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Calculate in days the expected period of rotation of the moon around the earth. Mass of earth is...

Question:

Calculate in days the expected period of rotation of the moon around the earth. Mass of earth is 5.977 x 10{eq}^{24} {/eq} kg, and the mean radius of the moon orbiting around the earth is 3.844 x 10{eq}^8 {/eq} m. Use {eq}\displaystyle T = \frac{4 \pi^2 r^3}{GM} {/eq}.

Kepler's Third Law

Kepler's third law of planetary motion states that the period of an object orbiting a star/planet is related to the semi-major axis of the elliptical orbit. The relationship of the third law is:

{eq}\displaystyle T^2 = \frac{4 \pi^2 r^3}{GM} {/eq}

Here:

{eq}\displaystyle T {/eq} is the period of the object's orbit in seconds, {eq}\displaystyle r {/eq} is the semi-major axis (radius for a circular orbit) of the elliptical orbit in meters, {eq}\displaystyle G \approx 6.67 \times 10^{-11} \: \text{m}^3/\text{kg s}^2 {/eq} is the gravitational constant, and {eq}\displaystyle M {/eq} is the mass of the star/planet that is being orbited (assuming it to be much larger than the orbiting object's mass) in kilograms.

Answer and Explanation:

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To calculate the expected period of the Moon's orbit around the Earth, we will use Kepler's third law.

{eq}\displaystyle T^2 = \frac{4 \pi^2...

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Kepler's Three Laws of Planetary Motion

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Chapter 22 / Lesson 12
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Find out about the interesting life and major contributions of Johannes Kepler. This lesson will also teach you how to find out how long it takes a planet to revolve around the sun!


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