Astronomy Question: Please explain the rising and setting of the sun to me.

Factual Questions
#1

I was wondering what effect latitude has on the amount of sunlight a place gets, especially during the Autumn and Winter months. So I went to the Old Farmers Almanac and picked two places with similar longitudes but different latitudes:

Edgeworth, PA - 40:33:15 N, 80:11:31 W

Miami, FL - 25:46:32 N, 80:12:39 W

Then I started punching numbers into the sunrise/sunset calculator. The following rising and setting times are for Eastern Standard Time at sea level. The site gives EDT for August, September and October, but I corrected it for the purposes of this question. I made no adjustment for leap year.



             |      Edgeworth, PA           |              Miami, FL       |
Date         | Sunrise  |  Sunset |  Total  |  Sunrise |  Sunset |  Total  |
             |          |         |         |          |         |         |
Aug 21, 2003 |  5:37AM  |  7:11PM |  13:34  |  5:56AM  |  6:52PM |  12:56  | 
             |          |         |         |          |         |         |
Sep 21, 2003 |  6:07AM  |  6:20PM |  12:13  |  6:09AM  |  6:19PM |  12:10  | 
             |          |         |         |          |         |         |
Oct 21, 2003 |  6:38AM  |  5:33PM |  10:55  |  6:22AM  |  5:48PM |  11:26  |  
             |          |         |         |          |         |         |
Nov 21, 2003 |  7:13AM  |  4:59PM |   9:46  |  6:43AM  |  5:31PM |  10:48  |  
             |          |         |         |          |         |         |
Dec 21, 2003 |  7:40AM  |  4:57PM |   9:17  |  7:03AM  |  5:35PM |  10:32  |  
             |          |         |         |          |         |         |
Jan 21, 2004 |  7:39AM  |  5:25PM |   9:46  |  7:08AM  |  5:56PM |  10:48  |  
             |          |         |         |          |         |         |
Feb 21, 2004 |  7:07AM  |  6:03PM |  10:56  |  6:51AM  |  6:18PM |  11:17  |
             |          |         |         |          |         |         |
Mar 21, 2004 |  6:21AM  |  6:35PM |  12:14  |  6:23AM  |  6:33PM |  12:10  |
             |          |         |         |          |         |         |

The Pennsylvania data is pretty much what I expected. Sunrise gets later and later until the sometime around the Winter Solstice, when it starts getting earlier again. Likewise, sunset gets earlier and earlier until sometime around the Winter Solstice, when it makes a turnaround and starts getting later again.

But Miami is different. Sunrise appears to continue to get later every day until long after the Winter Solstice. According to the Farmer’s Almanac site, the first day in 2004 that the sun will rise earlier than the day before will be between January 8th and January 19th. It’s probably only a matter of seconds, and the site only gives the time in minutes, so you can’t tell from that exactly which day it will be. Is there a name for that event?

The same thing happens with the sunset in Autumn. The sun will first set later than the previous day sometime between November 21st and December 9th, and will continue to set later from that point on. Is there a name for that event?

Another thing I notice when I advance the calculator day-by-day is that, even though the sun starts setting later in Miami on an earlier date, there is still a net loss of daylight until sometime around the Winter Solstice, because until that time, the sunrise is getting later faster than the sunset is. Then it reverses course, and the lateness of the sunset starts to outpace the lateness of the sunrise, until January 8-19, when the sun just gives up and starts rising earlier like it’s supposed to.

So the question (besides whether there’s a name for the time when the tropical sunrise starts getting earlier, or when the tropical sunset starts getting later) is simply this: Do the tropical latitudes get more total daylight hours than the temperate zones? Or does it all balance out somehow? If so, how? Are the longest days not as long in the tropics as they are up here, while the shortest days aren’t quite as short? Is there a good book or website out there which explains the astronomy of tropical sunrises and sunsets?

Thanks.

#2

To understand why the latest sunset, earliest sunrise, and the solstice don’t all happen on the same day, google “equation of time.” It’s fundamentally because the Earth doesn’t go around the Sun in a perfect circle.

