Question

Find the acceleration of the moon with respect to the earth from the following data : Distance between the earth and the moon = 3.85 × 10⁵ km and the time taken by the moon to complete one revolution around the earth = 27.3 days.

Answer 1

Distance between the Earth and the Moon:
$r=3.85\times {10}^5\mathrm{km}=3.85\times {10}^8\mathrm{m}$

Time taken by the Moon to revolve around the Earth:

$$\begin{gathered} T=27.3\mathrm{days} \\ =24\times 3600\times 27.3\mathrm{s}=2.36\times {10}^6\mathrm{s} \\ \mathrm{Velocity}\mathrm{of}\mathrm{the}\mathrm{Moon}: \\ v=\frac{2\pi r}{T} \\ =\frac{2\times 3.14\times 3.85\times {10}^8}{2.36\times {10}^6}=1025.42\mathrm{m}/\mathrm{s} \\ \mathrm{Acceleration}\mathrm{of}\mathrm{the}\mathrm{Moon}: \\ a=\frac{v^2}{r}=\frac{(1025.42{)}^2}{2.36\times {10}^6}=0.00273\mathrm{m}/{\mathrm{s}}^2 \end{gathered}$$
$\Rightarrow a=2.73\times {10}^{-3}\mathrm{m}/{\mathrm{s}}^2$