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For an object of mass the energy required to escape the Earth's gravitational field is GMm / r, a function of the object's mass (where r is the radius of the Earth, G is the gravitational constant, and M is the mass of the Earth, M =5.9736Ã10 24 kg).or a mass equal to a Saturn V rocket, the escape velocity relative to the launch pad is 253.5 am/s (8 nanometers per year) faster than the escape velocity relative to the mutual center of mass.
We assume you mean the work done in order to change the velocity of the moving mass. Easiest way is to calculate the change in the kinetic energy of the moving mass, and realize. that it's equal to the amount of work either put into the motion of the mass or taken out of it. Initial kinetic energy = 1/2 m Vi2. Final kinetic energy = 1/2 m Vf2. Change in kinetic energy = 1/2 m (V f 2 - V i 2). If the final velocity is greater than the initial velocity, the change in kinetic energy is positive, and represents work done by the pusher to speed up the mass. If the final velocity is less than the initial velocity, the change in kinetic energy is negative, and.