Question

I'm having trouble finding radius and period on these types of questions, I've not worked on them for a while so I might need a refresher on variable meanings and such.

Answer 1

Given:

The mass of the mars, M=6.42×10²³ kg

The orbital period of the satellite, T=88640 s

To find:

The radius of the orbit of the satellite.

Step-by-step explanation:

The orbital period is given by the equation,


Where G is the gravitational constant.

On rearranging the above equation,


On substituting the known values,



Final answer:

The radius of the orbit of the satellite is 20.43×10⁶ m

Answer 2

Given:

The mass of the mars, M=6.42×10²³ kg

The orbital period of the satellite, T=88640 s

To find:

The radius of the orbit of the satellite.

Step-by-step explanation:

The orbital period is given by the equation,

`T=2\pi\sqrt[]{(r^3)/(GM)}`

Where G is the gravitational constant.

On rearranging the above equation,

`\begin{gathered} (T^2)/(4\pi^2)=(r^3)/(GM) \\ \Rightarrow r=\sqrt[3]{(T^2GM)/(4\pi^2)} \end{gathered}`

On substituting the known values,

`\begin{gathered} r=\sqrt[3]{(88640^2*6.67*10^(-11)*6.42*10^(23))/(4\pi^2)} \\ =20.43*10^6\text{ m} \end{gathered}`

Final answer:

The radius of the orbit of the satellite is 20.43×10⁶ m