Escape Velocity

 
Escape velocity is the speed at which an object will be able to escape the gravity of a planet, moon or other body. In other words, it must travel fast enough so that it will not fall back down. If you throw a ball in the air, it will fall back down. If you throw it harder (faster) it will go further but still fall back to earth. If you could throw it fast enough it would continue to travel and never fall back down. That speed is called the escape velocity. The formula is:

Where M and R are the mass and radius of the planet and G is the gravitational constant.


The gravitational constant is 0.0000000000667 and never changes - that is why it's called a constant. The mass of the earth is 5,970,000,000,000,000,000,000,000 kg (that's really heavy!). The radius of the earth is 1,700,000 m.

Now do the math. You'll need a special scientific calculator. If you do it right you'll get about 11,000 meters per second. That is about 25,000 miles per hour. In other words, you have to travel really fast to escape mother earth.

This site has a good escape velocity calculator.

 


Note: to make things easy we have ignored the units on all numbers. If you use mass in kilograms (kg) and radius in meters (m) your answer will be in meters per second (m/s). you can convert to miles per hour (m/h) by multiplying your answer by 2.24. Here is a good online converter.
Here is a table of the mass and radius of moon and other planets. See if you can calculate the escape velocity of the moon, Mars or other planets. If you were going to travel to deep space, where would you prefer to take off from given that you need more fuel to go faster?

Teachers: Click here for more information. PhysLink.com is another good site.

This site has a good lesson for 5-8 and 9-12 grades on escape velocity.

Source: The Cosmic Perspective