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.)

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

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:

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

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