I think the other question you have is why, at the equinoxes, does PA get more daylight than FL. It’s because the refraction of the atmosphere makes the sun appear to set when it’s actually already down over the horizon by a half-degree or so, and since the PA people see the sun set at a steeper angle, it takes longer to get there. I think.

#3

The reason that the sunrise/set times don’t behave symmetrically around the solstices is that the earth’s orbit isn’t a perfect circle and our axis is tilted. The elliptical path means the speed in our orbit changes throughout the year (fastest in the winter, when we’re closest to the sun), so the day isn’t 24 hours long and “clock noon” isn’t when the sun is directly overhead.

The graphical representation of this variation is the analemma, which is the figure-8 looking symbol you might see on a globe.

Here is more info, and

Here is some more.

#4

Okay, I’ve looked at a few links, and I think I understand a little better how the tilt of the Earth and proximity of the Earth to the Sun play a role in the rising and setting times.

But I’m still trying to figure something out about latitude. So far, I understand that there’s a day when the sun sets earlier than any other day of the year. The higher the latitude of a location, the closer the “earliest sunset day” for that location will fall to the actual Winter Solstice. Also, the difference between sunset on “earliest sunset day” and sunset on the Winter Solstice gets larger as latitude decreases.

And then my head explodes. Does all this mean that lower latitudes experience more total daylight hours than higher ones throughout the year? Or does every latitude get the same amount of daylight time in the end, after you factor in all the different movements and angles and stuff?

Or do lower latitudes get more total daylight in Winter in exchange for less total daylight in Summer? Or vice versa?

I suppose I could have phrased this question much more simply. Do points closer to the equator experience more total daylight hours than points further from the equator in a given year or don’t they?

#5

IIRC, the latest sunset is not on the solstice, but several days after. Solstice marks the shortest day, not the latest sunrise. Sunsets may start getting later before Dec 21, and sunrises lag for a while, but the overall effect is that the amount of daylight gets shorter until Dec 21, then increase.

So you may need more data. Check the dates after Dec 21 and see if the sunrise time goes later than 7:08 before slowly dropping back down.

On the other hand, my memory could be completely wrong.

-dave-

#6

Although the equation of time gives the whole story, for me at least, it is not the best way to think about it. I think of it in terms of two cycles. One is the length of daylight and the other is the analemma, the fact that the astronomical day (that is, day + night) is not exactly 24 hours, but varies by a few seconds more than that or less. This is a result of the eccentricity of the earth’s orbit and results in true solar noon (the time the sun crosses the meridian) varying from about 11:44 AM to 12:16 PM IIRC. Now the length of daylight cycle varies a lot with latitude from 0 at the equator to 24 hours at the poles. So at 40 deg it is a lot more than at 25. When you have two such cycles, the maximums and minimums vary depending on the contribution of each one. And at 40 deg the analemma cycle has more impact, while at 25 it has much less.

There is one other complication. The sun is about a 1/2 degree in diameter and sunrise is the instant that the first limb of the sun appears and sunset is the instant that last limb of the sun disappears below the horizon. This lengthens the day by the time that it takes the sun to first touch the horizon and the time it last touches. At the equator this can be worked out quite easily to be 2 minutes since the sun moves 15 deg every hour so half a degree in 1/30 of that time. At the pole it takes a couple days. In between it takes in between lengths of time. I am not sure how to calculate this; my spherical trigonometry is non-existent. But this does confuse the issue somewhat as well as explain why the sun sets so fast in the tropics. Finally, there is said to be refraction, although I am not convinced that that is real.

#7

If (contrary to the Farmer’s Almanac), we define “sunrise” and “sunset” in terms of when the center of the Sun crosses the horizon, and if we neglect refraction, then over the course of a year, any point on the globe will be day exactly half the time and night exactly half the time. As you guessed, the extremes for a particular date are greater farther from the Equator: On the Equator, day and night both last exactly 12 hours each, no matter what the date, and in the arctic (past the arctic or antarctic circle) the “day” is 24 hours long on the Summer Solstice, and the night is 24 hours long on the Winter Solstice.

