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What is escape velocity? What is the derivation for escape velocity?

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Detailed Solution

Escape velocity is the minimum speed needed for an object to break free from Earth’s gravitational pull without any extra force.

It depends on the mass and radius of the planet but not on the mass of the object. For Earth, the escape velocity is about 11.2 km/s.

Derivation:

Consider energy conservation:

Kinetic Energy = Potential Energy at infinity
(1/2)mv² = GMm/R

Where G = gravitational constant, M = mass of Earth, R = radius of Earth, m = mass of object, v = escape velocity.

So, v = √(2GM/R).

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