Question

Find the acceleration of the moon with respect to the earth from the following data :
Distance between the earth and the moon $=3.85\times {10}^5$ and the time taken by the moon to complete one revolution around the earth $=27.3$ days.

Answer 1

Distance between Earth and Moon

$r=3.85\times {10}^{5}km=3.85\times {10}^{8}m$

$T=27.3days=24\times 3600\times \left(27.3\right)sec=2.36\times {10}^{8}sec$

Time period of the moon will be

$T=\frac{2\pi r}{v}$

$v=\frac{2\pi \times 3.85\times {10}^8}{27.3\times 24\times 60\times 60}$

$=1025.98m/s$

the acceleration of the moon is,

$a=\frac{v^2}{r}$

$a=\frac{{\left(1025.98\right)}^2}{3.85\times {10}^8}$

$=2.73\times {10}^{-3}m/s^2$

This is the acceleration of moon with respect to Earth.