It is known that the Earth’s orbit , as well as any 3 (or more) body orbit is chaotic (see f.ex Malhotra,Holman, Ito) .That of course doesn’t mean that the orbits are random or that they can do anything crazy in short times . However it means that the orbits are never the same and that the distance between 2 orbits with as close initial conditions as one wishes will increase exponentially with time . This exponential parameter is called Lyapunov coefficient and is for the Earth orbit between 5 – 10 millions years . That means that any calculation , be it forward or backward in time for more than let’s say 100 millions year gives an orbit whose parameters have no significance and could be completely random for all that matters .

Your post came to my mind when reading this on the news

Jacques Laskar of the Observatoire de Paris in France authored the other study. He ran 1001 computer simulations of the solar system over time, each with slightly different starting conditions for the planets based on the range of uncertainties in the observations. In 1 to 2% of the cases, Mercury’s orbit became very elongated over time due to gravitational tugs by Jupiter. In these cases, its orbit reached an “eccentricity” of 0.6 or more (an eccentricity of 0 means the orbit is a perfect circle, while 1 is the maximum possible elongation). ..

In one of Batygin and Laughlin’s simulations, Mercury was thrown into the Sun 1.3 billion years from now. In another, Mars was flung out of the solar system after 820 million years, then 40 million years later Mercury and Venus collided.

http://space.newscientist.com/article/dn13757-solar-system-could-go-haywire-before-the-sun-dies.html

]]>Give him a little time. He is currently debugging the last few lines of LaPlace’s demon ;-)

]]>2. Why THESE parameterizations, and not some other intermediate ones? (Why are the dots located where they are?)

3. Why this RANGE of parameterization and not something wider? (Why not more dots on either end of the curve?)

[Hint: These are fudgings, err, tunings. They are the free parameters whose governance by hard physics is uncertain.]

The floor is yours, Eric. Maybe you have a nice YouTube dodge for us?

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