How to measure the radius of earth?

Answer 1

There are many ways this can be done.

The ancient Greeks measured the lengths of shadows at two different locations a few hundred miles apart on a roughly north-south baseline at noon on the same day of the year. From this using trigonometry the circumference was computed, then using the relationship of circumference to radius the radius can be computed. Almost surprisingly the figure they got was very close to the modern figure.

Columbus repeated this calculation, but due to a combination of bad data in the sources he used (he did not make the measurements himself) and calculation errors on his part he got a result roughly 2/3 of the correct value (an error equivalent to elimination of the Pacific Ocean and the Americas); which convinced him he could easily sail to China & India.

An equivalent calculation can be done using measurements of star positions at night from different locations, using any baseline (e.g. north-south, east-west, diagonals) between the locations as long as the time and day are identical when the measurements are made.