Question

how would i solve this question?A geostationary satellite of mass 1250 kg is in a circular orbit around the earth at an altitude of 48,570km as measured from the centre of the earth. If the force of gravity between the satellite and the earthis 211.34 N, determine:a) the speed at which the satellite is orbiting the earth.b) the period of the satellite’s motion in hours

Answer 1

The first part is to find the speed. For this, you have to get the equilibrium between the gravitational force (attraction), and the centripetal force (repulsion). So you can get the force equilibrium

`\begin{gathered} F=(mv^2)/(r) \\ 211.34N=(1250kg\cdot v^2)/(48570000m) \\ 8211827m^2/s^2=v^2 \\ v=2865.63m/s \end{gathered}`

Now the period

`\begin{gathered} T=(2\pi)/(w)=(2\pi\cdot r)/(v) \\ T=(2\pi\cdot48570000)/(2865.63) \\ T=106494.72s \end{gathered}`