The reason that the arctic regions have lower average temperatures than the tropics is that when the Sun is up in high latitudes, it’s not up as far. At the poles, for instance, the Sun never gets higher than 23.5 degrees above the horizon, whereas anywhere in the tropics, it can get as high as directly overhead.

#8

No, they do not. Contrary to what your intuition would tell you, the poles receive the most daylight of any location on Earth, and the equator the least. This is because of the lofting effect of atmospheric refraction (yes, it’s real), the angular diameter of the solar disk, and the angle of sunrise and sunset at different latitudes.

Here is one way to think about it: If the Sun is “near” the horizon, at least part of it will appear to be above the horizon. The Sun spends more time “near” the horizon at the poles than at the equator.

The Sun rises and sets once each year at the poles, but it takes about 30 hours (each way) to do so. It rises and sets every day at the equator, but does so in two minutes. Do the math–3600 total “rising and setting” minutes at the poles, versus 1460 at the Equator.

#9

This is the type of question that will make me waste hours on end until I get it right. Here is the straight dope:

We can neglect to consider refraction and semidiameter because the effect is small nad pretty much constant. We then consider strictly the geometric Local Hour Angle (LHA) of the sun at sunrise.

During the course of the year this varies due to two effects: the Equation of time and the effect of the varying declination of the sun. The effect of the Eq.o.T is constant for all latitudes while the effect of latitude-sun dec is zero at the equator and increases with latitude.

If the Eq.o.T were constantly zero then the sun would rise at the equator at exactly 6 am every day of the year. With increasing latitude it would rise correspondingly later in winter and earlier in summer.

At the equator there is no effect due to the changing declination of the Sun. After the winter solstice, due to the Eq.o.T, sunrise happens later every day until February 15 when it starts to get earlier.

After the winter solstice, as you move north in latitude, the effect of the variation of the declination of the sun is to make the sunrise happen earlier but the effect of the Eq.o.T is to make it happen later. Depending on the latitude, the effect of lat-dec will become greater than the effect of the Eq.o.T at a different date. As you move up north it happens earlier.

lat 00N = 15 feb
lat 15N = 24 jan
lat 30N = 11 jan
lat 45N = 04 jan
lat 60N = 29 dec

In summary, until those dates, the effect of the Eq.o.T is greater than the effect of lat-dec.

I have the spreadsheet calculating both factors for any given latitude but it is too much information to post here.

#10

With respect to the question, “When is the latest sunrise or earliest sunset at a given latitude?”, that is entirely correct.

With respect to the question, “Which location on Earth experiences the most daylight in the course of a year?”, however, these factors are determinative.

#11

That is the only question I answered.

I did not answer that question because I believe it is not well defined. You would need to define it further. I believe the simplest definition would be daylight is when the sun is above the horizon or between the horizon and an arbitrary number below. In any case I do not believe it would make much difference from one latitude to another. That is considering only hours of daylight. If you consider the intensity of the daylight (sunlight), then the tropics win (obviously).

Hari Seldon, refraction under standard conditions, on the horizon is 34.5 minutes of arc. What you see on the horizon is 34.5 minutes below the horizon. Roughly speaking that is the diameter of the sun so, when you see the lower limb touching the horizon, the upper limb has just sunk (geometrically) below the horizon.

#12

Thank you all for your effort, especially sailor. I guess the question wasn’t as well-formed as it could’ve been. I was looking for a way to wrap my mind around the way the sun rises and sets throughout the year at different latitudes, and I think I sorta get it now.

At some point it finally hit me exactly what question I was asking, and a good way to answer it for myself. I went back to the Farmer’s Almanac site and plugged in the longest and shortest days of the year for those two latitudes:

At 40:33:15 (Pennsylvania) on December 21, the sun will rise at 7:40AM and set at 4:57PM EST, for a total of 9hrs 17min of daylight time. On June 21, it’ll rise at 5:50AM and set at 8:55PM, for a total of 15hrs 5min of daylight. A difference of 5hrs 48min.

