# Chapter 13 - Newton's Theory of Gravity - Exercises and Problems - Page 372: 11

(a) The mass of Planet Z is $3.0\times 10^{24}~kg$ (b) The free-fall acceleration at a distance of 10,000 km above the north pole is $0.89~m/s^2$

#### Work Step by Step

(a) We can find the mass $M_z$ of Planet Z. $\frac{G~M_z}{R_z^2} = 8.0~m/s^2$ $M_z = \frac{(8.0~m/s^2)~R_z^2}{G}$ $M_z = \frac{(8.0~m/s^2)(5.0\times 10^6~m)^2}{6.67\times 10^{-11}~m^3/kg~s^2}$ $M_z = 3.0\times 10^{24}~kg$ The mass of Planet Z is $3.0\times 10^{24}~kg$ (b) We can find the free-fall acceleration $g_z'$ at a distance of 10,000 km above the north pole. $g_z' = \frac{G~M_z}{R_z^2}$ $g_z' = \frac{(6.67\times 10^{-11}~m^3/kg~s^2)(3.0\times 10^{24}~kg)}{(1.5\times 10^7~m)^2}$ $g_z' = 0.89~m/s^2$ The free-fall acceleration at a distance of 10,000 km above the north pole is $0.89~m/s^2$

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