Respuesta :
Answer:In 240 BC, how did Eratosthenes calculate the size of the earth? Using simple trigonometry, we compared whether daylight could reach water in water wells in two cities at different latitudes. The earth's system to set and a line that connects the globe to the sun are perpindicular on the spring equinox.
Explanation:
In 240 B.C., the Greek astronomer Eratosthenes made the first good measurement of the size of Earth. By noting the angles of shadows in two cities on the Summer Solstice, and by performing the right calculations using his knowledge of geometry and the distance between the cities, Eratosthenes was able to make a remarkably accurate calculation of the circumference of Earth. Let's take a closer look at how he did it!
Eratosthenes lived in the city of Alexandria, near the mouth of the Nile River by the Mediterranean coast, in northern Egypt. He knew that on a certain day each year, the Summer Solstice, in the town of Syene in southern Egypt, there was no shadow at the bottom of a well. He realized that this meant the Sun was directly overhead in Syene at noon on that day each year.
Eratosthenes knew that the Sun was never directly overhead, even on the Summer Solstice, in his home city of Alexandria, which is further north than Syene. He realized that he could determine how far away from directly overhead the Sun was in Alexandria by measuring the angle formed by a shadow from a vertical object. He measured the length of the shadow of a tall tower in Alexandria, and used simple geometry to calculate the angle between the shadow and the vertical tower. This angle turned out to be about 7.2 degrees.
