Theorem: Third Law of Planetary Motion (Kepler) 

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 the following ratios are equal to a constant \(C\), called the Keplerian constant:

\[\frac{a_1^3}{t_1^2}=\frac{a_2^3}{t_2^2}=\ldots=C\]

| | | | | created: 2016-11-27 20:14:27 | modified: 2019-08-24 07:47:00 | by: bookofproofs | references: [6301]

1.Proof: (related to "Third Law of Planetary Motion")