Question

Two satellites of masses 'M' and 'm' respectively, revolves around the Earth in same circular orbit. The satellite with mass 'M' is far ahead from the another satellite, then how can it be overtaken by another satellite?? Given, M>m & their speed is same

Answer 1

A satellite of mass `M` having orbital velocity `v_o` revolves around earth having mass `M_e` at a distance of `R` from earth's center. While the system is in equilibrium centripetal force due to circular motion is equal and opposite to gravitational force of attraction between the earth and satellite. Equating both we get

`(Mv^2)/R=G(MxxM_e)/R^2`
where `G` is Universal gravitational constant.

`=>v_o=sqrt((GM_e)/R)`

We see that orbital velocity is independent of mass of satellite. Therefore, once placed in a circular orbit, satellite stay at the same spot. One satellite cannot overtake another in the same orbit.

In case it has to overtake another satellite in the same orbit, its velocity needs to be changed. This is achieved by firing rocket-thrusters associated with the satellite and called maneuvering.

Once appropriately placed, the velocity of the satellite is again restored to `v_o` so that it enters the desired orbit.