Calculate the location of the center of mass of the earth-moon system (that is, find the distance of thecenter of mass from the earth's center). The mass of the earth is mp =5.97 x 10" kg and the mass ofthe moon is mM =7.35 x 10 kg. The distance between the earth and the moon isd=D3.84x 10 m. Assume the orbital radius of the moon is equal to the distance between the centers ofthe earth and the moon.Express your answer with the appropriate units. Part BWhere is the center of mass with respect to the earth's surface? Assume the radius of the earth is6.38 x 10Express your answer with the appropriate units. Enter positive value if the center of mass is abovethe earth's surface and negative value if it is below.

Answered: Calculate the location of the center of…

Glencoe Physics: Principles and Problems, Student Edition

1st Edition

ISBN:9780078807213

Author:Paul W. Zitzewitz

Publisher:Paul W. Zitzewitz

Chapter7: Gravitation

Section: Chapter Questions

Problem 3STP

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Calculate the location of the center of mass of the earth-moon system (that is, find the distance of the
center of mass from the earth's center). The mass of the earth is mp =5.97 x 10" kg and the mass of
the moon is mM =7.35 x 10 kg. The distance between the earth and the moon is
d=D3.84x 10 m. Assume the orbital radius of the moon is equal to the distance between the centers of
the earth and the moon.
Express your answer with the appropriate units.

Part B
Where is the center of mass with respect to the earth's surface? Assume the radius of the earth is
6.38 x 10
Express your answer with the appropriate units. Enter positive value if the center of mass is above
the earth's surface and negative value if it is below.

Expert Solution

Step 1

Part A:

Center of Mass of the Earth-moon system from earth's Center = $\frac{(M_{E a r t h} \times 0) + (M_{M o o n} \times d)}{M_{E a r t h} + M_{M o o n}} = \frac{M_{M o o n} \times d}{M_{E a r t h} + M_{M o o n}} = \frac{7.35 \times 10^{22} \times 3.84 \times 10^{8}}{5.97 \times 10^{24} + 7.35 \times 10^{22}} = 4.67 \times 10^{6} m$

Note since moon's weight is very less compared to the earth, the center of mass of the earth-moon system when measured w.r.t. earth center is below the surface of the earth.

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