Through Kepler’s third law a certain relation is expressed between the spatial dimensions of the different planetary spheres and the time needed by the relevant planet to circle once round the circumference of its own sphere. It says: ‘The squares of the periodic times of the planets are always in the same proportion as the cubes of their mean distances from the sun.’ In mathematical symbols this reads:
t₁² / t₂² = r₁³ / r₂³
We shall see later how Kepler arrived at this law. The point is that there is nothing in it which is not accessible to pure observation. Spatial distances and lengths of time are measured and the results compared. Nothing, for instance, is said about the dynamic cause of the movements. The assertion is restricted – and this is true also of the first and second law – to a purely kinematic content, and so precisely to what the earthly onlooker can apprehend. Now it is said that Kepler’s third law is a necessary consequence of Newton’s law of gravitation, and that – since it is based on pure observation – it therefore establishes the truth of Newton’s conception. In this assertion we encounter a misconception exactly like the one in the statement that the theorem of the parallelogram of forces follows by logical necessity from the theorem of the parallelogram of velocities. For: