[meteorite-list] Earth Trojan asteroids

[MexicoDoug at aol.com]

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
> >