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Example G.9: Escape Velocity of a Satellite

Example:

The escape velocity from a planet is 17 km/s. What will be the new escape velocity if the planet suddenly contracts such that its radius is 1/8 times its original value and its mass increases by 8 times?

Solution:

The escape velocity from a planet is given by equation (G.25). Substituting Mn = 8 M and Rn = 8 R, we get the relationship

vn = 8 v.

Here subscript n denotes the new values. Thus the new escape velocity = 8 x 17 = 136 km/s.

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