Question:
Find the acceleration of the moon with respect to the earth from the following data: Distance between the earth and the moon $=3.85 \times 10^{5} \mathrm{~km}$ and the time taken by the moon to complete one revolution around the earth $=27.3$ days.
Solution:
Speed of the moon=distance/time
$=\frac{2 \pi T}{T}$
$=\frac{2 \times 3.14 \times\left(3.85 \times 10^{8}\right)}{27.3 \times 86400}$
$=1025.4 \mathrm{~m} / \mathrm{s}$
Acceleration of moon $=$
$\mathrm{A}_{\mathrm{r}}=\frac{v^{2}}{r} \frac{(1025.4)^{2}}{\left(3.85 \times 10^{8}\right)}$
$A_{r}=2.73 \times 10-3 \mathrm{~m} / \mathrm{s}^{2}$