Orbital speed of a satellite

What is 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.

Orbital speed of a 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 v₀ is the required orbital velocity for the satellite, then centripetal force exerted by the earth on the satellite is mv₀²/r.

3. Now the gravitational force exerted by the earth on the satellite will be GM_em/r². Because the gravitational force provides the required centripetal force, hence we can write
G(M_em/r²)=mv₀²/r or GM_e = v₀²/r
Or v₀= √(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_e² or GM_e=gR_e²

Putting this value of GM_e is eq. (1), we get

v₀=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.