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    Re: Long-term orbit predictability: was [Nav-l] Delta-T
    From: Alexandre Eremenko
    Date: 2004 Dec 5, 13:23 -0500

    I think the question of whether we can make a Nautical
    Almanach for a hundred of thousands years or for a million
    years is out of the scope of this list, but because George seems
    to be highly interested in this subject, I can tell what I know.
    The question of stability of Solar system is unsolved.
    I mean we just do not know whether it is stable or not.
    There were several attempts to prove stability mathematically
    (beginning from XVIII century to some recent works) but they
    failed. But there is also no mathematical demonstration that
    it is unstable, not speaking of "chaotic".
    There were indeed some recent works claiming that instability
    was demonstrated by calculation (over the period of hundreds
    of millions to billions of years). I read some
    of these papers published in "Science" and "Nature" in 1990-s.
    But the
    validity of these
    calculations was disputed by mathematicians.
    From which I made a
    that reliable numerical solution for such long times is impossible.
    For what period of time we can really make a reliable almanach,
    I don't know. But surely for several thousands years.
    I also think that the motion of the main planets
    (say, those 4 used in navigation) can be predicted for much
    longer periods than the motion of the Moon, which is
    by far the most complicated.

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