Final answer:
Eratosthenes' observation of differing shadow angles in Syene and Alexandria is analogous to the varied shadows cast by flagpoles on planets of different sizes, illustrating the effect of planetary curvature on sunlight angles. A smaller planet will result in longer shadows, while a larger planet will have shorter ones due to the curvature's influence on the angle of incoming sunlight.
Step-by-step explanation:
The phenomenon observed by Eratosthenes where a well in Syene (modern Aswan, Egypt) had no shadow at noon but a well in Alexandria did, relates to the curvature of the Earth. If we consider flagpoles on planets of various sizes, the shadows cast by these flagpoles would differ due to the planet's curvature affecting the angle of incoming parallel light rays. For example, on a smaller planet, the surface curves more sharply compared to a larger planet, thus a flagpole would cast a longer shadow when the sunlight rays strike at an angle.
On a large planet, the curvature is gentler, and the shadow may be shorter for an identical flagpole. This is because the angle at which the sunlight strikes the surface is closer to the 'straight down' position as seen in Syene. The difference in shadow lengths and angles between these flagpoles on three different-sized planets highlights the connection to Eratosthenes' discovery. He realized that the differing shadow angles in Syene and Alexandria were due to the Earth's round shape, which he used to calculate the Earth's circumference to be approximately 250,000 stadia by using the 7° angle difference between the two cities.