There are many satellites in orbit about the earth. The ones in circular orbits are
examples of uniform circular motion . Uniform circular motion is the motion of an
object traveling at a constant (uniform) speed on a circular path.
Each satellite is kept on its circular path by a centripetal force. The gravitational
pull of the earth provides the centripetal force and acts like an invisible guideline
for the satellite.
It is interesting that a satellite can only have one speed if the satellite is to remain
in an orbit with a fixed radius.
To see how this characteristic arises, consider the centripetal force provided by the
earth due to gravity.
| = centripetal force |
| = mass of the satellite |
| = mass of the earth |
| = distance from the center of the earth to the satellite |
| = universal gravitational constant |
But centripetal force can be generally written as :
| = mass of object |
| = velocity of satellite |
| = radius of circular path |
If these two equations are equated :
Solving for the speed of the satellite gives :
If the satellite is to remain in an orbit of radius ,
the speed must have precisely this value. Once in orbit at the correct speed,
the satellite continues in uniform circular motion forever, assuming that effects
such as friction due to residual atmosphere do not reduce the speed.
This equation :
holds for man-made earth satellites and the moon. Notice that mass
of the satellite does not appear in this equation, having been eliminated algebraically.
Consequently, for a given orbit, a satellite with a large mass has exactly the same
orbital speed as a satellite with a small mass.