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The velocity required for an object to escape from the gravitational influence of the planet is known as escape velocity or escape speed
Expression for escape speed:
Consider a body of mass 'm' projected vertically upwards from the surface of the earth with velocity ve. In other to escape from the gravitational pull of the earth ,the body should be given kinetic energy which is equal to the potential energy of the body.
Gravitational potential energy = -GMm / R
Kinetic energy =1/2 mve2
----> 1/2 mve2 = GMm / R
----> 1/2 ve2 = GM / R
----> Ve2 = 2GM / R
But g = GM / R2
----> GM = gR2
Substituting the value;
----> ve2 = 2/R (gR2) = 2gR
----> ve2 = under root 2gR
put value of Ve FOR RWEUIRED RELATION
thanks
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