[meteorite-list] There IS an Earth Trojan Asteroid (probably)!

[Ron Baalke]

> 
> Hi, Ron, List,
> 
>     I chose the single word "share" from the following early
> introductory paragraph:
>     "The near-Earth asteroid 3753 Cruithne is in an unusual orbit about
> that of the Earth, one which is known in the lingo of celestial
> mechanics as being co-orbital with the Earth (meaning it SHARES [my
> emphasis] the Earth's orbit with it) and, more particularly, as being of
> the "horseshoe" type. 

'Share' is a bad choice of word, since Cruithne does not share an orbit with Earth.
By applying the same co-rotating frame logic on the Sun and Earth, you can
then claim that the Sun and Earth share the same orbit.  While Cruithne
is in 1:1 resonance with Earth, and that is interesting, it does not mean
they share an orbit.  When this  news about this resonance first 
came out, the co-rotating diagrams were used to make it look like it was
Earth's second moon (it is not, Cruithne does not orbit the Earth), and
the fact remains that Cruithne is in distint and separate orbit around the Sun,
different from the Earth.   Also, Cruithne is not an Earth trojan.

Ron Baalke





Horseshoe orbits are named because of their shape
> in a reference frame which corotates with their accompanying planet, and
> have been known theoretically for many years. A corotating frame just
> means one in which the viewer orbits along with one of the planets, in
> this case the Earth. It is analogous to imagining oneself floating above
> the north pole of the Earth as our planet goes around its orbit, and
> watching the path the asteroid from this vantage point. By looking at
> the asteroid in this way its unusual behaviour becomes apparent: it is
> much more difficult to distinguish when viewed in a non-rotating frame."
> 
>     When Cruithne is viewed in the ROTATING frame of reference:
>     "Cruithne is on an spiraling horseshoe orbit... but its behaviour is
> even stranger. First, it is an even more tightly-wound spiral, with
> kidney-bean shaped loops. Secondly, one part of the horseshoe actually
> overlaps the position of the Earth when viewed from above. A series of
> four frames (to be read left to right) showing a time lapse of
> Cruithne's horseshoe is shown below. Note again that Cruithne's
> horseshoe is composed of tightly wound kidney-bean shaped spirals which
> are almost impossible to distinguish individually in the picture.
> Remember, there are two types of motion going on: 1) every year, the
> asteroid traces out a kidney bean, 2) over time, this kidney bean drifts
> along the Earth's orbit, tracing out a spiral which, when complete
> (after 385 yrs) fills in an overlapping horseshoe."
>     They do not claim the Cruithne "orbits" the Earth in the direct
> sense, and indeed their multi-colored orbital diagrams show the same
> elements of eccentricity and inclination, etc. (see below) as the NASA
> page you cite.  Unfortunately, my computer's MicroSoft mind has
> difficulties with  JAVA applets for some reason, and won't execute the
> one on the page you cite, so I can not get it to visualize and therefore
> cannot compare the two directly.
>     Even Wiegert and company regard Cruithne as a very strange duck.
> They have an MPEG movie showing it in the heliocentric frame of
> reference, about which they say: "Note the highly eccentric and
> inclined... orbit of Cruithne, and the lack of obvious connection to the
> Earth, except that they both go around the Sun in about the same amount
> of time."
>     This is then followed by another MPEG movie in the rotating
> Earth-centric frame of reference: "After a few orbits, the lines of
> sight connecting Cruithne to the Earth are drawn in green. Note that,
> though they both go around the Sun, both are always on the same side of
> the Sun. Then, the Earth will begin "picking up" the lines of sight,
> constructing the apparent path of Cruithne as seen from the rotating
> Earth. Their motions are such that Cruithne appears to perform a
> kidney-shaped loop around the Earth. Though the asteroid thus appears to
> orbit the Earth, this is a result of the frame of reference we are
> using. Also note that the presence of the Earth at the centre of the
> kidney is simply a result of their mutual synchronization: the Earth is
> lined up with the asteroid and Sun when the asteroid is at perihelion
> (its closest approach to the Sun)... Because the asteroid and the Earth
> do not go around in exactly the same amount of time (the asteroid
> currently goes around slightly faster than the Earth), the position of
> the kidney-shaped loop relative to the Earth varies over time. If the
> asteroid and the Earth were not in a special arrangement, the Earth
> would face potential danger as the asteroid drifted inexorably towards
> our planet. However, in their current relationship, the kidney's
> direction of drift is reversed every time it approaches the Earth."
>     See, I said it was a COMPLICATED horseshoe.
>     The webpage which I cited is also cited on the the Lunar and
> Planetary Laboratory asteroids page in a positive sense (as in, look at
> this; it's truly weird.):
> <http://seds.lpl.arizona.edu/nineplanets/nineplanets/asteroids.html>
>     Further, NASA's own site <http://impact.arc.nasa.gov/> on the NeoDys
> Object List points to the same source: "The motion of this object is
> quite interesting. See:
> <http://www.asteroid.yorku.ca/~wiegert/>."
>     However, this is a broken link, since Wiegert left York and went to
> UWO, but it was the same page.
>     If there are those who disagree with this very complicated dynamic
> argument, I couldn't find them.  Maybe you ran into one, I dunno.  I
> doubt I could judge such a dispute if there was one, anyway.  Dueling
> ephemerides at twenty paces?
>     Holy Moly, Ron!  All I did was use the word "SHARE"!!  They are not
> using the word "share" to mean a Trojan or a Earth centered orbit,
> either.  It is a helocentric orbit that oscillates back and forth in a
> 385 year pattern, and that oscillation is dominated by the Earth's
> gravity.  Thus, in this very special way, it is "tied" to the Earth.
>     OK?
> 
> 
> Sterling K. Webb
> -----------------------------------------------------------------------------
> 
> Ron Baalke wrote:
> 
> > >
> > > 3753 Cruithne and several other asteroids share the Earth's
> > > orbit but are not Trojans, but complicated "horseshoes":
> > > <http://www.astro.uwo.ca/~wiegert/3753/3753.html>
> > >
> >
> > 3753 Cruithne does not share Earth's orbit:
> >
> > http://neo.jpl.nasa.gov/cgi-bin/db_shm?sstr=3753
> >
> > Cruithne's orbit crosses the orbits of Venus and Mars, and comes near
> > the orbit of Mercury.  Earth's orbit is not like that at all. Cruithne
> > and Earth do not share an orbit, and they are in separate orbits
> > around the Sun.
> > Cruithe's orbital period is 0.9966 years, which means it is very close
> > to Earth's orbital period.  Cruithne is also not
> > a satellite of Earth like some people have claimed. Cruithne
> > orbits the Sun, not the Earth.
> >
> > Ron Baalke
> >
> 
> Orbital elements:
>     "The following elements are for the epoch JD 2450500.5 (Feb 21 1997)
> and relative to the equinox J2000.0. Semimajor axis = 0.99778030
> astronomical units, eccentricity 0.51478431, inclination i=19.812285
> degrees, longitude of the ascending node = 126.373212 degrees, argument
> of perihelion = 43.640637 degrees, mean anomaly = 40.048932 degrees, and
> epoch of perihelion passage = 1997 Jan 11.50 UT = JD 2450460.00. These
> elements are derived from the Asteroid Orbital Elements Database
> maintained by Ted Bowell at Lowell Observatory. You can also find them
> at Minor Planet Center's Near-Earth Object page."
> 
> 
>