Question

eratosthenes measured the radius of earth by: a. estimating the size of the shadow of earth on the moon during a lunar eclipse. b. measuring the angular position of the pole star from several positions on earth. c. timing the disappearance of the sun at sunset for two different positions on earth on the same day of the year. d. noting the different angles of the sun at midday on the same day of the year at different positions on earth. clear my choice

Explanation:

Eratosthenes measured Earth's radius by noting the Sun's midday angles at different locations (e.g., Alexandria and Syene) on the same day. This angle difference related to the arc length between the locations, allowing calculation of Earth's circumference (and then radius). Option d describes this method. Option a is incorrect (lunar eclipse shadow for Earth's size, not radius). Option b (pole star) and c (sunset timing) are not his methods.

Answer:

d. noting the different angles of the Sun at midday on the same day of the year at different positions on Earth.