At 25:46:32 (Miami, FL), however, the sun will rise at 7:03AM and set at 5:35PM, for a total of 10hrs 32min of daylight, while on June 21 it will rise at 6:30AM and set at 8:16PM for a total of 13hrs 46min. A difference of only 3hrs 14min.

So it would seem logical that both latitudes receive roughly the same amount of total daylight throughout the year, it’s just that the higher latitudes vary more in the amount of daylight they receive by season. The lower latitudes don’t have super-long days in the Summer, but their days don’t get super-short in the Winter either. Do I have that much right, at least?

#13

cuauhtemoc, you got that quite right. You can go to http://www.time.gov/timezone.cgi?Eastern/d/-5/java and see the map of the earth showing where it is dark and where there is daylight at any given moment. The illuminated part moves left (west) during the hours of the day. If you look at it now you will see the upper (north) part is narrower so the norther hemisphere is receiving fewer hours of daylight than the southern hemisphere. At the time of the solstice the difference is most marked. At the time of the equinox the lines are vertical and every place on earth receives 12 hours.

You can even neglect to consider the Eq.o.T and only considering the north-south motion of the sun you would get pretty much the same thing. The effect of the Eq.o.T is to make the leftward motion of those lines wobble a tiny bit back and forth during the year. The sun, instead of rising and setting the same amount of minutes around mean noon, can be slow or fast by a number of minutes so that it rises a few minutes late and then sets (roughly) the same number of minutes late.

In a very simplified way you can say that

#14

Please keep in mind the old Firesign Theater line:
“The sun’s not going down, the horizon’s moving up…”
Sorry, I couldn’t resist… :wink:

#15

Roughly, yes, but not exactly. You can see the difference in the figures you quoted. Add the daylight times at the solstices. You get 24 hours and 22 minutes for Pittsburgh, and 24 hours and 18 minutes for Miami.

  1. Why don’t the figures sum exactly to 24 hours? Because of refraction and the angular diameter of the Sun.

  2. Why does Pittsburgh add to a higher total than Miami? Because the Sun sets at a shallower angle in Pittsburgh, which accentuates the above two effects.

So, using the standard astronomical definitions of sunrise and sunset (when the Sun’s upper limb drops out of sight), the poles get the most “daylight”, and the Equator the least.

Quite obviously, this has no effect on average temperature, which depends primarily on the intensity of sunlight, and not on its duration.

But precisely because it has no effect, and contradicts what you would expect based on temperature, I think it’s a fascinating bit of trivia.

#16

For a good live visual, check out this site below. It helps you understand -by showing you where sunlight is shining right now -how light cascades across the globe, affecting daylight and nightime lengths for various positions. You can see how the curvature of earth and the tilt affect the timing.

Very helpful to me for the same kind of issue.

http://www.time.gov/timezone.cgi?Eastern/d/-5/java

#17

Hey, Philster, good site. Where did you find it? :wink:

Regardless of refraction and semidiameter the average day is only 12 hours at the equator because the average declination of the sun is not zero. The sun spends more time in the northern hemisphere which means days in the northern hemisphere are longer. The average declination of the sun over one year is 0.4 degrees north. Defining day as time during which the center of the sun is above the horizon (in other words, not taking into account semidiameter and refraction) the average length of day at latitude 40 N is 12 h 8 min whereas at latitude 40 S it is 11 h 52 min. That is what my calculations show. Maybe someone can cofirm or correct this.

#18

I just realized I made a mistake when converting fractions of hours to minutes (I divided, instead of multiplied, by 0.6). The average length of a “geometrical” day at 40N is 12h 3m and at 40S it is 11h 57m. The difference from 12 hrs is +/- 3 min. At latitude 50 it is +/- 4 minutes.

#19

Hey, it’s my turn to resurrect an old thread. I found some more information on this. This comes from responses posted to a column by everyone’s favorite anti-Cecil, Marilyn vos Savant.

I was wrong in saying the poles get the most daylight and the equator the least. Spherical geometry is a little more complicated than that. Assuming that the program is correct, here are the figures for hours of daylight per year at various latitudes:

For those interested in intensity as well as duration of daylight, the thread discusses that as well.