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Hunter-Best [27]
3 years ago
6

Find earth's approximate mass from the fact that the moon orbits earth in an average time of 27.3 days at an average distance of

384,000 kilometers. (hint: the moon's mass is only about 180 of earth's.)
Physics
1 answer:
Aleks [24]3 years ago
4 0

We can solve the problem by using Kepler's third law, which states:

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

where T is the period of revolution of the Moon around the Earth, G is the gravitational constant, M the Earth's mass and r the average distance between Earth and Moon.

Using the data of the problem:

T=27.3 d \cdot 24 \cdot 60 \cdot 60 = 2358720 s=2.36 \cdot 10^6 s

r=384000 km=3.84 \cdot 10^8 m

We can re-arrange the equation and find the Earth's mass:

M=\frac{4 \pi^2 r^3}{GT^2}=\frac{4 \pi^2 (3.84 \cdot 10^8 m)^3}{(6.67 \cdot 10^{-11})(2.36 \cdot 10^6 s)^2}=6.0 \cdot 10^{24} kg

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