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What is escape speed?.How Escape speed √(2GM/R)=√(2gR)?

What is escape speed?.How Escape speed √(2GM/R)=√(2gR)?

Grade:11

1 Answers

SAHIL
3783 Points
4 years ago

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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