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Determine whether the center of mass of the system consisting of the earth and moon lies inside or outside the earth. Assume that the radius of the earth is 6.37 x 10^3 km, the mass of the earth is 5.98 x 10^24 kg, the mass of the moon is 7.35 x10^22 kg, and the distance between the centers of the earth and the moon is 3.84 x 10^5 km. When computing the center of mass, consider the earth and the moon as point masses.

Respuesta :

Answer:

R_cm = 4.66 10⁶ m

Explanation:

The important concept of mass center defined by

         R_cm = 1 / M   ∑  x_i m_i

where M is the total mass, x_i and m_i are the position and masses of each body

Let's apply this expression to our case.

Let's set a reference frame where the axis points from the center of the Earth to the Moon,

       R_cm = 1 / M (m_earth 0 + m_moon d)

the total mass is

      M = m_earth + m_moon

     

the distance from the Earth is zero because all mass can be considered to be at its gravimetric center

let's calculate

      M = 5.98 10²⁴ + 7.35 10²²

      M = 6.0535 10₂⁴24 kg

we substitute

      R_cm = 1 / 6.0535 10²⁴ (0 + 7.35 10²² 3.84 )

      R_cm = 4.66 10⁶ m

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