Question

Measured the size of Earth by observing the _____ at which the sun’s rays hit our planet’s surface. The sun’s rays come in but Earth’s surface curves. So, a ray at Syene whereas a ray at Alexandria that means, in effect, that at Alexandria, Earth’s surface has curved away from Syene by 7° of 360°, or 1/50 of a full circle. Thus, the distance between the two cities must be 1/50 the circumference of Earth.

a. Tides
b. Latitude
c. Eclipses
d. Horizon

Answer 1

Eratosthenes estimated Earth's circumference by noting the 7° angle difference between the Sun's position at zenith in Syene and its position in Alexandria, which he translated to mean Alexandria was 1/50 of Earth's circumference north of Syene. Multiplying the distance between the two cities by 50 gave him Earth's total circumference.

Step-by-step explanation:

Eratosthenes measured the size of Earth by observing the angle at which the Sun's rays hit our planet's surface. When there was no shadow at the bottom of a well in Syene at noon on the first day of summer (June 21st), it meant that Syene was on a direct line from the center of Earth to the Sun and the Sun was at zenith. Conversely, at the same time in Alexandria, objects cast a shadow, indicating that the Sun's rays made a 7° angle with the vertical, or about 1/50 of a full circle.

Hence, if the distance between Syene and Alexandria was known to be 5000 stadia, and this distance represented 1/50 of Earth's circumference, Eratosthenes concluded that the circumference of Earth was 50 times this measurement: 50 x 5000, which totals 250,000 stadia.