Example:

The escape velocity from a planet is 18 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 M_n = 8 M and R_n = 8 R, we get the relationship

Here subscript n denotes the new values. Thus the new escape velocity = 8 x 18 = 144 km/s.