Example:

The escape velocity from a planet is 22 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 M_n = 9 M and R_n = 9 R, we get the relationship

Here subscript n denotes the new values. Thus the new escape velocity = 9 x 22 = 198 km/s.