Given that the angular speed of the moon in its orbit about the earth is greater than that of the earth around the sun,

Question

Given that the angular speed of the moon in its orbit about the earth is greater than that of the earth around the sun, identify the reason.

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Given: The angular speed of the moon about the earth is greater than that of the earth around the sun.

Find: The reason for this comparison.

Angular speed is given by

\omega = \frac{2\pi}{T}

where $T$ is the time period of revolution.

For the moon revolving around the earth,

T_{\text{moon}} \approx 27.3\,\text{days}

For the earth revolving around the sun,

T_{\text{earth}} \approx 365.25\,\text{days}

Since

T_{\text{moon}} < T_{\text{earth}}

it follows that

\omega_{\text{moon}} = \frac{2\pi}{T_{\text{moon}}} > \frac{2\pi}{T_{\text{earth}}} = \omega_{\text{earth}}

Therefore, the moon has greater angular speed because its period of orbit is shorter. The correct option is A.

Given: Angular speed comparison between the moon and the earth.

Find: Which listed reason explains the larger angular speed.

Use the inverse relation

\omega \propto \frac{1}{T}

A smaller time period immediately means a larger angular speed. Since the moon completes its orbit in much less time than the earth, its angular speed is greater.

Therefore, the correct option is A, Shorter period of orbit.

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