Question

Compute the moon's centripetal acceleration in its orbit around the earth. Recall that the moon orbits the earth every 28.0 ���� and that it is about 240000 ����� from the earth. What force causes this acceleration? Be sure to convert to �� �����.

Answer 1

Answer:

0.0026 m/s²    

Explanation:

Centripetal acceleration is given as follows:

$a=\frac{v^2}{r}\\where, v =\frac{2\pi r}{T}$

$a=\frac{(\frac{2\pi r}{T})^2}{r}=\frac{4\pi^2r}{T^2}$

$T=28.0 days\times 24hours\times 3600 s= 2.4\times10^6s$

$r=240000 mi = 384.4\times 10^6 m$

Substitute the values:

$a=\frac{4\pi^2 \times 384.4\times10^6}{(2.4\times10^6)^2}=0.0026m/s^2$