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Science/Math question about the time of the year and sunrise

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Science/Math question about the time of the year and sunrise

Old 08-07-04, 01:58 PM
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Science/Math question about the time of the year and sunrise

I'm doing an IB HL math portfolio right now. . .just to get it straight, I'm not asking you to do any homework for me. It goes pretty indepth with longitude and latitude, but I'm stuck at the concept of sunrise in relation to the time of the year.

How does the time of the year affect sunrise time?

I think I understand the orbit of the earth around the sun. In the norther hemisphere, during summer, the earth is tilted to where the north pole gets the sun, but the south pole doesn't. I'm not sure about the exact measure of the tilt, but it's there, and it's the opposite in winter. So that's why Northern and Southern Hemispheres are opposite in that respect.

I also know of the equinox, when the sun shines exactly at a 90 degree angle, i.e. there is no tilt. Same with fall. The days and nights are equal on these days.

I think I also understand how this affects temperatures. Is it because the sun doesn't directly shine on us during the winter, but it does during the summer?

But the more important thing I don't understand is how this affects sunrise time. Can someone explain that to me?

I've viewed the data and I recognize it is cyclical in that you could graph it as a sinusoid function, but in logical terms I'm not understanding the relation, I just know it's there.
Old 08-07-04, 02:01 PM
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day and night aren't equal during the equinox (well maybe at the equator).


the tilt "changes" the sunrise time. it also changes with the latitude. the further toward the poles you are, the shorter the night is during the summer. kinda hard to explain. get out a globe and shine a flashlight at it and see how because of the tilt the light is skewed twoard the poles
Old 08-07-04, 02:11 PM
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ok, I think I see why. The flashlight was a good idea. Does the moon factor into any of this?
Old 08-07-04, 02:12 PM
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Math is hard. Tee Hee.
Old 08-07-04, 02:15 PM
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Originally posted by theneobez
ok, I think I see why. The flashlight was a good idea. Does the moon factor into any of this?
no, unless you want to talk about eclipses or tides
Old 08-07-04, 02:17 PM
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k, thanks Venusian.
Old 08-07-04, 02:22 PM
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i think i found a way to explain it, in case the flashlight thing isn't clear....


the closer you get to the pole, the smaller the distance you travel when you do a rotation, right? at the pole, you essentially travel no distance during a day (ignore revolution around the sun).

so, imagine an earth with no tilt. now pick any random point and draw a line that it travels during a day (it will be a line of latitude). now imagine a few more (like the equator). now imagine the sun shining on this no tilt earth. all the lines will have half of it in the dark and half in the light. the length on each side will be different since the lenghts are different of each line but 1/2 of each line will be on each side.

now tilt this earth (and lines) in your head. now the lines closer to the poles have a higher percentage of themselves in the light than the lower lattitude lines do. thats why sunrise/sunset change
Old 08-07-04, 02:27 PM
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I don't know how much math detail you wish to get into. The location of the sun is defined at any instant by declination and Greenwich Hour Angle. Declination can be thought of as the latitude where the sun is directly overhead. During the year, it varies between 23.5 degrees north and south of the equator, the equinox is when it is exactly at the equator.

The Greenwich Hour Angle is kind of the longitude where the sun is directly overhead at any instant, except it is expressed as 0-24 hours instead of 360 degrees. It moves about 15 degrees of longitude per hour. These values can be looked up in the astronomical or nautical almanac.

At any moment, the sun is directly overhead some point on earth and illuminates 1/2 the earth, or 1/4 of the way around in each direction. In summer, the sun is near 23.45 degrees north latitude. Because the north pole is less than 90 degrees away, it is illuminated 24 hours a day, points more than 90 degrees away from the sun's "ground point" are experiencing night. Under the same (northern summer) conditions, the south pole is always more than 90 degrees away from GP and dark 24 hours a day.

Near the equator day and night are always pretty close to 12 hours each. At latitudes in between the equator and the poles, length of day varies.

Last edited by OldDude; 08-07-04 at 02:36 PM.
Old 08-07-04, 02:31 PM
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Originally posted by Venusian
day and night aren't equal during the equinox (well maybe at the equator).


Well, almost. For a point sun and an airless earth, they would be. The sun has a finite semidiameter, and sunrise and sunset are defined by the upper limb at the horizon, not the center. In addition, the earth's atmosphere bends the light rays, this is called refraction. The "standard conditions" for both is to allow 50' of arc beyond geometric sun rise and set, but refraction varies with temperature and air pressure, the sun's semidiamter varies plus and minus 1.6% from nominal, so "real" may be off from standard by 1-2 minutes.
Old 08-07-04, 02:35 PM
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The US Naval Observatory has calculators for a lot of astronomical things on this page. There are some FAQs near the bottom of the page that help with (rather formal) definitions of sunrise and set. They may be too detailed, but really good stuff.
http://aa.usno.navy.mil/AAmap.html
Old 08-07-04, 03:36 PM
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actually olddude I was already using that site, heh, it's given on the portfolio instruction sheet. Yeah that explanation was even better venusian.

Olddude before I came back to check the thread I actually discovered that about the longitude, with every 15 degrees being an hour. This is actually getting more and more interesting as I'm analyzing the results.

Thanks for the explanations Olddude and Venusian.
Old 08-08-04, 05:45 PM
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Hey, would any of you be willing to read my portfolio to see if it makes sense, if I'm using the right notation, if I'm using mathematic terms, etc.? I'm finished at this point.

It's around 20 pages, mostly because of the huge tables and such. I'd be grateful for any help. . .
Old 08-08-04, 06:18 PM
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hey olddude...are you pulling this stuff from memory?
Old 08-08-04, 06:38 PM
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Originally posted by D.Pham00
hey olddude...are you pulling this stuff from memory?
Yes, except for the link to USNO, I pulled that from my "Favorites" list.

I have an amateur interest in computational astronomy. Want to chat about how to compute the position of the sun to better than 3 arcseconds?

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