[meteorite-list] PV and Lunar-New Photos and Links

From: Sterling K. Webb <kelly_at_meteoritecentral.com>
Date: Fri Sep 9 17:50:36 2005
Message-ID: <43220387.3B7F83D0_at_bhil.com>

Hi, Martin

    The other motions you are seeing are
    NUTATION and
    LIBRATION.

    The Moon has a very complex set of motions
about the Earth. These allow us to see "over the edges"
and actually view, however obliquely, more than
the 50% you'd think we could. The Moon "nods" its
head and turns side to side as it approaches and
recedes from the Earth.

    The complexity of the Moon's motion has been a
boon to the development of celecstial mechanics over
the last three centuries. The ultimate statement of an
orbit is called the Time Equation, which will allow us
to predict the exact position and motion of a body
at a given point in time, past or future.

    Because the Time Equation for the Moon is
decidedly difficult, trying to work it out has sharpened
the wits of celectial mechanics for several centuries.
Without the Moon's complex behavior to explain,
we wouldn't know as much as we do about celestial
motion calculation.

    Writing the time equation of the Moon's orbit is
perhaps the most daunting task that faced applied
mathematics in the past few centuries. The last word
in this immense job is the work of E. W. Brown and
W. J. Eckert, Brown working on paper for his entire
life and Eckert applying the Brown equation to execution
with early computers.

    "Since 1923 the work of E W Brown has
constituted the basis for the published ephemerides
of the moon. His monumental calculation, which
occupied most of his lifetime, consists of two distinct
steps. The first is the development of the theory or
the solution of the differential equations of motion
expressing the coordinates of the moon as explicit
functions of time. Secondly, in order to reduce the
necessary labor involved in computing the coordinates
of the moon for any given date from these formulae,
Brown computed from his theory a set of Tables
which, including the necessary explanations, comprise
over 650 large quarto pages. ... In order to bring
the Tables within even their present length, various
parts of the basic equations were curtailed whenever
permissible in the light of observational requirements
(as then visualised). However by the 1950s it was
realised that the Tables were not accurate enough.
Eckert therefore decided not to recompute new tables
but to compute the ephemeris directly from Brown's
equations. The task was immense for, Brown's
formulae involved some 1,650 trigonometric terms,
many of them with variable coefficients. The accuracy
of Eckert's calculations of the Moon's orbit was so
good that in 1965 he was able to correctly show
that there was a concentration of mass near the lunar
surface. In 1967 he produced theoretical work which
improved on Brown's theory of the Moon."

    The Eckert program is so immense that until recently
it took WEEKS of computer time to run. In 1997, both
the Brown equation (published in seven volumes! Brown,
Ernest, W. Tables of the Motion of the Moon, Yale Univ.
Press, 1919) and the Eckert revision were run checked
on supercomputers that were able to zip through them
in ONLY 17 hours of continuous operation! Only two
totally trivial errors were found in Brown's lifelong work
and only one (misprint) in Eckert's computer program.

    The second most daunting task is Milancovitch's
calculation of the changes in the Earth's orbit with time
and its climatological consequences (the Ice Ages),
again done entirely "on paper" (without any mistakes)
and occupying his entire working life time.

    The original animation, much larger, was an APOD
some years ago, but I can't find it in their index.


Sterling K. Webb
see: <www-groups.dcs.st-and.ac.uk/
~history/Mathematicians/Eckert_Wallace.html>
---------------------------------------------------------
"Martin H." wrote:

> Hi Robert,
>
> I was looking at your Dhofar 1180 page:
>
> http://www.portalesvalleymeteorites.com/Lunar.htm
>
> And was intrigued by the moon phase gif. On my
> computer it was cycling faster than once per second.
>
> At this speed, it is obvious there is other motion and
> rotation active in the composite. Forgetting about
> other photography//computer issues, it appears, taking
> the gif at face value of course, that one can easily
> see some rolling back and forth of the visible lunar
> surface, some precession, and some distance changing
> between the earth (photographer) and the moon.
>
> Just an early morning observation. Oh, great pics of
> great meteorites as well!
>
> Martin
>
> --- Robert Woolard <meteoritefinder_at_yahoo.com> wrote:
>
> > Hello List,
> >
> > I have just updated my website with new photos and
> > links that I hope/believe a lot of you would find
> > interesting and enjoy seeing, even if you are not
> > presently looking to add to your collection. ( But
> > IF
> > you are, well, that would be fine, too. ;-)
> >
> > I would welcome any thoughts or comments on the
> > new
> > photos and links.
> >
> > Best wishes,
> > Robert Woolard
> > http://www.portalesvalleymeteorites.com
> >
> >
> >
> >
> >
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Received on Fri 09 Sep 2005 05:50:00 PM PDT