Escape velocity
, the minimal launch speed at which an object can reach without falling back; approximately for the Earth.
Suppose we throw an object into space and want it to never fall back down. The minimal velocity this object must have is called the escape velocity.
As the object is thrown,
To not fall back, the object must be able to reach without the velocity going to zero. Hence
Therefore we require
Hence the escape velocity is
The mass is cancelled out, since the gravitational mass (that appears in the inverse square law) is the same as the inertial mass (that appears in Newton’s 2nd law).
Independence of mass
The mass cancels out of the escape velocity, since the gravitational mass (that appears in the inverse square law) is the same as the inertial mass (that appears in Newton’s second law).
Related
Stated in
- Example 2.5§2.3 Conservation of Energy