Sorry, if vacations are not your thing, and you don't have any friends, here is a simple way to prove the radius of the earth.
1. Lie down and face the horizon (supine), as soon as you see the top of the Sun disappear below the horizon, start a stopwatch.
2. Stand-up as quickly as possible. The Sun will reappear above the horizon
3. Once the top of the Sun disappears again, stop the stopwatch. (Example 11.5 seconds)
We know that the earth revolves 360 degrees in 24 hours or in 86,400 seconds. So in 11.5 seconds, the angle that it revolves through is (360 degrees) * (11.5 86400) = 0.04791666 degrees.
4. Now you know angle rotated by earth (Ɵ) in 11.5 seconds, and you know your height H, you can use a little trigonometry to calculate the radius of the Earth R.
H you know, Ɵ you know the only unknown is R in this equation which is radius of Earth which can be calculated easily by putting values of known in the above equation.
cos(0. 04791666 degrees) = R (R + H)
R = H * cos(0.04791666 degrees) (1 cos(0.04791666 degrees))
R = 6.22 * 106 m (close to the actual value of 6.38 * 106 m) = 6220 km
https://www.quora.com/When-and-how-did-scientists-measure-the-radius-of-the-earthI'm sure someone else can dumb this down for you if you need.
