Question:
What is the distance around the earth at 23 1/2 degrees north?

Replies:
First, let's calculate the distance around the earth at
the equator. The distance around a circle is also
called the circumference. The circumference is given
by 2 times pi times the radius, where pi is 3.14.
The radius of the earth at the equator is about
6378 kilometers so the distance around the earth
at the equator is 2 time 3.14 times 6378 which
equals 40,074 kilometers.

Now imagine if we were to
slice through the earth at 23.5 degrees north.
This slice would be a circle whose circumference
we wish to calculate. The radius of this circle
will be smaller than the radius at the equator.
How much smaller? The radius at 23.5 degrees north
will be the radius
at the equator times the cosine of the latitude.
So the radius at 23.5 degrees north is
6378 times cosine(23.5) which is 5849 kilometers.
The distance around the earth at 23.5 degrees
north is then 2 times 3.14 times 5849 which is
36,750 kilometers. Hope you followed that-
it's a little hard to explain without being
able to draw a picture.

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