Chapter 11.1, Problem 73E

a.

To determine

To find the number of meters is satellite from the earth.

Answer to Problem 73E

  $2.15\times {10}^4\text{ meters}$

Explanation of Solution

Given:

The distance of an object from center of earth is given by $r^3=\frac{G{M}_e{t}^2}{4{\pi }^2}$ where $G=6.67\times {10}^{-11}N{m}^2/k{g}^2$ and $M_e=5.98\times {10}^{24}$ Kilograms.

Calculation:

The distance of satellite is calculated as follows-

  $\begin{array}{l}{r}^3=\frac{G{M}_e{t}^2}{4{\pi }^2}\\ r^3=\frac{6.67\times {10}^{-11}\times 5.98\times {10}^{24}}{4{\pi }^2}\\ r=\sqrt[3]{1.009\times {10}^{13}}\\ r=2.15\times {10}^4\text{ meters}\end{array}$

b.

To determine

To find how far the satellite if the radius of earth is approximately $6380$ kilometers.

Answer to Problem 73E

  $r=\text{21}\text{.5km}$

Explanation of Solution

Given:

The distance of an object from center of earth is given by $r^3=\frac{G{M}_e{t}^2}{4{\pi }^2}$ where $G=6.67\times {10}^{-11}N{m}^2/k{g}^2$ and $M_e=5.98\times {10}^{24}$ Kilograms.

Calculation:

The distance of satellite is calculated as follows-

  $\begin{array}{l}{r}^3=\frac{G{M}_e{t}^2}{4{\pi }^2}\\ r^3=\frac{6.67\times {10}^{-11}\times 5.98\times {10}^{24}}{4{\pi }^2}\\ r=\sqrt[3]{1.009\times {10}^{13}}\\ r=2.15\times {10}^4\text{ meters}\\ r=2.15\times 10\text{ km}\\ r=\text{21}\text{.5km}\end{array}$