Escape Velocity

Earth's Escape Velocity

The escape velocity is the velocity required to send a body into orbit around another body, such as a planet. The escape velocity of Earth can be found by using geometry.

There is no escape...

To calculate the velocity, we need to know two numbers: the radius of the body you want to escape from, and the distance an escaping body will fall in one second. In the case of Earth, the radius is 6,380km and the distance fallen in one second in half of the figure for accelaration due to gravity, so we will call it g/2 for now.

Therefore we can say:

R = 6380000m

S = g/2

We can show the Earth as a two dimensional circle like this:

We can use a theorem of plane geometry to help us in our calculation. The tangient to a circle is the mena proportion between two parts of the diametre cut by an equal chord...

...and in algebra speak we get this which can be easily solved for x:

Remember: S = g/2

We can just plug in the values of the radius and for g (9.81ms^-2) to get 7900km if we are using 3 sig. fig.

Thus, as x is the distance we need to send our rocket ship in one second, we can divide by this one second to get a velocity. Thus:

For our friends in Europe.

For those using old money.

Thus, in order to escape the gravitational pull of the Earth and go into orbit, we will have to travel with a velocity close to 8 kilometres (5 miles) a second.

QED

Geometrical diagram made with Geogebra.