### Orbital speed of a satellite

1. Orbital speed of a satellite is the speed required to put the satellite into orbit. When a satellite (such as moon) revolves in a circular orbit around the earth, a centripetal force acts upon the satellite. This force is actually the gravitational force exerted by the earth on the satellite.

2. Suppose a satellite of mass m has to be put circular orbit around the earth at height h above its surface. Consider earth to be a sphere of mass M_{e} and radius R_{e}. Then radius of the orbit of the satellite will be r (=R_{e} + h). If v_{0} is the required orbital velocity for the satellite, then centripetal force exerted by the earth on the satellite is mv_{0}^{2}/r.

3. Now the gravitational force exerted by the earth on the satellite will be GM_{e}m/r^{2}. Because the gravitational force provides the required centripetal force, hence we can write

G(M_{e}m/r^{2})=mv_{0}^{2}/r or GM_{e} = v_{0}^{2}/r

Or **v _{0}= √(GM_{e}/r)= √(GM_{e}/R_{e}+ h)**………..(1)

If the acceleration due to gravity on the earth’s surface is g, then

g = GM

_{e}/ R

_{e}

^{2}

**or**GM

_{e}=gR

_{e}

^{2}

Putting this value of GM_{e} is eq. (1), we get

**v _{0}=R_{e}√[g/(R_{e}+h)]**……..(2)

Thus eq(1) and (2) provide the speed of revolution of the satellite in its orbit.

**Note:**a) Orbital speed of the satellite depends only upon its height above the earth’s surface. Greater is the height h of the satellite above earth’s surface, smaller is the speed of the satellite.

b) Because the speed of a satellite is independent of the mass of the satellite, therefore, two satellites of different masses revolving in same orbit around the earth will have the same speed.