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Ignoring the turbulent beginnings of our solar system I wonder if there is a meaningful way to calculate the relative position of the planets of our solar system 100 million years into the future using the standard parameters N / i / w / a / e / M / +- pertubations , {assuming no unannounced black hole or neutron star zips through our solar system in the meantime.} How far can the orbital calculations be projected into the future before error accumulation make these calculations completely meaningless?

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    $\begingroup$ That sure is a lot of questions in what ideally is a single question. There are four question marks, most of which each ask multiple questions. I suggest you do some research and then ask more pointed questions. Individually. A good place to start is to ask your favorite search engine about the stability of the solar system. You'll see several questions and answers on this topic at this site and at sister sites on the stackexchange network. $\endgroup$ – David Hammen Dec 8 '16 at 17:19
  • $\begingroup$ I asked a similar question on the Earth orbit here: astronomy.stackexchange.com/questions/11243/… $\endgroup$ – userLTK Dec 8 '16 at 19:27
  • $\begingroup$ @DavidHammen It's basically the same question just asked with different time periods and perhaps asked with some redundancy. It's still basically one question and/or 2 very related questions. What do we know about planets orbits over long periods of time and how accurate? $\endgroup$ – userLTK Dec 8 '16 at 19:33
  • $\begingroup$ Fun fact, you can actually search for this on Wolfram Alpha, using phrases like "position of the planets 10000 years ago". I tried it for 1 million, and it didn't have a result, so there appears to be a limit. Also, I can't comment on the accuracy of the calculation. $\endgroup$ – Cody Dec 8 '16 at 21:27
  • $\begingroup$ @DavidHammen. Thank you for counting my question marks. I am sorry that I was not aware of the "one question mark only" policy at this site. I only just joined this forum in my quest to find an answer to this question and all my previous research was not successful. I will endeavour to mend my ways and edit my question accordingly. $\endgroup$ – Volker Dec 9 '16 at 0:04
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Jacques Laskar, at IMCCE, has been working on describing planetary motions on long term time scales.

Quoting and translating a paper by him:

  • Motion in the solar system is chaotic, meaning that trajectories diverge exponentially: an error on the location of a planet gets multiplied by 10 every 10 million years
  • This means that a 15 meter error on the initial location of the Earth yields an error of 150 meters after 10 million years, and 150 million km afer 100 million years. Long term predictions involving a single trajectory are impossible.

For predictions over longer periods, it becomes necessary to study multiple possible trajectories. Laskar and Gastineau have published results of a simulation of the solar system involving 2501 variations of the location of Mercury. In this simulation, "initial conditions differ by only 0.38 mm in the semi-major axis of Mercury". Some of those trajectories involve "possible collisions of Mercury, Mars or Venus with the Earth".

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  • $\begingroup$ I haven't translated his paper, but a multiple of 10 over 10 million years sounds very small and if that's accurate, that's very impressive. It sounds a little too optimistic to me, but using those numbers, The "error" is still negligible after 50 million years, but as you point out, enormouS at 100 million. $\endgroup$ – userLTK Dec 9 '16 at 16:05

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