how can you prove that the earth is a sphere by looking at the horizon
Answers
Compare shadows
The first person to estimate the circumference of the Earth was a Greek mathematician named Eratosthenes, who was born in 276 B.C. He did so by comparing shadows case on the day of the summer solstice in what is today Aswan, Egypt, with the more northerly city of Alexandria. At noon, when the sun was directly overhead in Aswan, there were no shadows. In Alexandria, a stick set in the ground cast a shadow. Eratosthenes realized that if he knew the angle of the shadow and the distance between the cities, he could calculate the circumference of the globe.
On a flat Earth, there wouldn't have been any difference between the length of the shadows at all. The sun's position would be the same, relative to the ground. Only a globe-shaped planet explains why the sun's position should be different in two cities a few hundred miles apart.
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Fortunately, there are plenty of cheaper ways than a satellite launch to show that the Earth is round. In the spirit of scientific inquiry, here are seven.