How is the circumference of the earth calculated?

Question

Hunter Arthur · Accepted Answer

From visible horizon.

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.

Hailey Alexander · Answer

undefined The circumference of the Earth is calculated using various methods, including geometric calculations, satellite measurements, and direct measurements using landmarks and GPS technology. One of the earliest methods involved measuring the angle of the Sun's rays at different locations on Earth during the same time. Today, satellite technology allows for more precise measurements, such as using satellites equipped with radar to measure distances between points on the Earth's surface. These measurements are then used to calculate the circumference of the Earth.