Question

1000 kg rocket is fired straight away from the surface of the earth.What speed does the rocket need to escape from the gravitational pull of the earth and never return? assume a non-rotating earth.

Answer 1

For escape, the initial kinetic energy must over come the potential energy of the gravitational field, such that at infinity, the velocity of the object will not be less than zero. So equate the K.E. of the object, with that of Potential energy. \[K.E. = P.E.\] or \[\frac{1}{2}mv^2=\frac{GM_{E}m}{r}\] Where \(M_{E}\) is the mass of the earth, \(m\) is the mass of the rocket, \(G\) is the gravitational constant, and \(r\) is the radius of the earth. Thus escape velocity is calculated to be \[v=\sqrt{\frac{2GM_{E}}{r}}\]. You will see that the mass of the rocket is not important in the calculation, as it cancels out.