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*10^(24)kg`

Distance is

`d=1.92*10^8m`

To find

The orbital period.

Step-by-step explanation

The orbital speed is given by

`v=\sqrt[]{(Gm)/(d)}`

where G is the gravitational constant

Putting the values,

`\begin{gathered} v=\sqrt[]{6.67*10^(-11)*5.98*(10^(24))/(1.92*10^8)} \\ \Rightarrow v=1441.33\text{ m/s} \end{gathered}`

The orbital period is

`\begin{gathered} T=\frac{2\pi\text{ d}}{v} \\ \Rightarrow T=(2\pi*1.92*10^8)/(1441.33) \\ \Rightarrow T=836985s\text{ =9.7 days} \end{gathered}`

Conclusion

The orbital period is 9.7 days