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Example G.9: Escape Velocity of a Satellite

Example:

The escape velocity from a planet is 12 km/s. What will be the new escape velocity if the planet suddenly contracts such that its radius is 1/9 times its original value and its mass increases by 9 times?

Solution:

The escape velocity from a planet is given by equation (G.25). Substituting Mn = 9 M and Rn = 9 R, we get the relationship

vn = 9 v.

Here subscript n denotes the new values. Thus the new escape velocity = 9 x 12 = 108 km/s.

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