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## 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")

### Bibliography (further reading)

[6301] Ruhrländer, Michael: “Aufstieg zu den Einsteingleichungen”, Pro BUSINESS GmbH, 2014