contestada

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

A geosynchronous satellite is to be placed in orbit about a planet that has a radiusof 6000 km mass 600 x 1024 kg and whose period of rotation 20 hours Howfar f class=

Respuesta :

We will have the following:

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

[tex]\frac{T^2}{R^3}=\frac{4\pi^2}{GM}[/tex]

Where M is the mass of the planet, thus:

[tex]\begin{gathered} R^3=\frac{GMT^2}{4\pi^2}\Rightarrow R=\sqrt[3]{\frac{GMT^2}{4\pi^2}} \\ \\ \Rightarrow R=\sqrt[3]{\frac{(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}[/tex]

So, the radius is approximately 37500 km.

Otras preguntas