Answer
The multiple of the energy needed to escape from Earth which gives the energy needed to escape from Jupiter is $~~28.3$
Work Step by Step
We can write a general expression for the escape speed:
$v = \sqrt{\frac{2GM}{R}}$
We can write a general expression for the kinetic energy required to escape:
$K = \frac{1}{2}mv^2$
$K = \frac{1}{2}m(\sqrt{\frac{2GM}{R}})^2$
$K = \frac{GMm}{R}$
We can find the ration $\frac{K_J}{K_E}$, which is the ratio of the kinetic energy required to escape from Jupiter to the kinetic energy required to escape from the Earth:
$\frac{K_J}{K_E}= \frac{\frac{GM_Jm}{R_J}}{\frac{GM_Em}{R_E}}$
$\frac{K_J}{K_E}= \frac{M_J~R_E}{M_E~R_J}$
$\frac{K_J}{K_E}= \frac{(318~M_E)~(6.37\times 10^6~m)}{(M_E)~(7.15\times 10^7~m)}$
$\frac{K_J}{K_E}= 28.3$
The multiple of the energy needed to escape from Earth which gives the energy needed to escape from Jupiter is $~~28.3$
