Escape velocities

Written on 25 September 2019, 10:38pm

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Back in the secondary school I worked on a physics project about the escape velocities. Really interesting stuff – it was the first time when school intersected space – but looking back 20 years I can’t help but notice that I was missing the big picture. Here’s why.

The escape velocity is the minimum speed need for an object in order to escape from the gravitational influence of a celestial body. For the Moon, it’s 2.38km/s at its surface. For Jupiter, it’s 60km/s. For a black hole, it’s infinity.

There are 3 important things to remember when talking about the escape velocity:

  1. it is independent of the mass of the object. It doesn’t matter if you’re shooting a small bullet or a big spaceship. However, the escape velocity depends on the mass of the celestial body
  2. it assumes that the object travels in vacuum, not in an atmosphere. So no friction
  3. it assumes that the object is no longer subject to thrust after reaching the escape velocity

With these 3 things in mind, a good example to illustrate the escape velocity would be an imaginary cannon launching a projectile on the Moon. Launch it with an initial speed inferior to 2.38km/s and it will come back; anything above that will cause the projectile to leave the gravitation influence of the Moon (well, until it reaches the gravitational sphere of another massive body).
On the other hand, using the Earth as the celestial body is a terrible example. Not only Earth has an atmosphere (until an altitude of about 100km) which introduces friction and makes the object mass and shape important, but in a subliminal way, everybody would imagine that the object reaching the escape velocity is a rocket. But at the Earth surface, the escape velocity is 11.2km/s, and no material known to man would resist the combined effect of the brutal acceleration and aerodynamic forces or heating.

So how did Apollo missions did reach the Earth’s escape velocity? Well, in short, they didn’t.