A satellite revolves from east to west in a circular equatorial orbit of radius `R=1.00*10^4km` around the Earth. Find the velocity and the acceleration of the satellite in the reference frame fixed to the Earth.

Explanation

The velocity of the satellite in the inertial space fixed frame is `sqrt((gammaM)/(R))` east to west. With respect to the Earth fixed frame, from the `overset(rarr')v_1=vecv-(vecwxxvecr)` the velocity is
`v^'=(2piR)/(T)+sqrt((gammaM)/(R))=7*03km//s`
Here M is the mass of the earth and T is its period of rotation about its own axis.
It would be `-(2piR)/(T)+sqrt((gammaM)/(R))`, if the satellite were moving from west to east.
To find the acceleration we note the formula
`moverset(rarr')w=vecF+2m(overset(rarr')vxxvecomega)+momega^2vecR`
Here `vecF=-(gammaMm)/(R^3)vecR` and `overset(rarr')v_|_vecomega` and `overset(rarr')vxxvecomega` is directed towards the centre of the Earth.
Thus `w^'=(gammaM)/(R^2)+2((2piR)/(T)+sqrt((gammaM)/(R)))(2pi)/(T)-((2pi)/(T))^2R`
toward the earth's rotation axis
`=(gammaM)/(R^2)+(2pi)/(T)[(2piR)/(T)+2sqrt((gammaM)/(R))]=4*94m//s^2` on substitution.