Answer
See the detailed answer below.
Work Step by Step
To solve this problem, we need to use table 13.2 data.
From the given formula we can see that the first term is the universal gravitational constant, the second term is the mass of Saturn, the third is the mass of Earth, and the fourth is the radius of Earth.
a) If you know that the free-fall acceleration on the Earth at the ground is equal to the free-fall acceleration at the planet Saturn at some height $r$ from its center.
What is the distance from the center of Saturn to this point at which the free-fall accelerations of the two planets are equal?
b) See the figure below.
c) Solving for $r$;
$$r=\sqrt{\dfrac{(5.68\times 10^{26})(6.37 \times10^6)^2}{(5.98\times10^{24})}}$$
$$r=\color{red}{\bf 6.21\times 10^7}\;\rm m$$
To find at which height from its surface, we need to subtract its radius.
$$h=r-R_{\rm Saturn}$$
$$h=(6.21\times 10^7)-(5.85\times 10^7)=\bf 3.6\times 10^6\;\rm m$$
