[meteorite-list] Earth Trojan asteroids

From: MexicoDoug_at_aol.com <MexicoDoug_at_meteoritecentral.com>
Date: Sat Jun 25 15:45:10 2005
Message-ID: <54.46fb31d1.2fef0e3e_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
> >
 
Received on Sat 25 Jun 2005 03:45:02 PM PDT