We are asked to find the centripetal acceleration of the earth in its nearly circular orbit about the sun. The time it takes the earth to orbit around the sun is 365 days. Let's convert 365 days to seconds. Therefore,
[tex]365\times24\times60\times60=31536000=3.15\times10^7[/tex]
We were given the speed. Therefore,
[tex]v=30\text{ km/s}[/tex]
we will have to convert v to m/s. Recall our centripetal acceleration must be in m/s2. Therefore,
[tex]v=30000\text{ m/s}[/tex]
Finally, let's find the centripetal acceleration.
[tex]\begin{gathered} a_c=\frac{v^2}{r} \\ v=30000\text{ m/s} \\ r=1.5\times10^{11} \\ a_c=\frac{30000^2}{1.5\times10^{11}}=\frac{900000000}{150000000000^{}}=0.006=6\times10^{-3}m/s^2 \end{gathered}[/tex]
