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    Re: Chauvenet, Moon motion
    From: Alexandre Eremenko
    Date: 2004 Sep 16, 18:45 -0500

    On prediction of the Moon motion
    On Thu, 16 Sep 2004, George Huxtable wrote:
    > To me, this was something of an eye-opener.
    > ...
    > But I had thought that by the mid 1850s lunar predictions
    > would have
    > improved to the point at which errors in the predictions
    > were negligible
    > compared with the errors in the measurement.
    > Not so, however, according to
    > Chauvenet.
    The modern mathematical theory of the motion of the Moon is due to
    American mathematician G. B. Hill (published in 1888).
    Based on this theory, the set of tables was constructed
    by E. B. Brown of Yale University, probably in 1915.
    Let me briefly explain the essence of the problem.
    It is true that the Moon motion can be "completely explained"
    by Newton's laws. But the system of differential equations
    coming from these laws cannot be solved exactly.
    This is the famous "3 body problem" on which the
    research continues to this day. The conclusion,
    roughly speaking, is that one cannot
    predict the motion for very long time.
    One has to resort to approximate solutions.
    One such "almost satisfactory" solution was obtained by Euler,
    who got his share in the famous  Longitude Prize,
    The XIX century tables were essentially based on this Euler's
    solution, but it was not completely satisfactory for
    navigation purposes. So intensive
    mathematical research continued during most of the XIX century.
    It cluminated in the work of Hill. As I understand, the precision
    of prediction reached after this work was sufficient for all
    practical purposes.
    Many of the great mathematicians of XVIII and XIX century
    contributed to this effort, I will only list some names:
    Clairaut, Laplace, Delaunay, Hansen.

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