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Question

Assume that the Earth is a sphere of a radius of 3950 miles.

Find the distance along the Earth’s surface from Burlington (44.5 degrees north latitude) to the closest point in the equator.

Find the distance from Burlington to the North Pole.

Brattleboro is at 42 degrees 51 minutes north latitude. Find it’s distance to the closest point on the equator.

Answer 1

OK. The circumference of the earth is 2π r, where r = 3950 miles. So the circumference is about 24800 miles.

The distance along the surface from the Equator to the North Pole is about one-quarter of that distance, or about 6200 miles.

Now, if you move from the Equator to the North Pole you cover one-quarter of the angle given by latitude, or 90 degrees of a possible 360.

The distance from Burlington to the Equator is (44.5 deg / 90 deg) * 6200 miles, or 3065 mi.

The distance from Burlington to the North Pole is the difference between a quarter of the circumference and the distance from Burlington to the Equator, or 6200 - 3065 = 3135 mi.

The distance from Brattleboro to the Equator is (42.85 / 90) * 6200, or about 2950 mi. (This is because 51 minutes of angle is about 0.85 degrees - there are 60 minutes in a degree.)