The Earth has a mass of 5.97x 10^24 kg. Then Moon has a mass of 7.35x10^22kg The

Question

The Earth has a mass of 5.97x 10^24 kg. Then Moon has a mass of 7.35x10^22kg The center of the Moon is a distance d = 3.84x10^8m from the center of the Earth. Imagine the Earth and the Moon are on a long massless stick which rests on a surface without friction between the stick and the surface (this is essentially true if you think about it). The Moon now "walks" from a place that was a distance d on the left side of the Earth to a place which is a distance d on the right side of the Earth.

1) How far did the Moon move?

2) How far did the Earth move?

3) The radius of the Earth is 6,400km. Convert your answer to part 2 to units of Earth radii. (For examply, "The Earth moved 0.014 Earth radii" or "The Earth moved 3.2 Earth radii" or whatever is correct based on your answer to part 2.)

Explanation / Answer

so consider the earth initially at 0

the xcom initial = (5.97E24*0 + 7.35E22*3.84E8)/(5.97E24 + 7.35E22)= 4.67E6 m

now if the earth moves to x then moon is at x-d

so

xcom final = (5.97E24*x + 7.35E22*(x-3.84E8))/(5.97E24 + 7.35E22)

x = 4.67E6

so moon moves = d - (x-d) = 2d - x = 2*3.84E8 - 4.67E6= 7.63E8 m

2)

earth moves 4.67E6 m

3)

moon moves 7.63E8/6.4E6=119.2 earth radii

and earth moves 4.67E6/6.4E6=0.73 earth radii

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