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choli [55]
3 years ago
14

g HW 5.6.The Moon and the Earth both orbit the center of mass of the Earth-Moon system.Earth is 81 times more massive than the M

oon. Assume that the distance between the centerof the Earth and the Moon is 384,400.0 km. Determine the distance of the center of mass of theEarth-Moon system from the center of the Earth. Does it lie inside or outside the Earth with theradius of 6,371.0 km
Physics
1 answer:
Law Incorporation [45]3 years ago
6 0

Answer:

R_{cm}  = 4.688 106 m

Explanation:

The expression for the center of mass is

       R cm = 1 / M ∑ r_{i} m_{i}

Where M is the total mass of the system, ri and m1 are the distance and mass of each particle from a defined origin

Let's look for the total mass, the mass of the moon is m and that of the earth Me

    M = M_{e} + m

    M = 81m + m

    M = 82 m

The distance from the earth to the moon is R = 384.4 106 m

    R_{cm} = 1 / M (M R1 + m R)

   R_{cm}  = 1 / 82m (0 + m R)

    R_{cm}  = R / 82

   R_{cm}  = 384.4 106/82

   R_{cm}  = 4.688 106 m

The radius of the earth is

    R_{e} = 6371 103 m

    R_{e}  = 6.371 106 m

We can see that the center of mass of the system is within the beating radius

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