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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.
Tsiolkovsky came up with a rocket equation based on all of this: The change in speed of a rocket is equal to the exhaust velocity of the fuel times the natural log of the initial mass of the rocket divided by the final mass. The final mass is the initial mass minus the fuel that was ejected out of the rear of the rocket.