Question

On July 19, 1969, the lunar orbit of Apollo 11 was adjusted to an average height of 122 kilometers above the Moon's surface. The radius of the Moon is 1840 kilometers, and the mass of the Moon is 7.3 x 1022 kilograms. How long did it take to orbit once? Include units in your answer. Answer must be in 3 significant digits.

Answer 1

Given data:

* The mass of the Moon is,

$m=7.3\times10^{22}\text{ kg}$

* The radius of the Moon is,

$\begin{gathered} R=1840\text{ km} \\ R=1840\times10^3\text{ m} \end{gathered}$

* The height of the Apollo 11 is,

$\begin{gathered} h=122\operatorname{km} \\ h=122\times10^3\text{ m} \end{gathered}$

Solution:

The period of revolution of the Apollo 11 around the Moon is,

$T=2\pi\sqrt[]{\frac{(R+h)^3}{Gm}}$

where G is the gravitational constant,

Substituting the known values,

$\begin{gathered} T=2\pi\sqrt[]{\frac{(1840\times10^3+122\times10^3)^3}{6.67\times10^{-11}\times7.3\times10^{22}}} \\ T=2\pi\times\sqrt[]{\frac{(1962\times10^3)^3}{48.69\times10^{11}}} \\ T=2\pi\times1245.46 \end{gathered}$

Thus, the value of time period is,

$\begin{gathered} T=7825.46\text{ s} \\ T=\frac{7825.46}{60\times60}\text{ hr} \\ T=2.17\text{ hr} \end{gathered}$

Thus, Apollo 11 takes 2.17 hours to complete orbit once around the Moon.