According to the first law, the planets \(P_1, P_2,\ldots\) have orbits being ellipses. Let \(a_1,a_2,\ldots\) denote the major axes of the respective ellipses and let \(t_1,t_2,\ldots\) denote the time intervals each planet needs to complete its orbit (orbital periods). Then the following ratios are equal to a constant \(C\), called the Keplerian constant:
\[\frac{a_1^3}{t_1^2}=\frac{a_2^3}{t_2^2}=\ldots=C\]
Proofs: 1
Persons: 1
