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

From: Martin Horejsi <accretiondesk_at_meteoritecentral.com>
Date: Sat Sep 10 11:55:22 2005
Message-ID: <9c2f96d2050910085575ca7e_at_mail.gmail.com>

Wow Sterling! What a great reply.

In fact, I am so impressed with the detail and obvious amount of time
you put into the reply that I nominate you for a Harvey Award for
"Extreme Information Generosity via Electronic Means." Did you hear
that Geoff?

Thank you! Now I have to do is digest what you wrote.

Cheers,

Martin


On 9/9/05, Sterling K. Webb <kelly_at_bhil.com> wrote:
> 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 Sat 10 Sep 2005 11:55:20 AM PDT