Math that Launches You

Have you ever seen a rocket launch on-screen or in-person, and wondered why a rocket has to blast off with such tremendous speed to get into space?

Well, math gives us the answer! It tells us that in order for a rocket (or any object) to escape the gravitational pull of a planet, it has to go at a speed called the escape velocity, which can be calculated as follows:

Plugging in the mass and radius numbers for the earth, we get 11.2 km/s (25,000 mph) as the velocity needed to escape the earth's gravity and launch into outer space! Note that this is different from the velocity of 7.8 km/s needed to get into a stable low orbit around the earth (the subject of a future post!).

The above equation tells us some interesting things:

• The mass of the object launching into space does not matter. Whether it's a rocket or a soccer ball, both have to achieve the same velocity to get into space!

  
  

• The escape velocity is inversely proportional to the radius r, which is really the distance between the center of the planet and the object that is trying to escape. As the object moves away from the surface of the planet (i.e., as the distance between the object and the center of the planet increases), the escape velocity decreases. If the object is far enough away, the escape velocity will essentially be zero!

  
  

• The escape velocity is proportional to the planet's mass. Planets more massive than the earth have larger escape velocities. For example, Jupiter has an escape velocity of about 60 km/s (135,000 mph)! The animation below shows how fast a rocket would have to go to escape each planet in our solar system.

Source: Business Insider