How is the size of earth measured?

1 Answer
Feb 12, 2016

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)#.


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.