You are an astronomer on planet Nearth, which orbits a distant star. It has recently been accepted that Nearth is spherical in shape, though no one knows its size. One day, while studying in the library of Alectown, you learn that on the equinox your sun is directly overhead in the city of Nyene, located 1400 kilometers due north of you. On the equinox, you go outside and observe that the altitude of your sun is 76. What is the circumference of Nearth?

The circumference of the planet Nearth is 36,000km.

Explanation:

This problem can be solved using the Eratosthenes' method which considers the angular distance between two points on the planet to estimate the circumference of the planet.

When the Equinox is directly overhead the city of Nyene, this means the sin is 90° over the city.

According to your measurement, the sun is 76° to Alectown, where you are.

Therefore, the angular separation between the city of Nyene and Alectown is 14°.

Since it is known that your planet Nearth is spherical, then the full angle of the planet is 360°.

This means the angular separation of your two cities is a fraction of the planet, 14°/360°.

Given that the city of Nyene is due north to Alectown. This means Alectown is 1400 kilometers south of Nyene.

Then, the circumference of the whole planet can be estimated from the angular fraction.

i.e 14/360 × X = 1400km

where X = The circumference of the planet Nearth

X = 1400km × 360 / 14 = 36,000km

Hence, the circumference of the planet Nearth is 36,000km