Circular Orbits

We first consider the motion of planets and satellites in circular orbits.

  

Figure 5: Circular Orbit

Total energy of a satellite of mass m in an orbit of radius r around a planet of mass M is :

$$E = 1/2mv^2 - \frac{GMm}{r} = -1/2\frac{GMm}{r}$$ (7)

where we have used the fact that the centripetal force is provided by the force of gravity: $$\frac{mv^2}{r} = \frac{GMm}{r^2}$$         ( F_grav = ma_centripetal)
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