## Relationaship Between Radius of Orbit of Planet and Orbital Speed

\[\frac{GM_{Sun} m_{Earth}}{r^2}=\frac{m_{Earth}v^2}{r}\]

Hence

\[v=\sqrt{\frac{GM}{r}}\]

As the radius of the orbit increases the speed of the planet decreases. The kinetic energy decreases, but because the total energy (kinetic plus gravitational potential energy is negative and equal to half the gravitational potential energy

\[GPE= - \frac{GM_{Sun} m_{Earth}}{r}\]

) the total energy of the planet will increase.