Question

If the Moon takes 27.3 days to complete its orbital path around the Earth, and the orbit has a radius of 3.8 x 108 meters, what is the Earth's Mass

Answer 1

Answer: If the Moon takes 27.3 days to complete its orbital path around the Earth, and the orbit has a radius of 3.8 x 108 meters, then, the Earth's Mass is $6*10^{24}kg$.

Explanation: To find the answer, we have to know more about the Law of periods or the harmonic law.

What is the law of periods or harmonic law?

• The law of periods states that, the square of the period of revolution of a planet is proportional to the cube of the semi major axis of the elliptical path.
• We can express it as,

                                              $T^2$∝ $r^3$

                                            $T^2=\frac{4\pi ^2r^3}{GM}$

How to solve the problem?

• From the above given equation, we can reduce mass of earth as,

                                     $M=\frac{4\pi ^2r^3}{GT^2}$

• Substituting the values given in the question, we get,

           $M=\frac{4\pi ^2(3.8*10^8)^3}{6.67*10^-11*(27.3*24*60*60s)^2} =\frac{2.164*10^{27} }{371.08} =5.831*10^{24}=6*10^{24}kg$

Thus, we can conclude that, the mass of earth is $6*10^{24}kg$ .

Learn more about the law of periods here:

https://brainly.com/question/28044814

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