– English Lyrics

Lyrics & Translation

[English]

have you ever stood on a Sandy Beach

gazing out at the vast sea or at the

edge of a high hill and wondered where

does the Horizon end how far can my eyes

see those disappearing boats it's one of

those questions that Sparks curiosity in

everyone but before we get into math

let's understand what the Horizon is the

Horizon is the line where the Earth's

surface seems to meet the sky but here's

the catch the Earth isn't flat it's a

giant sphere sorry flat earthers so what

you're seeing is actually the curved

edge of the Earth and that's why the

Horizon appears where it does the

distance to this line depends on how

high you are above the ground the higher

you go the farther you can see imagine

the Earth as a giant ball if you were

standing on the surface of this ball

your eyes would form a straight line

line pointing outward this line

eventually meets the curved surface of

the ball creating what we call the

Horizon to calculate how far this point

is from where you're standing we'll need

to think about this triangle whose one

side is the straight line from your eyes

to the Horizon another side is this one

which is equal to Earth's radius plus

this height now this can be anything on

the surface of the Earth if you are

standing on a Sandy Beach be gazing out

at the vast sea then this height will be

your actual height and if you are at the

edge of a high hill then this height

will be the same as the height of the

Hill plus your actual height and the

third side is this one which is simply

the Earth's radius because the Horizon

is on the Earth's surface since this is

the tangent line and this is the radius

therefore this angle will be the right

angle now to solve this problem we need

two important measurements

the radius of the Earth and your height

above the ground as explained before

scientists have already measured the

Earth's radius to be about

6,378

km now if you're standing at sea level

your height might be around 6 ft or

nearly 1.8 m thus we can simply use the

Pythagoras Theorem to solve for this

length label this as H for Horizon let

us label the radius of the Earth as R

and our height as l so we get h² + r² =

R + L whole Square expanding this gives

us r² + 2 R L + L S R square gets

canceled out and after taking L as

common here we are left with L * 2 R + L

that is simply amazing so we have H

equal the square < TK of L * 2 R + L let

us substitute the values of R and L to

get H as nearly 4.8 km so if you're

standing at sea level The Horizon is

about 4.8 km away this is mind-blowing

isn't it now what happens if you go

higher assume if you're on a hill or a

tall building this L will be greater

let's say you're stand standing on a

hill that is 100 m High including your

height now when we substitute the values

of R and L we get H as nearly 35.7 km

which is about the distance between two

small towns or across a large part of a

city that's a big difference if you

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[Music]