how did eratosthenes estimate the size of earth in 240 b.c.? how did eratosthenes estimate the size of earth in 240 b.c.? by measuring the size of earth's shadow on the moon in a lunar eclipse by comparing the maximum altitude of the sun in two cities at different latitudes on the summer solstice by sending fleets of ships around earth by observing the duration of a solar eclipse we don't know how he did it since all his writings were destroyed.