Tanning around the earth

It's a lot easier to get a suntan in the summer than the winter. The suntanning issue (and the seasons) is due to the the tilt of the earth's axis with respect to the plane of the earth's orbit. The earth's axis is tilted 23 degrees with respect to the normal to the plane of its orbit. see here for a nice discussion and animation).

Consider someone who lives 23 degrees north of the equator. Let the maximum intensity of sunlight on the Earth's surface for this person during the summer day when the Earth's axis is tilted most towards the Sun be \(I_{sum}\). Similarly \(I_{win}\) will be the maximum intensity of sunlight during the winter day when the Earth's axis is tilted most away from the sun.

What is \(I_{win}/I_{sum}\)?

Details and assumptions

  • You may consider the Earth as a perfect sphere and the orbit of the Earth as a perfect circle.
  • Since the Sun is so far away, all the rays of sunlight may be considered to hit the Earth parallel to the orbital plane.
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