From: Henry Spencer <henry@zoo.toronto.edu>
Newsgroups: sci.physics,sci.space.science,sci.astro
Subject: Re: Questions About Sun-Earth Libration Points
Date: Wed, 24 Apr 1996 15:02:35 GMT

In article <john.lyons-1804960840120001@lyonsmac.gsfc.nasa.gov> john.lyons@gsfc.nasa.gov (JWLyons) writes:
>The Sun-Jupiter L4 and L5 points are known to be stable because the Trojan
>asteroids have been observed to stay there. What about the Sun-Earth L4
>and L5 points? Would they be less stable because of the relative proximity
>of Earth to the Sun? Or because of the smaller mass of Earth relative to
>the Sun? Have any bodies been observed to cluster around these points? ...

The proximity does not matter, nor does the smaller mass of the Earth
relative to the Sun.  (Indeed, the Trojan points become unstable if the
planet in question is too *big* relative to the Sun -- for example, they
are unstable in most two-star systems.)

What does matter is the smaller mass of Earth relative to perturbing forces
(notably Jupiter!).  Jupiter's large collection of Trojan asteroids is
partly because it's close to the asteroid belt, and partly because its
influence is strong enough to dominate most perturbing forces.

However, it is definitely possible to have "Earth Trojans".  It's harder
than you might think to find them, because particularly for a small planet
like Earth, the Trojan points are not sharply-defined points but long
comma-shaped regions extending along the orbit.  Earth Trojans could
wander a long way from the Trojan points proper.  No Earth Trojans are
currently known, but one Mars Trojan was found a few years ago.
-- 
Americans proved to be more bureaucratic           |       Henry Spencer
than I ever thought.  --Valery Ryumin, RKK Energia |   henry@zoo.toronto.edu

Newsgroups: sci.space.policy
From: henry@spsystems.net (Henry Spencer)
Subject: Re: Economically important planets/moons/asteroids?
Date: Wed, 7 Jul 1999 15:03:18 GMT

In article <7lug82$hu4@peabody.colorado.edu>,
Frank Crary <fcrary@rintintin.colorado.edu> wrote:
>...be very surprising if the Earth did not have trojan asteroids.
>Unfortunately, they would be very hard to discover, and that may
>explain why we haven't found any. By definition, the L4 and L5
>points are 60 deg away from the Sun, as seen from the Earth...
>Those are pretty bad viewing conditions...

Also, a "Trojan" asteroid isn't locked rigidly at a point 60deg away from
the planet involved.  Even Jupiter's Trojans wander 20deg or so, and for a
smaller planet like Earth or Mars, it's much worse.  In fact, it's quite
possible for a loosely-bound "Trojan" to wander from one Trojan point to
the other and back, the long way.  So to find them, you have to search a
240deg arc of the orbit... and in Earth's case, viewing conditions for
most of that arc range from poor to impossible.  Even without that
problem, there is so much space to search that a small object is very hard
to find; the one or two Mars Trojans now known were found by accident.
--
The good old days                   |  Henry Spencer   henry@spsystems.net
weren't.                            |      (aka henry@zoo.toronto.edu)