First let's fill the things we know from the table:
G=6.67e-11 m3/kgs2
M=1.99e30 kg
r=7.33e11 m
Now, to find the acceleration of the asteroid we use:
[tex]a=\frac{GM}{r^2}[/tex]Plugging the values we know we have that the acceleration of the asteroid is:
[tex]\begin{gathered} a=\frac{(6.67\times10^{-11})(1.99\times10^{30})}{(7.33\times10^{11})^2} \\ a=2.47\times10^{-4} \end{gathered}[/tex]Therefore the acceleration is 2.47e-4 m/s2.
The velocity is given by:
[tex]v=\sqrt[]{ar}[/tex]then we have:
[tex]\begin{gathered} v=\sqrt[]{(2.47\times10^{-4})(7.33\times10^{11})} \\ v=1.35\times10^4 \end{gathered}[/tex]Therefore the velocity is 1.35e4 m/s
Finally the period is given as:
[tex]T=\frac{2\pi r}{v}[/tex]then:
[tex]\begin{gathered} T=\frac{2\pi(7.33\times10^{11})}{(1.35\times10^4)} \\ T=3.41\times10^8 \end{gathered}[/tex]Therefore the period is 3.41e8 seconds. Now, this is the same as 10.8 years; to get this we divide the seconds by 3.154e7
