Question

How is the size of earth measured?

Answer 1

The arc to the visible horizon, from height h subtends an angle `theta`, at the center of Earth, The Earth radius r is given by the implicit formula `cos(theta) = r / (r + h)`.

Explanation:

The angle `theta` can be obtained from the arcual distance s of the visible horizon and r, using
`theta` radian = s / r.
There are iterative numerical methods to solve this r-implicit equation cos`(theta) = r / (r + h)`, using a starter (estimated) value for r.
There are alternative methods for which observations are to be made against two conveniently chosen s values.The formula here will be explicit.