# How can altitudes be used to calculate the circumference of the earth?

##### 1 Answer

See explanation for a nice approximation, using altitude H km and visible horizon ( nautical ) distance D km :

Circumference =

#### Explanation:

Let B be the beacon from the top of a Light House (LH), at a

height H meters, from sea level.

Let D be the nautical distance traveled by a ship S,

sailing away from the LH, and

center C of [the Earth](https://socratic.org/astronomy/our-solar-

system/the-earth).

When the beacon B just disappears beneath the horizon, from

the sea-level Telescope of the ship, then

BS touches the Earth at S, and so,

Now,

D = R

Also,

As D/R is small,

Now, H/R is small, and so, the RHS

.

Circumference =

For sample data H = 100 meters = 0.1 km, D = 11.3 km.

circumference = 40, 116 km, nearly.

Here, the assumed visible-horizon ( nautical ) distance D = 11.3 km,

against the altitude 100 meters,

For this formula and R = 6371 km, the visible-horizon (nautical )

distance, for the Statue

of Liberty of height H = 41 meters is

D = 22.9 km, nearly