How is the circumference of the earth calculated?

1 Answer
Nov 16, 2016

From visible horizon.

Explanation:

From visible horizon:

Let h be the height of the flag mast of a ship, from sea level. If d is

the maximum sea-level distance from which the top could be seen.

the circumference of the Earth is nearly

2pi(d^2/h+h).

Explication:

If h = 20 meters = 0.02 km and d = 11288 meters,

the radius of the Earth

= d^2/h+h=

= (11.288)^2/0.02+0.02

=6370.967 km

The circumference

=2pi x (radius)

=40029.966 km, nearly

Proof:

d=(radius)(angle subtended at the center, in radian)=Ralpha

Here the proportion alpha/R is very small.

If T is the Top of flag mast, O is the observer, C is the center of the

Earth,

cos alpha = 1-alpha^2/2=1-(d/R)^2, nearly

= (CO) / (CT)= R/(R+h)=(1+h/R)^(-1)=1-h/R+(h/R)^2, nearly,

as h/R is very small.

So, the approximation formula is

d^2/R^2=h(R-h)/R^2 to R = d^2/h+h, nearly.