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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.
U is the mechanical energy used by the rocket between initial and final velocity (in other words, for a given delta-v). This amount of energy is less than the total chemical energy in the propellant, due to naturally occurring losses, such as waste heat generated by the rocket engine. is the acceleration of the rocket engine. u is the velocity of the exhaust gases relative to the rocket, which is approximately constant. dme / dt is the burn rate of the propellant. The right side of the above equation is derived using the same method that was used for deriving equation (1).