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. (Figure 1) The Earth's gravity pulls on the Moon, causing it to orbit. However, by Newton'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."
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 7.35×1022 kg , the mass of the Earth is 6.00×1024 kg , and the mass of the sun is 2.00×1030 kg . The distance between the Moon and the Earth is 3.80×105 km . The distance between the Earth and the Sun is 1.50×108 km .
Part A:
Calculate the location xcm of the center of mass of the Earth-Moon system. Use a coordinate system in which the center of the Earth is at x=0 and the Moon is located in the positive x direction.
Express your answer in kilometers to three significant figures.
Part B:
Where is the center of mass of the Earth-Moon system? The radius of the Earth is 6378 km and the radius of the Moon is 1737 km. Select one of the answers below:
A) The center of mass is exactly in the center between the Earth and the Moon.
B) The center of mass is nearer to the Moon than the Earth, but outside the radius of the Moon.
C) The center of mass is nearer to the Earth than the Moon, but outside the radius of the Earth.
D) The center of mass is inside the Earth.
E) The center of mass is inside the Moon.
Part C:
Calculate the location of the center of mass of the Earth-Moon-Sun system during a full Moon. A full Moon occurs when the Earth, Moon, and Sun are lined up as shown in the figure. (Figure 2) Use a coordinate system in which the center of the sun is at x=0 and the Earth and Moon both lie along the positive x direction.