[Space] Multiple/Lots of Stars in one system

[jeff_wilson]

Originally Posted by Nemoricus

Okay, so this only refers to the zones for the planetary temperature, and has nothing to do with the valid orbital positions for planets?

Yes, sorry, I was thinking about the wrong sort of Zones. :(

[scc]

OK, somebody asked for numbers on the system, so here they are

The system is 3.7 billion years old with a F5V primary of 1.35 solar masses

Star	Mass	Type	Average Orbital Radius	Eccentricity Value	Minimum Separation	Maximum Separation
2	1.1	G0		550		.1				495			605
3	.95	G4		1000		.3				700			1300
4	.75	K2		300		.3				210			390
5	.85	G8		350		.3				245			455
6	.5	M0

The reason that the sixth star doesn't have any more details yet is that I wanted to get the whole thing working properly before I started on it

As for why there are so many distant companions, there's two predesigned habitable worlds in the system (+8 to the roll) and I see the -6 for sub-companions cancelling out the +6 Trianry stars get

[Nemoricus]

This star system is not likely be stable long term, given how severely the orbits of the subcompanion stars overlap. The orbits of 4 and 5 should be adjusted so that their maximum separation is less than 90 AU and preferably about thirty. Alternatively, move Star 3's orbit out by 500 to 1000 AU if you want to keep the subcompanions where they are.

Or take a third option and make a plot point of the instability of this star system. EDIT: More specifically, it would take active means for this configuration to be maintained. Who or what is responsible for this would be up to the GM.

Originally Posted by scc

As for why there are so many distant companions, there's two predesigned habitable worlds in the system (+8 to the roll) and I see the -6 for sub-companions cancelling out the +6 Trianry stars get

The +4 modifier for having a garden world should probably applied only once, as the description for the modifier only makes reference to 'a' garden world. As for the trinary modifier, it only applies to the second companion in a trinary system. As for the rest, see my earlier remarks in this thread.

[Agemegos]

Multiple systems are structured as strictly binary trees, with a star at each leaf, and a joint centre of mass at each branching. The orbital separations get a lot smaller, smaller by at least a factor of three, as you go down each layer. And all this is because it makes the orbital systems stable: a reasonably close approximations to a series of nested two-body problems—stable solutions to the three-body problem are unlikely to be struck by chance. Step 19 on page 105 will produce a simple such structure provided that that you do not forget the +6 modifier for a second companion and the -6 modifier to a sub-companion to rolls on the orbital separation table.

In any sub-system of such a system, a pair of stars jointly orbiting a third object create a single forbidden zone, not two. That is because their orbit around each other makes the less massive of them beat out the entire band from their close approach to the third body minus their separation from each other to their distant departure from the third body plus their separation. There is no possible orbit for a planet between their two separate orbits.

The GURPS Space 4th system generation sequence treats each pair of objects in orbit to be an ordered pair, with one main object and the other its companion or subcompanion. The main object is always at least equally massive to the companion, and objects orbiting the pair are generated as objects orbiting the main object. Consider the system as a binary tree with the main object on the left and the companion on the right. The most complicated system the sequence can produce is this:

NOT TO SCALE
         4
        / \
       /   5
      /   / \
     2   c   f
    / \
   /   \
  1     3
 / \   / \
a   d b   e

Letters represent stars. Numbers represent empty centres-of-mass.

That's a trinary system (a, b, c) where each star has a sub-companion. Space treats is as a having two companions b and c, where the separation a-b is rolled normally, and a-c is rolled with a +6 modifier. The separations a-d, b-e, and c-f are rolled with a -6 modifier on each roll. All per Step 19 on p.105

You proceed by starting with the bottom-left star, which is the main star of the system. Each node above it produces one forbidden zone. When you are generating the systems of companions and subcompanions you proceed only as far out as brings you to a forbidden zone that has already had objects outside it generated. Those were generated as orbiting the system on the left, but they are in joint orbit of the whole system you're working on now.

So when you are working on the main star of a system you calculate all its forbidden zones, and then you start at the usual place and work first inwards then outwards. When come to a forbidden zone you skip over it, and start again at its next edge inwards or outwards (as you were going) unless that puts you inside the inner limit or outside the outer limit of the system you are working on.

When you are working on a companion of subcompanion you do the same, except that when you go past a forbidden zone onto a link of the graph that has already been done you terminate.

The diagram above shows a star a with a near companion b and a distant companion c, where a has a sub-companion d, c has sub-companion e, and c has sub-companion f. It can't get more complicated than that. The order of steps implied by the sequence (in which a is treated as a main star with two companions, and all the rest as companions or subcompanions, is as follows.

• Start by generating a system around a, leaving forbidden zones for d, b, and c. The forbidden zones of b and c represent what are actually the forbidden zones of 3 and 5.
  
• Then do a system for d, but only inside the inner edge of the forbidden zone for a (this is probably trivial as being inside the inner limit.
  
• Then do b, leaving a forbidden zone for e. a creates a forbidden zone and you generate inside it but not outside it.
  
• Then do e. b creates a forbidden zone and you only do inside it. This is probably trivial.
  
• Then do c. a and f create forbidden zones. Generate both sides of the forbidden zone created by f (though inside this zone is probably inside the inner limit and therefore trivial), but only inside the forbidden zone created by a.
  
• Finally, do the system of f, but only inside the forbidden zone created by c.

