The Moon has an interesting relationship with the Earth, where the sameface of the Moon is always facing towards the Earth. This is called tidallocking, where the time it takes for the Moon to rotate once is exactlyequal to the time it takes for it to orbit the Earth. Given that the Moonperforms 13.5 rotations per year, and that the Earth has a mass of 5.971024 kg, find the center to center distance between the Earth and theXMoon. You must show your work in order to obtain credit. Thegravitational constant is G = 6.67 x 10 11 Nmkg2

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Asked Sep 23, 2019
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The Moon has an interesting relationship with the Earth, where the same
face of the Moon is always facing towards the Earth. This is called tidal
locking, where the time it takes for the Moon to rotate once is exactly
equal to the time it takes for it to orbit the Earth. Given that the Moon
performs 13.5 rotations per year, and that the Earth has a mass of 5.97
1024 kg, find the center to center distance between the Earth and the
X
Moon. You must show your work in order to obtain credit. The
gravitational constant is G = 6.67 x 10 11 Nm
kg2
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The Moon has an interesting relationship with the Earth, where the same face of the Moon is always facing towards the Earth. This is called tidal locking, where the time it takes for the Moon to rotate once is exactly equal to the time it takes for it to orbit the Earth. Given that the Moon performs 13.5 rotations per year, and that the Earth has a mass of 5.97 1024 kg, find the center to center distance between the Earth and the X Moon. You must show your work in order to obtain credit. The gravitational constant is G = 6.67 x 10 11 Nm kg2

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Expert Answer

Step 1

Given:

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Mass of the Earth = 5.97 x1024 kg Angular velocity of the moon,o= 13.5 rot/yr 13.5x27T 365x 24x 3600 = 2.69x 10 rad/sec

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Step 2

Gravitational force on moon due to Earth, FG = GMMME/r2

Centripetal force on moon, Fc =  MMrw2

Where,

G = gravitational constant

MM = mass of moon

M...

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since, both the force acting on the Moon GM ME - Mr мМE - М_ro? GME (GM E r = 6.67 x10x5.97 x102 2.68x10 x2.68x10 r = r = 3.8x 108 m - 3.8x 105 km

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