Exercise 5: Tides.

The earth-moon system is controlled by two forces. The centrifugal force tries to separate the two stellar bodies, their gravitational attraction tries to pull them together. The balance between the centrifugal force and the gravitational attraction establishes an equilibrium that keeps earth and moon rotating around their common centre of gravity. We now take a closer look at these two forces.

As the earth rotates around the centre of gravity of the earth-moon system, its axis (the thin red line) maintains its orientation in space. This means that each point on earth moves on a circle of identical size (e.g. point A on the black circle, point B on the green circle). The magnitude of the centrifugal force is determined by the diameter of the circles; it is therefore the same at points A and B (as indicated by the blue arrows) and at all other points on earth. Its direction is always perpendicular to the circles and points outward from the circle centres.

To enhance the clarity of the diagram, the common centre of gravity is placed outside the earth. In reality it is inside the earth. This does not affect the principle that all points on the surface of the earth move on circles of identical size.