[meteorite-list] More on Trojan asteroids

From: Matson, Robert <ROBERT.D.MATSON_at_meteoritecentral.com>
Date: Sun Jun 26 16:45:05 2005
Message-ID: <BE076B8CCE4CFE4D9598230D888B2ADF07C7D2_at_0005-its-exs01.mail.saic.com>

Hi Sterling, Doug and List,

Back from a couple-day computer break and see I missed a flood of
Trojan asteroid exchanges. Will try to fill in a few holes:

On the subject of phase angles, I note some defensiveness on
Sterling's part which means he probably felt I was correcting
him when bringing up the subject. Wasn't my intent -- I brought
it up only because the magnitude equations are based on solar
phase angle and not illuminated fraction. His illuminated
fraction information was fine -- I just shifted gears to phase
angle in order to compute magnitude.

> And while an asteroid would dim by a factor of 2.512 to the
> .64th power from opposition to the Trojan position, since we
> don't have the foggiest notion what its albedo would be (except
> that we casually assume it to be like most NEA's or in their
> range), it is a result of very high precision and only slight
> accuracy.

Agreed. The absolute relationship between asteroid size and
magnitude isn't known; however, the ~relative~ brightness change
from 0-degree phase to 60-degree phase is what we're talking about,
and that relationship has been empirically studied for thousands
of minor planets. I don't happen to know what the spread on this
function looks like (how fuzzy), but I think it's safe to say
that the phase effect more than cancels the factor of 4 brightness
increase of moving the asteroid from 2 a.u. opposition to 1 a.u.
L4/5. (Can provide the equations off-list for those interested --
too technical for this forum.)

> I had a lot of fun writing an "arithmetic" program in BASIC which
> converted numerical imputs to $tring functions, then digit by digit
> performing the same grade school arithmetic every child learns,
> constructing the "answer" as $tring functions again, with callable
> subroutines for each (addition, subtraction, etc., even roots)
> arithmetical operation.

I did the same thing as a teenager -- first computing e to a thousand
decimal places, and then pi. (Pi is much more difficult -- a subject
for another thread, which should definitely move off-list).

An interesting comment about Jupiter Trojans that you've probably
noticed, but didn't comment on -- Sterling wrote:

> JUPITER TROJANS EAST a = 4.90 to 5.37 AU e < 0.30 and i < 40?
> Lagrangian point L4 of Jupiter:
>
> NUMBER KNOWN AS OF MAY 20, 2004: 525 ESTIMATED TOTAL: 1039

> JUPITER TROJANS WEST a = 4.96 to 5.36 AU e < 0.28 and i < 44?
> Lagrangian point L5 of Jupiter:
>
> NUMBER KNOWN AS OF MAY 20, 2004: 352 ESTIMATED TOTAL: 628

I'm not sure what the difference is between "number known" and
"estimated total" since the number known is certainly greater
than the estimated totals, but the point I want to make is that
the greater number of Trojans at L4 vs. L5 is not a statistical
fluke or measurement bias -- there really ARE more at L4. And
I don't think anyone knows why that should be.

> ... I can't recall the names of 1783 Trojan characters in the
> Iliad!

Despite the size of that tome, I believe you are quite correct.
Not to worry -- the 1783+ will never all be named. Only a fraction
of them have multi-opposition orbits at this time, and even a
smaller fraction have orbits sufficiently well-established for
the Trojan to receive a numerical designation (a prerequisite for
naming). Since each discoverer (where a "discoverer" could be an
instrument team like LINEAR or NEAT) can currently name only 12
minor planets per year by CSBN rules, it will take some time
before they run out of appropriate names.

Best,
Rob
Received on Sun 26 Jun 2005 04:44:57 PM PDT