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Derive an expression for escape and orbital velocity?

Derive an expression for escape and orbital velocity?

Grade:9

1 Answers

Nirmal Singh.
askIITians Faculty 44 Points
7 years ago
Orbital velocity, for a small mass m orbiting a large mass M:

Centripetal force = gravitational force

mv^2/r = GMm/r^2

v = sqrt (GM /r)

Escape velocity: Potential energy relative to infinity = -GMm/r. Escape velocity is the velocity such that the initial KE is just enough to get you to infinity due to conservation of energy So
(1/2)mv^2 = GMm/r.

v = sqrt (2GM/r)

Regards,
Nirmal Singh
Askiitians faculty

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