Question about hours of daylight and distance from the equator (see details)?

Question

I started thinking about this as the hours of daylight are decreasing due to the approach of winter. As you move north (or south) of the equator, towards the poles, during the time approaching the winter equinox, there are fewer hours of daylight each day. Here in NY, for example, on Dec. 21, there are roughly 6 hours of daylight. However, at the north pole, there are 0 (zero) hours of daylight.
My question is, as you move away from the equator, is there some linear (or non linear) relationship between the distance from the equator and the number of hours of sunlight? For example, say on Dec. 21 there are 12 hours of sunlight at the equator, if you travel 1000 miles north of the equator, how many hours of sunlight will there be? Is there some equation that expresses, for N miles from there equator, there will be Y hours of sunlight per day? Does this equation change as we approach the winter equinox, or is it constant from one day to the next?

I'm not entirely sure if I am asking the question correctly, but I hope you understand the point I am getting at. Is there a way to calculate the hours of sunlight on a particular day if you know the distance from the equator? Or, can you calculate the marginal difference in hours of daylight with each mile you move away from the equator? And would the equation change from one day to the next or would it change as you move away from the equator because the earth is a sphere?
I'm not a mathematician, I just got to thinking about this the other day and became very curious about it.
Thanks!

Answer 1

you are right,lenght of day depends on : date (position of the earth on it's orbit); location on earth (latitude, elevation); to calculate day/night lenght, longitude is needed only to find mean time of sunrise/set,noon...in calculs, time should be converted to UTM, dates to Julianian dates.
i don't know formula to calculate length of day/night,but here's some usefull sites:
http://www.gcstudio.com/suncalc.html
http://susdesign.com/sunangle/
http://aa.usno.navy.mil/faq/docs/equinoxes.html

Answer 2

I can't give you an actual equation but there are two lines on the map that are relevant . The first ar the polar circles. On the winter solstice (Dec 22 for Northern Hemisphere and Jul 22 for Southern hemisphere) these days have no daylight and on the summer solstice they have 24 hours daylight.

The Tropics of Capricorn and Cancer have exactly 12 hours of daylight on the summer solstices.

The Equator has exactly 12 hours of daylight on the spring and autumn equinoxes and the north and south poles have no daylight from the autumn equinox to the spring equinox.

I think the equation for any day will be a function of a sine curve, and I suspect the equation for any particular latitude will also follow a sine curve.

Answer 3

Yes, there is.