How would I calculate the escape velocity from the earth?

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To calculate the escape velocity from Earth, one can use the conservation of energy principle, where the gravitational force is defined by the equation GMm/r². The work required to escape Earth's gravity is determined by integrating this force from the Earth's surface to an infinite distance. Starting with an initial speed and applying no additional force, the kinetic energy must equal the potential energy gained, leading to the equation (1/2)mv². The mass of the spaceship cancels out, simplifying the calculation. The discussion also raises questions about directly equating kinetic energy to gravitational force to find escape velocity.
Kaxa2000
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Assuming a vacuum above the Earth's surface
 
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Kaxa2000 said:
Assuming a vacuum above the Earth's surface
The simplest thing to do is to use "conservation of energy". The gravitational force on the rocket is GMm/r2 where G is the universal gravitation constant, M is the mass of the earth, m is the mass of the spaceship and r is the distance from the center of the earth. The work necessary to "escape from earth" is the integral of that, with respect to r, from the surface of the Earth to an infinite distance away. Assuming that you start with initial speed v and apply no more force (not what a spaceship does but the standard way of computing "escape velocity", you must have that much kinetic energy to exchange for potential energy. Set that integral equal to (1/2)mv2 and solve for v. Notice that the mass of the space ship, m, appears on both sides of the equation and can be cancelled.
 
What do you mean when you say the work is the integral of that with respect to r?
 
Can you just set the KE of the object equal to the Gravitational force and solve for v? Wouldnt that give you the escape v?
 
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