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    Re: The Three-body Problem
    From: Alexandre Eremenko
    Date: 2021 Oct 27, 12:52 +0000

    Is Moon "significant for navigation" at all in our lifetime?
    > I do not believe it to be navigationally significant in our lifetimes.
    This is correct:
    > As I understand it the 3-body problem is how will 3 gravitational bodies 
    interact.  As I understand it, that problem can't be solved analyitically, 
    only thru interative methods where errors slowly 
    > accumulated.  The closer the bodies the harder it becomes.
    But what was needed for navigation is prediction of position of the Moon, say 
    for 1-2 years in advance with 0'.1 accuracy.
    And this has been accomplished through approximate solving of the 3-body problem
    > As I understand it the solar system is spread out enough to ignore the 
    effects over the short and medium term.
    Concerning the whole Solar system, it is of course even more complicated. For 
    example the following question is unsolved:
    Is it stable? That is, assuming that the planets are material points that move 
    exactly according to the Newton's laws,
    will the motion that we observe now last forever? Or some planets will 
    collide, or some planets will escape?
    Using numerical methods and computers we can answer for the next hundreds of 
    millions years. But not forever.
    Of course this question is of little practical significance:-)

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