Escape velocity and Conservation of energy

Question

If a physical body leaves earth with 11.2 km/s escape velocity with a certain amount of Mechanical energy, then how can it be said that the body will have 0 Mechanical energy at a point at infinity without following the Conservation of energy?

Karim Chahine · Accepted Answer

The escape velocity is the minimum amount you need to escape the gravitational field. Note that the field has an infinite extent, as it goes to zero only at infinity. To escape a gravitational field you should have the kinetic energy to "reach" infinity and the minimum kinetic energy that allows so is the one that leaves you with 0 energy at infinity, otherwise, you would still have some kinetic energy left.
Energy is conserved because you start with zero energy, positive kinetic energy and negative potential energy.

Escape velocity and Conservation of energy

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