[meteorite-list] Earth Trojan asteroids

From: Sterling K. Webb <kelly_at_meteoritecentral.com>
Date: Fri Jun 24 05:32:57 2005
Message-ID: <42BBD323.3DFC0C9D_at_bhil.com>

Hi,

    Yes, phase would be about 2/3rds if it was spherical, but small bodies rarely
are, so that value could be highly variable. The distance would be just one AU
(149,597,870 kilometers). Sky angle roughly 60 degrees up from the horizon, with
the proviso that you are searching for a point located along the Earth's orbital
path, not an angular position.
    With the biggest telescopes and darkest skies, the sky background itself (used
to be) about 24-25th magnitude, Maybe that has been pushed back by the amazing
complexity of light detectors in the last few decades; don't know. For a big
telescope based in space, the limiting magnitude is about 32!
    Naturally, you search the trailing Trojan point after sunset and the leading
Trojan point before dawn. No choice there.
    Instead of calculating a telescope's theoretical reach, just examine a list of
a given telescope's discoveries of NEA's by size and the distance at which they
were detected, and a good empirical measure of they can be expected to do should
fall out of the data.
    One kilometer NEA objects are discovered at about magnitude 18 consistently
enough for magnitude to be used as a first scale to estimate the size of newly
detected bodies. While many telescopes used to find NEA's have limiting
magnitudes of 20 or 22, most discoveries are made around magnitude 18.
    Absolute magnitude is defined as the brightness when an object is seen at a
distance of one AU, so in our case the absolute magnitude of the object is the
same as our hopefully observed or measured visual magnitude. Isn't that
convenient?
    Here's a table that converts absolute magnitude to diameter for NEA object
albedo ranges, with all that nasty work already done for us:
<http://neo.jpl.nasa.gov/glossary/h.html>
    Here's another:
<http://cfa-www.harvard.edu/iau/lists/Sizes.html>

Magnitude 15.0 3 km - 6 km
Magnitude 16.0 2 km - 4 km
Magnitude 17.0 1 km - 2 km
Magnitude 18.0 670 m - 1500 m
Magnitude 19.0 420 m - 940 m
Magnitude 20.0 270 m - 590 m
Magnitude 21.0 170 m - 380 m
Magnitude 22.0 110 m - 240 m
Magnitude 23.0 65 m - 150 m
Magnitude 24.0 40 m - 95 m

    The number of 18th magnitude objects in the night sky is, well, astronomical!
(Pardon the little joke.) We have not found all the minor bodies down to
magnitude 18 (or 17 or 16...) yet. The estimate is that there are between
1,000,000 and 1,400,000 minor planets greater than 1000 meters in diameter. There
are plenty more to be discovered; they keep popping up!
    However, an Earth Trojan would have a more or less constant magnitude and be
among the easier objects to find of its size.


OTHER TROJANS:
   Back in the 1950's there was an astronomer who claimed to have observed diffuse
and spotty luminosities and dim objects at one of the Moon's Trojan points. But
fast response was not the style of the 1950's. After two months of debate, one
big telescope photographed that lunar Trojan point. Nothing there. Of course,
the Moon's Trojan points are very unstable, and a newly captured object would
quickly be perturbed again and be gone, so no surprise there. I think it was
probably dust.
    If Mars can have Trojans, even though it's closer to mighty Jupiter, and with
three intra-orbital planets tweaking the orbit, I don't seen why our good old
Earth can't have'em too. Unless the 8:5 near resonance with Venus would disturb
it. Anybody want to calculate that?! I don't see any raised hands here...
    Of course, we all know that Jupiter has Trojans (149 are known -- Jupiter has
more of everything!) and even Nepture has one (known).
    Hey! Hey! As far as that goes, did you realize that VENUSIAN TROJANS would
pass within 40,000,000 kilometers of the Earth! At this much closer distance,
they should be detectable. Perhaps the failure to detect them means there aren't
any...
    There are 4 (or 3 or 6) Mars Trojans; some are doubtful. There could be as
many as 50. These are mostly recent detections. I went to the minor planet pages
at Harvard to check the Martian Trojan List, and was confronted with a prose
notice that "in light of some recent ill-informed speculations on an
astronomy-related Yahoo group to which the MPC has been made aware, this list is
being removed for the forseeable future." Now, what the heck is that about?
    OK, from another excellent source: "Nearly 50 or so Mars Trojans larger than a
kilometer could exist. Trojan orbits near to Mars are very stable. Photometric and
spectroscopic studies of 3 of the Mars Trojans have not revealed any striking
similarities between them (5261 Eureka, 1998 VF31 and 1997 UJ7). There must
therefore not have been a common origin for these objects. 5261 Eureka and 1998
VF31 are however of a rare mineralogical type (Sr/A) not common in Belt N?1. 2003
OX7 (a = 1.5293 AU) is virtually on the same orbit as Mars, but is not a Mars
Trojan. It made its closest approach to Mars on 4 July 2003 at 0.045 AU, at least
for the period 1800-2200 (MPML 02/09/03)."

    Rob said, "It would be an interesting exercise to compute the maximum size an
Earth Trojan could be and still have managed to go undetected." Part of that
detection factor is luck and completeness, not completely computable. He was
right, though. It was interesting. But now it's four in the ayem. Time to sleep
under the light of the minor planets.


Sterling K. Webb
-----------------------------------------------
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 Fri 24 Jun 2005 05:32:19 AM PDT