Question

A geosynchronous satellite is to be placed in orbit about a planet that has a radiusof 6000 km, mass - 6.00 x 1024 kg, and whose period of rotation - 20 hours. Howfar from the center of the planet should be the orbit of the satellite? Mass ofsatellite = 500 kg.O 37,500 km© 400,000 km0 75.000 kmO 23,300 km

Answer 1

We will have the following:

We must solv using the orbital period eqiation, that is:

`(T^2)/(R^3)=(4\pi^2)/(GM)`

Where M is the mass of the planet, thus:

`\begin{gathered} R^3=(GMT^2)/(4\pi^2)\Rightarrow R=\sqrt[3]{(GMT^2)/(4\pi^2)} \\ \\ \Rightarrow R=\sqrt[3]{((6.674\ast10^(-11))(6.00\ast10^(24)kg)(20h\ast3600s/1h)^2)/(4\pi^2)}\Rightarrow R=37462136.66...m \\ \\ \Rightarrow R\approx37500km \end{gathered}`

So, the radius is approximately 37500 km.