Intro to Center of Mass Video Lessons

Concept

# Problem: (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) =

###### FREE Expert Solution

(a)

The position from the center of the earth:

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

xe = 0 km (distance of earth from earth), xm = 384400 km (distance of moon from earth), Me = 5.972 × 1024 kg (mass of earth), and Mm = 7.34767 × 1022 kg (mass of moon)

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###### Problem Details

(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) =