MadSci Network: Astronomy

Re: Do all places on earth get the same amount of daylight in a year?

Date: Mon Jun 19 19:21:28 2000
Posted By: Angelle Tanner, Grad student, Astronomy, UCLA
Area of science: Astronomy
ID: 957913951.As

Dear Dermot,

You have asked a very good and thought provoking question.
I think that the answer is 'yes', but lets think about it
using a little geometry.

First here are the assumptions:

1) We are going to ignore surface features like mountains

2) We are going to assume the Earth's orbit around the Sun is a perfect 

3) We are going to assume a year is 365 days long (its actually 365.25 days)

4) We are going to assume that there are an equal number of days and nights
for all seasons throughout the year.

Now, consider the fact that every point on the Earth has a point that is
symmetrically opposite to it through the center of the Earth.
For example, a point at a 40 degree latitude in the Northern
Hemisphere will correspond to a point at a 40 latitude in the
Southern hemisphere. One of these points is dark when the other
is light, always. Both of these points have the same latitude, and during
the year
will have the same seasons. Therefore each of the points will have the same
amount of
light and dark. Since one point is in the light while the other is in the 
one of the points has the same amount of light as the other has dark.

The symbols below represent the amount of time a point on Earth is in the
light or the dark throughout the year:

L1 = point 1 in light
D1 = point 1 in dark
L2 = point 2 in light
D2 = point 2 in dark

Remember, points 1 and 2 are at the same latitude but in
different hemispheres. Now, lets make some relationships between the 

1) L1 = D2 - while point 1 is in the light, point 2 is in the dark
2) L2 = D1  - while point 1 is in dark, point 2 is in light
3) L1 = L2 - points at the same latitude in opposite hemispheres receive
the same amount of light in a year
4) L1 + D1 = 100% - it is either light or dark

Therefore, L1 = D1 = L2 = D2 - from 1,2 & 3

5) Substitute the above result into equation 4 then

L1 + L1 = 100%

L1 = 50%

This works for any pair of points on earth, so all points on Earth get 50%
light over the course of a year. The length of any individual day is
dependent on the season and the latitude.
Also, this discription is just considering the amount of time each location 
in the light or dark and not the amount of light incident
on the surface of the Earth. At the higher latitudes, the Sun might be up
for the same amount of time as for the lower latitudes but it will be lower
in the sky. The amount of sunlight incident on the ground will be much lower
than if the Sun were overhead. I hope this is helpful.

                                        Angelle Tanner
                                        UCLA Astronomy

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