Kepler’s formula-
r₁³ / r₂³ = t₁² / t₂²
may be written also
r₁³ / t₁² = r₂³ / t₂²
and this again in the generalized form:
r³ / t² = c.
Obviously, by each of these steps we diminish the reality-value of the formula. In its original form, we find spatial extension compared with spatial extension, and temporal extension with temporal extension. Each of the two comparisons is a fully concrete one, because we compare entities of like nature, and only then test the ratios of the two – that is, two pure numbers against each other – to find that they are identical. To compare a spatial and a temporal magnitude, as is done by the formula in its second form, requires already a certain degree of abstraction. Still, it is all spectator’s work, and for the spectator time is conceivable and measurable only as a rate of spatial displacement. Hence the constant number c, by representing the ratio between the spatial extension of the realm inside a planet’s orbit and the time needed by it to perform one round on this orbit – a ratio which is the same for all planets – represents a definite structural element of our cosmic system.