**(a)**

The position from the center of the earth:

$\overline{)\begin{array}{rcl}{\mathbf{x}}& {\mathbf{=}}& \frac{{\mathbf{M}}_{\mathbf{e}}{\mathbf{x}}_{\mathbf{e}}}{{\mathbf{M}}_{\mathbf{e}}\mathbf{+}{\mathbf{M}}_{\mathbf{m}}}\mathbf{+}\frac{{\mathbf{M}}_{\mathbf{m}}{\mathbf{x}}_{\mathbf{m}}}{{\mathbf{M}}_{\mathbf{e}}\mathbf{+}{\mathbf{M}}_{\mathbf{m}}}\end{array}}$

x_{e} = 0 km (distance of earth from earth), x_{m} = 384400 km (distance of moon from earth), M_{e} = 5.972 × 10^{24} kg (mass of earth), and M_{m} = 7.34767 × 10^{22} kg (mass of moon)

(a) How far is the center of mass of the Earth-Moon system from the center of the Earth? (Appendix C gives the masses of the Earth and the Moon and the distance between the two.)

(b) Express the answer to (a) as a fraction of the Earth's radius.

(Rcm / Rearth) =

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