Question

derive formula for escape velocity.​

Answer 1

Answer:

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Explanation:

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Answer 2

Answer:

The formula is V =√(2GM/Ri)

Explanation:

HOW TO DERIVE IT

The Law of Conservation of Energy states that the total energy of a closed system remains constant. In this case, the closed system consists of the two objects with the gravitational force between them and no outside energy or force affecting either object.

Thus the total final energy—potential energy plus kinetic energy—must equal the total initial energy:

TEi = TE∞

KEi + PEi = 0

Substitute values:

mve2/2 − GMm/Ri = 0

Add GMm/Ri to both sides of equation:

mve2/2 = GMm/Ri

Solve for ve2:

ve2 = 2GM/Ri

Take the square root of each expression to get:

ve = ± √(2GM/Ri)

Considering our gravitational convention for direction, ve is upward or away from the other object and is thus negative:

ve = − √(2GM/Ri)

Note: Although convention-wise, the negative version of the equation is correct, most textbooks will give the positive version of the equation. You should be aware of this fact.