Question

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.

Answer 1

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