons or about the equation of time.

To the questioner, do not make the mistake of assuming that conditions specific to Paris apply worldwide. It is now the time to go skiing in Chile, New Zealand, and Australia. While early July is the peak of summer in the northern hemisphere, it is the peak of winter in the southern hemisphere. Skiing fanatics with lots of disposable income take advantage of this fact and spend November to April in the northern hemisphere and then spend May to October in the southern hemisphere.

The shape of the Earth's orbit has very little to do with the seasons. It is the Earth's axial tilt that drives the seasons.

The other possible interpretation of the question is the time from one local noon to the next. This is the subject of the equation of time. Unlike the seasons, the time from one local noon to the next is the more or less the same from 66 degrees south latitude to 66 degrees north latitude. (Regions outside of those latitude limits can see days or nights that are several 24 hour days long.) Due to the Earth's axial tilt and it's slightly eccentric orbit, the time as measured by a clock between successive local noons varies somewhat over the course of a year.

The phenomenon you are asking about has nothing to do with the shape of Earth's orbit. Although it does affect sunrise/sunset times, it isn't the major influence on rate of change of sunrise/sunset time. It has everything to do with the Earth's axial tilt and the Sun's aspect to the Earth at different latitudes.

Day length is determined by how much the Earth's axis is tilted toward or away from the Sun. For some mid-latitude location, say New York, London, Tokyo, etc., we will have a normal day and night of some length, varying with the season.

From the perspective of a Sun-Earth line, the Earth's axis appears to wobble, with each pole uniformly describing a circle, and completing one rotation each year (bear in mind that the Earth's axis is fixed in space and only appears to wobble because our frame of reference is rotating in the opposite direction).

When the "wobble" is projected onto the Sun-Earth line, it will appear as a tilt that smoothly varies toward and away from the Sun. Imagine watching someone on a carousel from a distance. They travel around in a circle at a steady speed, but from your bystander perspective, they seem to be coming toward you, turning, and then receding. As they turn, they seem to slow, until, facing sideways for an instant, they are neither advancing toward you nor receding. The change in tilt between Earth and Sun is analogous to that person on the carousel.

• But what causes to slow down or to speed up. Is that due to the shape of the earth? – Marijn Jul 4 '16 at 13:53
• @Marijn I rewrote the last paragraph. Hopefully that will help. – Anthony X Jul 4 '16 at 22:35