[meteorite-list] Earth Trojan asteroids

[Dawn & Gerald Flaherty]

Ah HAH!! I think. Thank you and thank you cause you've answered both
questions. Billiards on a planetary scale. No wonder I never made it in a
pool  hall!! Jerry
----- Original Message ----- 
From: <MexicoDoug at aol.com>
To: <grf2 at verizon.net>; <francisgraham at rocketmail.com>;
<meteorite-list at meteoritecentral.com>
Sent: Saturday, June 25, 2005 3:45 PM
Subject: Re: [meteorite-list] Earth Trojan asteroids


> Jerry F. wrote:
> >Francis and List, could someone help me with the L4,  L5 points??
> >Jerry Flaherty
>
> Hola Jerry,
>
> L4 and L5:  These two zones (it would be a  point if it were unstable, but
> you will see that they are stable and hence,  zones) are one AU in front
of
> Earth or 1 AU behind Earth.
>
> They are  stable:  In the case of going co-orbital exactly 1 AU in front
of
> Earth in  our orbit (L4), or co-orbital 1 AU behind (L5), Earth, or
anything of
> reasonable  planetary size will either pull it back or drag it along.  If
it
> is wanders  by being pulled back from L4, it gets pushed in an arc right
into
> the Sun, and  if it gets dragged along, it gets pulled away from the Sun
> outwards (both pull  and push tangents from 1 AU around Earth are directed
exactly
> into or away from  the Sun - draw two equal circles, each that pass
through
> the center of the other  to convince yourself).  Well hypothetically
pushing it
> into the Sun in  front, and then the Sun speeds it up and presto it gets
sent
> right back to where  it started from, and when Earth pulls it along then
> presto the extra distance  pulled outward from the Sun slows it down, and
the
> hypothetical deviation pull  from Earth is compensated and it falls back
into its
> place - a stable  equilibrium.
>
> If you like algebra & trig instead of my handwaving summary, it is done
here:
> _http://www-spof.gsfc.nasa.gov/stargaze/Slagrng2.htm_
> (http://www-spof.gsfc.nasa.gov/stargaze/Slagrng2.htm)
> and more elegantly here:
> _http://www-spof.gsfc.nasa.gov/stargaze/Slagrng3.htm_
> (http://www-spof.gsfc.nasa.gov/stargaze/Slagrng3.htm)
>
> Each object has the property, on the case of the Earth-Sun-object, that
they
> have an orbit of one Earth year, locked-step in a dance with Earth until a
> collision or huge comet/asteroid or even another star happens by...and 60
> degrees is a magic number because it creates the equilateral triangle of
> connections among the three masses - which is why all the planets could
have  these
> regardless of size, within reason.
>
> Of course, it you placed it  exactly at the point L4 or L5 itself and the
> Universe were just three bodies, it  would stand still.  But due to
influences of
> other planets and significant  asteroids, you can get little halo like
> oscillatory "orbits" around the frame of  reference of the L-point.  Just
like
> pushing a pendulum -it doesn't  stop...
>
> Pluto wouldn't be a likely candidate to have "Pluto Trojans" in  my
opinion
> since Neptune gravity rules out there, for example...but: did you  know
that
> Pluto makes two orbits for every three of Neptunes?  It's  reasoning just
like
> this....catching up loss and pushing back gain equilibrium  and that is
why
> those two planets will never collide.
>
> Saludos,  Doug
>
>
>
> ----- Original Message ----- 
> From: "Francis Graham"  <francisgraham at rocketmail.com>
> To:  <meteorite-list at meteoritecentral.com>
> Sent: Friday, June 24, 2005 6:21  PM
> Subject: Re: [meteorite-list] Earth Trojan asteroids
>
>
> > MOON  Trojan objects exist.
> >   They are the Kordylewski clouds, small  faint patches
> > of dust, at the L4 and L5 points of the Earth-Moon
> >  system (not Earth-sun system).  The Kordylewski clouds
> > have been  photographed, and have even been seen by the
> > naked eye under total dark  skies. They may be variable
> > in their mass and integrated visual  magnitude.
> >   Very little has been studied about them, very  little
> > is known about their possible variability, nobody has
> >  anything like a reflectance spectrum of the dust. They
> > remain the  closest things about which so little is
> > known. They could well be the  subject of study of any
> > of you who wish to make a contribution to  science.
> >   One thing is known: unless you are under skies  so
> > dark the Milky Way is a BRILLIANT band of light, and
> > the  Gegenschein is easy, and the zodiacal light is an
> > obvious swath, unless  you are under those kinds of
> > dark skies, you have NO hope of seeing the  Kordylewski
> > clouds.
> >
> > Francis  Graham
> >
> >
> >
> > --- MexicoDoug at aol.com  wrote:
> >
> > > Hola Rob,
> > >
> > > Wouldn't that be  <= 2/3's  (gibbous) phase = about
> > > 66% illumination, and  a
> > > maximum average sky angle of a  comfortable,high 60
> >  > degrees max observed angle
> > > (+/- the "oscillation")   ...  checking they're
> > > equilateral triangles, though
> >  > intuition might be  wrong?
> > > Saludos, Doug
> >  >
> > > En un mensaje con fecha 06/23/2005 6:21:15 PM
> > >  Mexico Daylight Time,
> > > ROBERT.D.MATSON at saic.com escribe:
> >  > Certainly astronomers  have tried, but small objects
> > > at  L4 and L5
> > > would be hard to see due to a  combination of  range
> > > (150 million
> > > km), poorer phase angle, and a  maximum sky
> > > elevation of perhaps 45
> > > degrees at  astronomical twilight -- lower when the
> > > sky is darker.
> > >  It would be an interesting exercise to compute the
> > > maximum   size
> > > an Earth Trojan could be and still have managed to
> >  > go  undetected.
> > >
> > > --Rob
> > >
>
>