Example:

The escape velocity from a planet is 20 km/s. What will be the new escape velocity if the planet suddenly contracts such that its radius is 1/10 times its original value and its mass increases by 10 times?

Solution:

The escape velocity from a planet is given by equation (G.25). Substituting M_n = 10 M and R_n = 10 R, we get the relationship

Here subscript n denotes the new values. Thus the new escape velocity = 10 x 20 = 200 km/s.