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Old 03-11-2018, 06:10 PM   #1
AlexanderHowl
 
Join Date: Feb 2016
Default [Space] Trojan Objects

Within our Sol System, Jupiter and Neptune possess substantial asteroid belts in their Trojan Points while Saturn and Uranus seem to possess sparse asteroid belts. If we assume that every +1 RVM indicates a fourfold increase of the mass of the Main Belt and every -1 RVM indicates a fourfold decrease of the mass of the Main Belt (rounding to the nearest RVM), each of the Jupiter Trojans would have a RVM of -1 while each of the Neptunian Trojans would have a RVM of +1 (Saturn and Uranus probably possess Trojans with an RVM of -4 or -5). Since Trojan Points seem to exchange asteroids, each Trojan Point should possess equivalent mass. Mathematical models also suggest that gas giants in orbit around other stars might have Trojan Planets, which would be stable if they have a counterpart in their opposite Trojan Point, though we have no idea how common they might be.

In order to model objects in the Trojan Points, I would suggest adding the following modifications to the planetary creation rules in GURPS Space. When determining the contents of the Trojan Points of Gas Giants, roll 3d (no roll at 0.1 AU, -5 at 0.1 AU to 0.5 AU, -4 at 0.5 AU to 0.75 AU, -1 at 0.75 AU to 1.5 AU, +1 for Medium Gas Giants, and +2 for Large Gas Giants). On a result of '18' of higher, the Gas Giant possesses two Trojan Planets, which are created as if they were normal Terrestrial Planets, though they must have identical mass after any satellites are added. On a result of '17' or lower, the Trojan Points possess two Trojan Asteroid Belts, which are created as if they were normal Asteroid Belts.
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Old 03-12-2018, 02:22 PM   #2
Salabasama
 
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Default Re: [Space] Trojan Objects

So, all gas giants will always possess Trojan objects of some description?
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Old 03-12-2018, 03:23 PM   #3
AlexanderHowl
 
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Default Re: [Space] Trojan Objects

Well, as long as they are not within 0.1 AU of their primary, though I think that reflects our limited experiences. In the case of a Trojan Asteroid Belt, the mass can vary between 0.5 millionth's of the Earth (RVM -5) to 0.5 of the Earth (RVM +5), basically anything from a single asteroid with a diameter of 100 km to something resembling the asteroid belt from Empire Strikes Back. In the case of Terrestrial planets, the mass can vary from that of a dwarf planet like Ceres to that of a Mega Earth.

Last edited by AlexanderHowl; 03-12-2018 at 03:27 PM.
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Old 03-12-2018, 04:04 PM   #4
Anthony
 
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Default Re: [Space] Trojan Objects

The odds of orbital cruft being at the Trojan points approaches unity, but the stable area is fairly small so it may not be possible to accumulate enough mass for anything more than small asteroids. I'm not sure what 'exchanging asteroids' is about unless we're not actually dealing with Trojan objects, we're dealing with objects in a horseshoe orbit (in which case you would have a maximum of 1 such planet, not one per Trojan point).
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Old 03-12-2018, 04:45 PM   #5
AlexanderHowl
 
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Default Re: [Space] Trojan Objects

Some of the Jupiter Trojans change position over the course of tens of millions of years (probably temporarily becoming moonlets for Jupiter) and I would not be surprised if the Neptunian Trojans do the same thing (though over the course of hundreds of millions of years). I imagine that the process was much more common in the early Sol System, as the mass in the Trojan Points needs to balance out over time. The 'random crud' type of Trojan Asteroid Belts would be something like a RVM -5, one larger asteroid or a larger group of smaller asteroids (1,000 to 2,000 >1 km in diameter).

Another type of 'Asteroid Belt' to consider is stuff like NEA and Centaurs, both of which are temporary phenomena (with orbits that probably do not last more than 100 million years). There are probably enough NEA to make up an Asteroid Belt with a RVM of -5 and probably enough Centaurs to make up an Asteroid Belt of a RVM of -2. I think that it is possible to just give every system two intermediate asteroid belts (one inside the Snow Line and one outside the Snow Line), though they would only roll 1d+2 instead of 3d when rolling for RVM in GURPS Space. Such 'Asteroid Belts' would just be a convenient grouping for the random crud that crosses orbits and would give people an idea of the risk of asteroid impacts (an Earth like planet in system with an Interior Intermediate Asteroid Belt with a RVM of -1 would experience an average of 256 times more impacts than the Earth through its history).
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Old 03-12-2018, 04:51 PM   #6
Anthony
 
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Default Re: [Space] Trojan Objects

Quote:
Originally Posted by AlexanderHowl View Post
Some of the Jupiter Trojans change position over the course of tens of millions of years (probably temporarily becoming moonlets for Jupiter)
There isn't a sensible orbital solution for that. There is one for horseshoe orbits, but anything planet-sized will clear all other competing objects and will wind up being the only thing in the Trojans.
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Old 03-12-2018, 05:51 PM   #7
Salabasama
 
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Default Re: [Space] Trojan Objects

I think he's only speaking of asteroids transitioning.
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Old 03-12-2018, 10:34 PM   #8
AlexanderHowl
 
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Default Re: [Space] Trojan Objects

Yes, planets would probably be more stable.
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Old 03-12-2018, 10:46 PM   #9
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Default Re: [Space] Trojan Objects

Quote:
Originally Posted by AlexanderHowl View Post
In the case of Terrestrial planets, the mass can vary from that of a dwarf planet like Ceres to that of a Mega Earth.
Trojan orbits are not stable unless the smaller body is 1/25 the mass of the larger or less.
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Old 03-12-2018, 11:47 PM   #10
Anthony
 
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Default Re: [Space] Trojan Objects

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Originally Posted by thrash View Post
Trojan orbits are not stable unless the smaller body is 1/25 the mass of the larger or less.
That still allows a super-earth for a Jovian or Super-Jovian.
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