Question

Question #1: Consider Eratosthenes's experiment to measure the size of the Earth. Suppose the Earth were a smaller planet -- but the sun were still directly overhead in Syene at noon on the Summer Solstice, and it was still 500 miles from Syene to Alexandria. Would the shadow of the stick in Alexandria at noon on the Summer Solstice have been longer, shorter, or the same as it was on our Earth? Briefly explain your reasoning.

Answer 1

It would have been longer.

Step-by-step explanation:

Lets assume the Sun angle = θ

Distance between Syene and Alexandria = D

Circumference of Earth = C

As per Eratosthenes' calculations,

`(\theta)/(360) =(D)/(C)`

From the above equation it is evident that if the circumference decreases value of θ will increase which implies that the shadow length would be longer as compared to that on the Earth.