Conic Sections

And the rain descended, and the floods came, and the winds blew, and beat upon that house; and it fell: and great was the fall of it.

(Matthew 7:27) KJV

When we ask the question: what’s at the second focus in Kepler’s laws? there’s another stock response which comes up with surprising frequency. It appears that everyone has been trained to give this answer.

For our Kepler skeptic the 2-body problem should be enough. The analytical solution shows the orbits are conical sections: ellipses, parabolas or hyperbolas, depending on the initial conditions. For the speeds and positions of the planets of our solar system, it yields ellipses with very low eccentricity (thus very close to being circles).

FlatSlugBrains

Once again this is more of a rhetorical ploy than an actual solution. It’s more scientific sleight-of-hand. Yes, if we cut through a cone at an angle we’ll get an elliptical (conic) section, but what, at the scale of the solar system, is the physical cause for this effect? There still isn’t one. What cut through a cone the size of the solar system? Nothing. Where’s the evidence that planets were captured by the gravity of the sun? There isn’t any, it’s an inductive rationalization. Why aren’t the planetary orbits degrading as they slide into the sun? It’s not a testable hypothesis.



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