Question

Kepler's law is still confusing me even with all the info I've gathered, I attached an example question that I've been stuck on for a bit to work on.

Answer 1

Given

Mass is

$m=5.98\times10^{24}kg$

Distance is

$d=1.92\times10^8m$

To find

The orbital period.

Explanation

The orbital speed is given by

$v=\sqrt[]{\frac{Gm}{d}}$

where G is the gravitational constant

Putting the values,

$\begin{gathered} v=\sqrt[]{6.67\times10^{-11}\times5.98\times\frac{10^{24}}{1.92\times10^8}} \\ \Rightarrow v=1441.33\text{ m/s} \end{gathered}$

The orbital period is

$\begin{gathered} T=\frac{2\pi\text{ d}}{v} \\ \Rightarrow T=\frac{2\pi\times1.92\times10^8}{1441.33} \\ \Rightarrow T=836985s\text{ =9.7 days} \end{gathered}$

Conclusion

The orbital period is 9.7 days