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Karo-lina-s [1.5K]
3 years ago
8

The mass of the earth is 5.98 1024 kg, the mass of the moon is 7.36 1022 kg, and the distance between the centers of the earth a

nd the moon is 3.82 108 m. How far is the center of mass of the earth-moon system from the center of the earth
Physics
1 answer:
Setler [38]3 years ago
4 0

Answer:

 x_{cm} = 4.644 10⁶ m

Explanation:

The center of mass is given by the equation

         x_{cm} = 1 / M_{total}  ∑ x_{i}  m_{i}

Where M_{total} is the total masses of the system, x_{i} is the distance between the particles and m_{i} is the masses of each body

Let's apply this equation to our problem

        M = Me + m

        M = 5.98 10²⁴ + 7.36 10²²

        M = 605.36 10²² kg

Let's locate a reference system located in the center of the Earth

Let's calculate

       x_{cm} = 1 / 605.36 10²²   [Me 0 + 7.36 10²² 3.82 10⁸]

       x_{cm} = 4.644 10⁶ m

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