How did scientist measure the size of the earth?

1 Answer
Jul 21, 2016

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

PT2=PA.PB,

(rtan(dr))2=h(2r+h)

Using iterative numerical methods with a starter approximation

(say) r0=3900 miles, r can be obtained, within the limits of the

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 O((dr)3)=O(107), for the statue

of Liberty distance d of about 22 miles..

So, the formula for approximation is

(r (d/r))^2=h(2r+h#), nearly.

Explicitly, r=d2h22h

For sample data ( having Statue of Liberty in mind)

d=22.27 miles, h = 330.5'= 0.06259 mile.

Radius of the Earth

r=22.2720.0625922X0.06259

=3962 miles = 6375 km.. .