The Center of Mass of the Earth-Moon-Sun System In this problem, you will calcul

Question

The Center of Mass of the Earth-Moon-Sun System In this problem, you will calculate the location of the center of mass for the Earth-Moon system, and then you will calculate the center of mass of the Earth- Moon-Sun system. The mass of the Moon is 7.35x102 kg, the mass of the Earth is 6.00x1024 kg, and the mass of the sun is 2.00x1030 kg. The distance between the Moon and the Earth is 3.80x105 km. The distance between the Earth and the Sun is 1.50x10 km A common, though incorrect, statement is, "The Moon orbits the Earth. That creates an image of the Moon's orbit that looks like that shown in the figure. (Fiaure 1) Part A The Earth's gravity pulls on the Moon, causing it to orbit However, by Neton's third law, it is known that the Moon exerts a force back on the Earth. Therefore, the Earth should move in response to the Moon. Thus a more accurate statement is, "The Moon and the Earth both orbit the center of mass of the Earth-Moon system Calculate the location em of the center of mass of the Earth-Moon system. Use a coordinate system in which the center of the Earth is at0 and the Moon is located in the positive x direction Express your answer in kilometers to three significant figures. Hints Figure 1 1of1 Moon Submit My Answers Give Up Part B Earth This question will be shown after you complete previous question(s) Part C

Explanation / Answer

Part A )

Xcm = me xo + mm xm / ( mm + me )

= 6 X 1024 X 0 + 7.35 X 1022 X 3.8 X 105 / ( 6 X 1024 + 7.35 X 1022 )

Xcm = 4598.667 km

Part C )

Xcm = me xo + mm xm + ms xs / ( mm + me + ms )

Xcm = 6 X 1024 X 0 + 7.35 X 1022 X 3.8 X 105 + 2 X 1030 X 1.5 X 108 / ( 6 X 1024 +7.35 X 1022 + 2 X 1030 )

Xcm = 456 km

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