# Chapter 13 - Newton's Theory of Gravity - Exercises and Problems: 8

(a) The free-fall acceleration at the surface of the moon is $1.62~m/s^2$ (b) The free-fall acceleration at the surface of Jupiter is $25.9~m/s^2$

#### Work Step by Step

(a) We can find the free-fall acceleration $g_m$ at the surface of the moon. $g_m = \frac{G~M_m}{R_m^2}$ $g_m = \frac{(6.67\times 10^{-11}~m^3/kg~s^2)(7.35\times 10^{22}~kg)}{(1.74\times 10^6~m)^2}$ $g_m = 1.62~m/s^2$ The free-fall acceleration at the surface of the moon is $1.62~m/s^2$. (b) We can find the free-fall acceleration $g_j$ at the surface of Jupiter. $g_j = \frac{G~M_j}{R_j^2}$ $g_j = \frac{(6.67\times 10^{-11}~m^3/kg~s^2)(1.90\times 10^{27}~kg)}{(6.99\times 10^7~m)^2}$ $g_j = 25.9~m/s^2$ The free-fall acceleration at the surface of Jupiter is $25.9~m/s^2$.

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