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Asteroid belts are rare???

They would be Trojan (or Lagrangian) objects. ;)

Those at Jupiters L4 & L5 (IIRC, believed to be about as abundant in number as those of the asteroid belt) are called Trojan Asteroids.

We have at least one Trojan with us (L4, IIRC) - such have also been found for Mars and Neptune and probably have or will for others.

A Trojan moon is one that orbits a planet at a trojan point of a larger moon (still orbits the planet, not the moon) ... one could also have Trojan planets like around a gas giant...

Co-orbital planets I don't think have actually been found (one false?) - but they exist in theory. Minor planets and interchanging orbits could be added to the list (swap orbits, generally around a Lagrangian point).

Basically - Traveller to date probably has no support for these types of objects! (T5?)
 
Fixed.

I doubt the belt would remain as a belt. Most of it should be gathered by the GG - they're big enough to clear their orbits, mind you... What isn't cleared winds up in trojan points.

(Keeping in mind that, if they don't sweep their orbits clean, they aren't planets according to the IAU. )

Right - Planets clean their orbits. But they don't have to do so instantly, and we don't really know how long it took some of those inner orbit gas giants to spiral their way in.

Can we be sure that they didn't pass through fast enough that they cleared only half, or 90%, or 99% of the belt? Since there's no official definition of a minimum belt density I think some belts would still be there in Traveller terms. I don't think it would be many of them, therefore asteroid belts may be rare. It's just that "we haven't seen them" proves only that they're low mass.

Say the Gas Giant starts in orbit 6 (like Jupiter) and it's now in Orbit 0. How long did it take to move?
 
Certainly not. technically, they're moons with orbital distances measured in AU...

Probably not in Traveller terms:

"Patinir (Aramis 0807 C-000632-9): This system is dominated by a large gas giant in the life zone. Although an extensive asteroid belt is the system's primary source of mineral wealth, over half the population inhabits two self-contained space colonies in the gas giants Trojan clusters.

The government of Patinir is a select board of directors controlled by the company owners; it's authority effectively does not extend outside the Trojan points." [CT Library Date - Beltstrike - Bowman System Reference book p 10].

In other word when they've described a government which controls only the trojan points as the mainworld and they've called it a belt. I think that in Traveller an asteroid belt is defined as a bunch of size 0, atmosphere 0 objects, without worrying too much about their specific orbits.

This fits with the fact that a mainworld may really be a moon. It's not what you orbit that makes you the mainworld, it's if you're the most important/populous. Do you really think that when the Scout service decides that the chunks of rock/ice/metal/etc with the most people are the mainworld they're going to say "Oh, we can't call it a belt because it's really a Trojan point."? The Scout Service aren't astronomers and neither are the vast majority of the people on this site. Let's stick with functional definitions, as the Imperium appears to.
 
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Main worlds would not change - their size is their size.

Its only in the detailed system of LBB 6 that 'trojan' status would show up.

Trojan objects are co-orbital - so trojans are just another (usually smaller) 'world' in Traveller that would have the same orbit number (LBB 6).

Asteroid belts would be size 0 with no co-orbital defined. Or they would be Trojan belts around large planets.

Unfortunately, LBB 6, lacks any code for artificial world (colony) and any way to differentiate clusters of asteroid/minor planets*. So, size 0 is the dumping ground - and there would be no good way to include a small planet (ala Ceres) in a belt. A preferred solution would be something specific for belts. But a consistent solution (and not using B) would be to just list them like moons under the belt, with an orbit of 0.

[*Ignoring the IAU's BS Pluto/minor planet fiasco. If a stellar body shapes itself, and directly orbits or shares an orbit around a system center of mass, then its a planet in my book. <shrug>]

Some interesting links:
http://www.dtm.ciw.edu/users/sheppard/satellites/
http://www.dtm.ciw.edu/users/sheppard/satellites/trojan.html
http://www.dtm.ciw.edu/users/sheppard/trojans/

Hmmm... change 'belt' in Size 0 to 'field'. We call the asteroid belt between Mars and Jupiter the Main Belt, I suppose, because of the Kuiper belt. Along with Trojan belts, and the scattered disk, all these clusterings of objects in a shared orbital region (belt/disk/clouds) would be an example of an 'asteroid field'.
 
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