Escape Velocity(탈출속도)

Escape velocity is the speed that an object(let's say a rocket) needs to acheive in order to completely travel out of the area of a planet's gravity. It depends on the radius(if the rocket is launched from the surface), and the mass of the planet. The mass of the rocket does not affect the speed it needs to achieve. But why is it like this? To figure it out, the method of kinetic and potential energy must be used.

 

At ground level, the potential energy U=-mgR=-(GMm)/R, since the rocket is located at a distance R from the planet's center of mass. The kinetic energy K=1/2mv^2. Let's select a location infinitely far away from the planet where the gravitational force of the planet cannot be noticed. Here, the potential energy will also be U=0, and the kinetic energy K=0 if the velocity of the rocket at the start was exactly the escape velocity. By calculating the sum of energy, it can be led to the conclusion that the escape velosity is: v^2=(2GM)/R.

However, in fact, rockets don't travel this fast. And it is not only because they usually don't go much far. The real reson is that there are other ways to escape a planet's gravity. In the escape velocity, without considering friction, after once achieved a the point of launch, there is no need to additionally 'speed up' the rocket. In real situations, though, since escape velocity is hard to acheive, a rocket is propelled by several sequences.