How did scientist measure the size of the earth?
1 Answer
From the observable curvature of the Earth's surface and measurement of distance of visible horizon.
Explanation:
When observed from a boat moving away from the Statue of
Liberty on Ellis island, the top of Liberty torch would disappear at
about 22 nautical miles. Maintaining the speed of the boat at v mph,
this distance d nautical miles can be easily approximated, using the
time taken t hours, from d = v t miles.
If the height of the top of the torch, from sea level, is
h = height from the base of the pedestal = the height of the pedestal
from sea level
= 305.5'+ ( my guess ) 25' = 330.5'.
Assuming that the top of the statue is observed, from sea level
near the boat,, the radius r of the earth is given by the (tangent
and secant through the center ) formula for a circle
Using iterative numerical methods with a starter approximation
(say)
sd-precision in h, d and the tangent approximations)
As d is quite small compared to r.,
tan (d/r) is nearly d/r + error
of Liberty distance d of about 22 miles..
So, the formula for approximation is
(r (d/r))^2=h(2r+h#), nearly.
Explicitly,
For sample data ( having Statue of Liberty in mind)
d=22.27 miles, h = 330.5'= 0.06259 mile.
Radius of the Earth
=3962 miles = 6375 km.. .