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.

Explanation:

Eratosthenes measured the Earth's circumference (and relatedly, radius) by noting the angle of the Sun at midday on the same day (summer solstice) at two different locations (Alexandria and Syene). Option a is incorrect as lunar eclipse shadow size relates to Earth - Moon - Sun geometry for Earth's size relative to Moon, not radius measurement. Option b: pole star angular position is for latitude, not Earth's radius. Option c: timing sunset disappearance isn't how he measured. Option d matches his method of using solar angles at different locations to calculate Earth's size.

Answer:

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