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    Re: The Three-body Problem
    From: Fred Hebard
    Date: 2021 Oct 25, 09:39 -0400
    The three-body problem is that there is no known explicit solution of the differential equations that describe the motion of three bodies in orbit.  In fact, it has been proven there is no explicit solution.  An explicit solution for dx/dt = y might be x = y*t + c, where c is a constant.  

    Explicit solutions for equations make it easy to compute the position x in the above equation when y, t and c are known.  However, it is still possible to estimate x when no explicit solution exists, using numerical methods.  Start at some x, and then add dx/dt to get the next x, then rinse and repeat. That is how the Nautical Almanac is computed, at least from an abstract point of view.

    Chaos theory would not enter into the lack of explicit solutions of the three-body problem.  When the numerical solutions become chaotic it enters, but those conditions don’t happen in planetary motions in practical time frames, barring the solar system running into a rogue Jupiter or similar.


    Fred Hebard



    On Oct 24, 2021, at 23:45, Bob Goethe <NoReply_Goethe@fer3.com> wrote:

    I am reading an SF book now by a Chinese author, Liu Cixin, which has been translated into English:  The Three-Body Problem.  This led me to Wikipedia to see what the "three-body problem" was about.  It looked to me like a) the basic three-body problem that has intrigued people for some time has been the relative orbits of the sun, earth, and moon.  I had a little trouble following the article, but it seemed as though it might be a fundamentally unsolvable problem, influenced by factors we would describe as chaotic.

    Still we have all verified experimentally that the Nautical Almanc is enormously accurate.  On the other hand, it is generally difficult to get a copy of the Nautical Almanac for the next year more than just a few months in advance.

    I would appreciate anybody's musings about the three-body problem and whether or not it is navigationally significant.

    Thanks,

    Bob

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