Calculate the radius of the circular orbit of a stationary Earth's satellite, which remains motionless with respect to its surface. What are its velocity and acceleration in the inertial reference frame fixed at a given moment to the centre of the Earth?

Explanation

A satellite that hovers above the earth's equator and corotates with it moving from the west to east with the diurnal angular velocity of the earth appears stationary to an observer on the east. It is called geostationary. For this calculation we may neglect the anuual motion of the earth as well as all other influences. Then, by Newton's law,
`(gammaMm)/(r^2)=m((2pi)/(T))^2r`
where M=mass of the earth, `T=86400` seconds = period of daily rotation of the earth and r=distance of the satellite from the centre of the earth. Then
`r=root3(gammaM((T)/(2pi))^2)`
Subsitution of `M=5*96xx10^(24)kg` gives
`r=4*220xx10^4km`
The instantaneous velocity with respect to an initial frame fixed to the centre of the earth at that moment will be
`((2pi)/(T))r=3*07km//s`
and the acceleration will be the centripetal acceleration.
`((2pi)/(T))^2r=0*223m//s^2`