This simulation shows the motion of a moon around a planet under the influence of gravity. However, as the moon moves, the same force of gravity acts on the planet, making it move also. The net effect is that both the planet and the moon move in their own circles around the point which is the common centre of mass.

In this simulation, you can control the mass of both the planet and the moon. However, the simulation of the motion will not update until you click somewhere inside the simulation region.

As you run the simulation the planet is shown in red and the moon in blue. Also shown is the position of the centre of mass, indicated by the white dot. Note: that for a set mass of the moon and the planet, the centre of mass does not move.

This same effect can be seen in the motion of a planet around the Sun, in which case the (massive) Sun 'wobbles' due to the gravitational force between it and the much lighter planet. This effect has been exploited as a means of detecting planets around distant stars by observing the wobble of the star.