Re: Asteroids - Reply

[some may thing this is drifting off-topic, but if you want to deal with
'real', as opposed to fake Hollywood asteroid fields, it helps to
understand
them  ;-)  ]

[earlier I wrote:]
>>> ...and I indicated some asteroids range out as far as 5.2 AU from
the sun;
>these asteroids are part of the Kirkwood Gap phenomenon, and are called
>Trojan Asteroids, something some of you may have heard of before, in
some
>dim faint distant memory from a basic astronomy class. <<
>
>To which Sturart replied:
>
>> I think there are Trojan point asteroids described in the
Niven/Pournelle
>"Mote" series.  So for us non-physics guys, what does this really mean?
<
>
 Where Phil then pops in with:
>
>I'm no physics expert, but my understanding of the Trojan point concept
is that
>it's a quirk of gravitation. If you have two large masses (does one
have to be
>much bigger than the other?) orbiting each other -- or, for simplicity,
let's
>consider one of them orbiting the other -- then points in the orbit 60
degrees
>ahead and behind the mass are gravitationally stable, i.e., another
mass (and
>this time I think it has to be much smaller than either of the first
two) located at
>one of those points will stay there and won't be pulled out of position
by gravity
>(of course, you do have to deal with gravitational effects from any
other bodies in
>the system, but they will hopefully be small).

Yep, you essentially got it right. The Trojan points are indeed 60
degrees
ahead/behind Jupiter's orbit, and are stable areas in and of themselves.
This is one aspect of the Kirkwood gaps. The Kirkwood Gap phenomenon
takes
place where you have resonances with Jupiter's (or any other
sufficiently
large-massed body) orbit. These resonances are simple fractions of
Jupiter's
orbit (eg, 3/5, 1/2, 2/3, 1/1, etc). The further away (closer 'in' the
orbital
plane) from Jupiter's orbit, the more the gaps are *gaps* and cause the
asteroids to form orbital 'rings' (these gaps would correspond to
orbital
ratios with Jupiter of 3:1, 5:2, 7:3, 2:1, and 5:3). The closer you get
to
Jupiter's orbit the gaps go from being rings to clumps or groups (these
occur
at 3:2, 4:3, and 1:1, where the 1:1 groups are the Trojans).

Now...did that make any sense, or did I just confuse everybody?

>Which makes the Trojan points a really good place to put a space
station or an
>O'Neill colony. It also means that, given enough time, asteroids that
drift through
>these points may collect there -- which can mean that there's a ready
supply of
>raw material to make that O'Neill colony! Also that you need a good
asteroid
>defence for when the next Trojan-wannabe drifts through...

Welllll, yeah, it's a stable spot in space in the overall scheme of
things,
but within that little area there is a lot of oscillation. You'll need
to
be set for fending off constant potential collisions. This has been a
concern
for one of the possible NGST (Next Generation Space Telescope) orbits.
Some
are wanting to put it at one of the Lagrange points, but others are
concerned
about some of the debris that may have collected there colliding into
the
telescope (no, I don't know how they deal with this with the TDRSS
satellites,
but I do know they have some limited capability to manually move those
guys)

>>> (ps: knowing the above, I did run a PBeM FT game last year that took
place
>in a hellaciously dense asteroid field -- 30 or so asteroids in a 4900
square unit
>area. The purpose was mainly for terrain to force the players to
maneuver about
>the place, rather than fight in open space, but in reality this field
would not exist,
>unless it was from something recently broken up. I will likely create
fields just
>as dense in the future for gaming purposes, but not to reflect reality
any --
>unless you want to call it an asteroid 'clump', which might really
occur in very
>localized areas, but again, 30 was a heck of a dense field) <<
>
>So you were fighting in and around a Trojan point! They're prime
locations for
>battles, because they're where raw material collects.

Works for me.  :-)

>I hope no-one is going to tear my "explanation" apart, but whether they
do or
>not, could some of the _real_ astrophysics buffs answer these:
>
>-- Are the Trojans the same as the L-4 and L-5 Lagrange points?

Essentially, yes (though I'd have to go look up exactly where the L-4
and
L-5 points are in orbit wrt each other).

>-- Are points 120 degrees ahead and behind the orbiting mass stable? (I
know
>180 is!)

They are, but I don't *think* quite as stable as 60 degrees
ahead/behind.

>I should know this stuff! I did once, but, like Rabbit, I've forgotten.
<g>

S'okay. I knew it all once, too, long ago, then my job has taken me more
into
running a spacecraft than keeping up with things. I've been digging
through all
my books (and the library upstairs) as time has allowed me to refresh
myself on
this stuff again. Some I actually remember still...

Mk
------------------------------------------------------------------------
-
All that is gold does not glitter,
     all those who wander are not lost.

http://www.bcpl.lib.md.us/~indy/index.html