Escaping the Earths Gravity
Anything raised above the Earth's surface will tend to fall down. A force will be needed to raise it further and forces when require energy. Close to the Earth's surface the amount of energy required is mgh equal to the increase in gravitational potential energy. The expression mgh is only an approximation however. If we want move an object completely away from the Earth's gravitational influence, we have to use the true, more complicated equation equation for gravitational potential energy. The force of gravity is not the same in the region of the Earth – it decreases as we get further from the Earth, so less energy and force is required to move it the further from the Earth the object gets.
If a particle were to start from the surface of the Earth with all its energy in the form of kinetic energy, and travel vertically up, as it rises the kinetic energy is all transferred into kinetic energy. If at some point it completely escapes the gravitational influence of the Earth, it must have some kinetic energy left, so there is a least speed a particle at the Earth's surface could have and still be able to the Earth. This speed is called the escape velocity and is given by