In a computer program that treats this as on system rather than six, you might prefer a recursive depth-first approach.

[Agemegos]

Originally Posted by scc

I see the -6 for sub-companions cancelling out the +6 Trianry stars get

Incorrect. Those two modifiers are never applied to the same roll. And it is not a +6 modifier to trinary systems, it is a +6 roll to the second companion's orbit around a main start (actually around the centre-of-mass of the main star and its first companion).

You take a main star A with two companions, and you roll the orbit of the first companion B with no modifier and the second companion C with a +6. Then each star gets a sub-companion.

• The sub-companion of A is D. You roll D's orbit around A with a -6.
• The sub-companion of B is E. You roll E's orbit around B (not A) with a -6. B and E share an orbit around A-D while orbiting each other.
• The sub-companion of C is F. You roll F's orbit around C (not A) with a -6. C and F share an orbit around AB-CD while orbiting each other.

[scc]

Originally Posted by Nemoricus

This star system is not likely be stable long term, given how severely the orbits of the subcompanion stars overlap. The orbits of 4 and 5 should be adjusted so that their maximum separation is less than 90 AU and preferably about thirty. Alternatively, move Star 3's orbit out by 500 to 1000 AU if you want to keep the subcompanions where they are.

I thought as much, or at least something along those lines.

Originally Posted by Nemoricus

Or take a third option and make a plot point of the instability of this star system.

Was going to do something like that, a plot point was that Star 3 is going to be the closest it's going for a long time and Star 2 will very close to it at the time, perfect for a slowboat colony trip (Setting is TL 7)

Originally Posted by Nemoricus

The +4 modifier for having a garden world should probably applied only once, as the description for the modifier only makes reference to 'a' garden world. As for the trinary modifier, it only applies to the second companion in a trinary system. As for the rest, see my earlier remarks in this thread.

That +4 mod is very poorly worded, you could read it to be +4 * the total number of stars. And I want lots of Stars and thus planets in this system

[Agemegos]

Originally Posted by scc

That +4 mod is very poorly worded, you could read it to be +4 * the total number of stars.

I don't find it poorly worded. It is "+4 to each companion if a Garden world has been pre-generated for the system". Not +4 for each garden world.

I want lots of Stars and thus planets in this system

So write down what you want. The die rolls are for choosing things for you when you aren't sure what you want. If you know already what you want, cut out the middle man. Use GM fiat to over-rule the system rather than bending it out of shape.

[Agemegos]

Originally Posted by Nemoricus

I'm not sure that should be possible. Per the rules on page 105, a subcompanion is at a -6 penalty to its orbital separation roll, and as the maximum result on 3d6-6 is 12, the farthest a subcompanion can be is Wide. Since only Distant stars are eligible for the companion roll, a subcompanion may not have a subsubcompanion. The modifiers listed under the "Modifiers" heading are for companions, while the companion star of a compaion star is described as a subcompanion, so I don't think they apply here.

Correct in each respect.

There is a mention made of planets orbiting a binary pair, but there's no solid guidance on that and it gets quite complex as more stars get involved.

GURPS Space treats planets of a binary pair as planets of the main star in that pair orbiting beyond the outer edge of the forbidden zone created by the companion. That's what planets beyond the forbidden zone are. The guidance is rock solid, and it isn't even particularly complicated, except that combined luminosity ought to be used for temperature and this isn't included in the procedures.

Originally Posted by Nemoricus

This star system is not likely be stable long term, given how severely the orbits of the subcompanion stars overlap. The orbits of 4 and 5 should be adjusted so that their maximum separation is less than 90 AU and preferably about thirty. Alternatively, move Star 3's orbit out by 500 to 1000 AU if you want to keep the subcompanions where they are.

Or take a third option and make a plot point of the instability of this star system.

There is a problem with that: plots work on a scale of days to decades, orbital instabilities work out over a scale of centuries to millions of years, and habitable systems develop over a scale of billions of years. If any system has habitable planets in it then it must be at least billions of years too old to still have stars or even planets in unstable orbits.

Of course, there is nothing wrong with not caring about that. Just be aware that when you do that sort of thing and then ask SF fans for advice they are going to tell you about it.

The +4 modifier for having a garden world should probably applied only once, as the description for the modifier only makes reference to 'a' garden world. As for the trinary modifier, it only applies to the second companion in a trinary system. As for the rest, see my earlier remarks in this thread.

All correct.

[scc]

Originally Posted by Brett

There is a problem with that: plots work on a scale of days to decades, orbital instabilities work out over a scale of centuries to millions of years, and habitable systems develop over a scale of billions of years. If any system has habitable planets in it then it must be at least billions of years too old to still have stars or even planets in unstable orbits.

Of course to be realistic I have to figure out what ARE viable or semi-viable stable orbits of that sort, I suspect that it will be something to do with making the orbits resonate or based on some sort of ratio

[Agemegos]

Originally Posted by scc

Of course to be realistic I have to figure out what ARE viable or semi-viable stable orbits of that sort, I suspect that it will be something to do with making the orbits resonate or based on some sort of ratio

It's easy. The system has to be structured as a binary tree, with planets at the leaves. Each node in the tree has two orbiting objects (stars or lower nodes), and the [minimum] orbital separation of that orbit has to be at least three times the maximum, and preferrably at least four times the average, separation of the orbit of the nodes directly below it in the tree.

There are other solutions to the equations involving rosettes and so forth, but such systems are are never observed in Nature.