Chapter 14, Problem 31A

To determine

To Find: Whether the orbital velocity of satellite around the moon is greater than, less than or equal to 8 km/s.

Explanation of Solution

Introduction:

The orbital velocity of the satellite is the minimum horizontal velocity of a satellite during projection so that it should perform a circular motion.

The orbital velocity of earth is around 8 kilometers per seconds or 8000 meters per second.

The formula to find the value of orbital velocity depends on the acceleration due to gravity and radius of that planet.

In case of moon,

  $\begin{array}{l}{g}_{moon}=1.625{\text{ m/s}}^2\\ R_{moon}=1.737\times {10}^6\text{ m}\end{array}$

Orbital velocity formula is, $V_o=\sqrt{gR}$

Substituting the values of $g_{moon}and{R}_{moon}$

  $\begin{array}{l}{V}_o=\sqrt{g_{moon}{R}_{moon}}\\ V_o=\sqrt{1.625\times 1.737\times {10}^6}\\ V_o{V}_o=1680.07\text{m/s}\end{array}$

It has been found that orbital velocity of moon is 1680.07 m/s which is less than 8000 m/s.

Conclusion:

Therefore, the orbital velocity for moon is be less than 8000 m/s.