On Oct 26, 4:59*pm, Andy Walker wrote:
On 26/10/12 22:53, Dr J R Stockton wrote:

It is easy enough to state, without proof that (and roughly where) L1 L2
L3 exist, and are unstable as is a ball on the nose of a seal; and that
L4 L5 exist, and are stable as is a ball on the inside of a wok.

* * * * Easy to state, but wrong; *eg, in the restricted circular
problem, L4 and L5 are stable only if 27PS (P+S)^2, where P and
S are the masses of primary and secondary; *even then, it's more
like rolling around on an upturned wok [ie, "naturally" unstable],
but with the wok being twisted around so as to keep the ball up.
[Proof beyond the scope of this article, and just about at the
limits of undergraduate mechanics, I'd guess.]

--
Andy Walker,
Nottingham.

Empirical voodoo chanting is so diverting,people might even imagine
you both are saying something.

I look at where the modeling/predictions agenda originally arose and
specifically the technical details surrounding its acceptance in the
late 17th century with the idea that there is no perceptual boundary
between the motion and behavior of objects at a human level on one
side with the motion and behavior of objects at a planetary and solar
system scale on the other side.

What they did in the late 17th century was bundle the separate AM/PM
system and the Lat/Long system, which together contain the information
that the Earth turns once in 24 hours,into a calendar based clockwork
system known as Ra/Dec hence the clockwork solar system beloved of
modelers and why today it is close to impossible to find a scientist
who can keep one 24 hour day in step with one rotation.Without that
basic fact,our era can’t explain why the temperature goes up and down
daily in response to one rotation of the Earth but we can,with the Ra/
Dec system,predict when a star or the moon will rise and set,when a
lunar or solar eclipse will occur and things like that.The price for
being able to predict the locations of celestial objects within a
rotating celestial sphere (Ra/Dec) is terrible as we lose cause and
effect between planetary dynamics and terrestrial experiences such the
day/night cycle,the seasons,climate and many more topics.

I have a high regard for John Harrison and the monarchy that
eventually supported him as a triumph of mechanical innovation in
tandem with the astronomical principles which supply the core facts on
which clocks and watches are based and little regard for those who
can't follow those principles and especially the 'celestial mechanics'
- people who think they are following Newton but are really following
John Flamsteed's muddleheaded Ra/Dec conclusion.People make
mistakes,even a catastrophically disruptive one like this one,it is
how a people and a nation deals with that mistake and the iconic
characters that created them that matters and the English have every
opportunity to use Harrison as representative of AM/PM system and the
Lat/Long system which contains the Earth's core facts and the Ra/Dec
system which doesn't.

So far,this forum has behaved as the empiricists did with John
Harrison but there are signs in the wider community that people can
and will deal with iconic figures in an open and honest way.The idea
is to get the 'celestial mechanics' who followed the Ra/Dec system in
to adjust to its limitations and adopt the stable AM/PM and Lat/Long
systems once more otherwise it would be appealing to a Nazi mentality
that can't change and that is a distinct and dismal possibility.