Three Star model

I cleaned up my study last week and found a notebook that I did 30 years ago, attempting to reverse engineer the Tran system. I was trying to fit 3 stars and a planet to the conditions listed in “Janissaries”.
Hints given: Tran gets 90% the light & heat Earth gets, with an orbit around True Sun that is 2/3 longer than ours. True Sun is larger than Sol. Firestealer (the second star) gives 100 times the full Moon's light. Demon passes by every 600 years, bringing 20% of Earth's light & heat.
Tran's orbit around True Sun was easy. True Sun is about 1.2 times the Solar mass, with a luminosity of about 2 times our Sun and Tran is about 1.5 AU from True Sun.
Firestealer is a dim M4 or M5 with a mass of around 0.25 times solar mass and an absolute luminosity of 0.01. If Firestealer 's orbit is 5.2 AU, it varies between 100 & 300 Moon's luminosity.
The mass / Luminosity relation says that the luminosity goes up with the 3.5 to 4th power of the mass. Factors such as age and metallicity keep this from being a simple equation. If you have a star with double the mass of another, the luminosity will be 14 – 16 times the first star. When Demon comes by, you want the heat at Tran to go up 20%, but you don't want Demon's gravity to jerk Tran (or Firestealer) out of orbit.
With a spread sheet, one can tinker with the mass, and orbits to find a plausible balance. I like an A3 with a mass of 2.35 and luminosity of 28.3. With those values, Demon will give 20% of Earth's luminosity when it is 11.9 AU from Tran. A 600 year orbit, with semi major axis of 111 AU, and an eccentricity of 0.9 has a peri-astron of 11.1 AU.

Interesting features of this model:
At 300 years, Demon still provides about 300 lunar luminosity.

Before AU Luminosity
& after (rel Earth) Total >=
peak 11.1 23%
before 1.5 & after 12.3 19% 3 years > 19%
before 3.8 16.8 10% 7.6 years >10%
before 5.6 21.1 6% 11.2 years > 6%
before 20.8 53 1% 41.6 years > 1% ~ 4,500 lunar
At 180 years 200 0.07% (350+ Lunar luminosity) 360 years
At most distant; 211 AU, about 280 lunar luminosity, for 240 years.


Unfortunately, if Demon is in the plane with Firestealer, Demon gets close enough to Firestealer, that it would jerk it out of orbit. My last trick was to change the inclination of the Demon orbit so it's 90 degrees from the plane of Tran / Firestealer orbits. With this change, Demon passes the ecliptic while 21 AU from True Sun, and is above the other three stars it's closest, so the difference between gravity on Tran or Firestealer and True Sun is reduced.
A glaring problem with this model is that Demon is described as a red dwarf. In astronomy, any star still on the main sequence is a dwarf, but this is a blue white Demon, not a red one. Fortunately the description of the system was by Les, the star man, who is notorious for cryptic, evasive, and misleading answers.
I would not try to defend this system for long term stability. I fear it is too tight to have formed a planet with Firestealer so close. If any one can offer an improvement, I'd be interested.
Model summary:
Demon mass 2.36 lum 28.27 Axis 111 orbit 600 years ecc 0.9
True Sun – mass 1.18 lum 1.94
Firestealer mass 0.25 lum 0.0095 axis 5.2 orbit 9.9 years
Tran axis 1.47 lum 0.897 orbit 1.64 years

That was fun.

The brutal fact is that it's almost certain that the system as described is _not_ stable or anything close to it. Tran is simply too far out from True Sun to stay in its orbit, and probably too far out to have formed in the first place. I suspect that Demon's orbit is too eccentric for stability as well, but that isn't clear [and I admit to being too lazy to do the research needed to clarify it]. BTW, if you don't mind, I find your postulate of a 90° inclination for that orbit both unnecessary and implausible.

I don't think we can really blame Dr Pournelle for that, though. He probably didn't envisage it as stable anyway: for story purposes surviving for a few million years would have been good enough, and it wasn't until the late '90s that there was enough computing horsepower lying around for anybody to show that there could be stable planetary orbits in multi-star systems. Even the fact that the theories of the formation of multiple star systems current in 1980 were demonstrably wrong didn't become evident until 1992. I have no idea if he ever commented on it, but I would bet that if he mapped it out he envisaged Tran and its primary having been around as a system for the 2-4 billion years the ecology suggests, while the other 2 stars are recent, in cosmic terms, interlopers. With the whole schemozzle due to fly apart again in fairly short order.

Lego2Gpa wrote:I cleaned up my study last week and found a notebook that I did 30 years ago, attempting to reverse engineer the Tran system. I was trying to fit 3 stars and a planet to the conditions listed in “Janissaries”.
Hints given: Tran gets 90% the light & heat Earth gets, with an orbit around True Sun that is 2/3 longer than ours. True Sun is larger than Sol. Firestealer (the second star) gives 100 times the full Moon's light. Demon passes by every 600 years, bringing 20% of Earth's light & heat.
Tran's orbit around True Sun was easy. True Sun is about 1.2 times the Solar mass, with a luminosity of about 2 times our Sun and Tran is about 1.5 AU from True Sun.
Firestealer is a dim M4 or M5 with a mass of around 0.25 times solar mass and an absolute luminosity of 0.01. If Firestealer 's orbit is 5.2 AU, it varies between 100 & 300 Moon's luminosity.
The mass / Luminosity relation says that the luminosity goes up with the 3.5 to 4th power of the mass. Factors such as age and metallicity keep this from being a simple equation. If you have a star with double the mass of another, the luminosity will be 14 – 16 times the first star. When Demon comes by, you want the heat at Tran to go up 20%, but you don't want Demon's gravity to jerk Tran (or Firestealer) out of orbit.
With a spread sheet, one can tinker with the mass, and orbits to find a plausible balance. I like an A3 with a mass of 2.35 and luminosity of 28.3. With those values, Demon will give 20% of Earth's luminosity when it is 11.9 AU from Tran. A 600 year orbit, with semi major axis of 111 AU, and an eccentricity of 0.9 has a peri-astron of 11.1 AU.

Interesting features of this model:
At 300 years, Demon still provides about 300 lunar luminosity.

Before AU Luminosity
& after (rel Earth) Total >=
peak 11.1 23%
before 1.5 & after 12.3 19% 3 years > 19%
before 3.8 16.8 10% 7.6 years >10%
before 5.6 21.1 6% 11.2 years > 6%
before 20.8 53 1% 41.6 years > 1% ~ 4,500 lunar
At 180 years 200 0.07% (350+ Lunar luminosity) 360 years
At most distant; 211 AU, about 280 lunar luminosity, for 240 years.


Unfortunately, if Demon is in the plane with Firestealer, Demon gets close enough to Firestealer, that it would jerk it out of orbit. My last trick was to change the inclination of the Demon orbit so it's 90 degrees from the plane of Tran / Firestealer orbits. With this change, Demon passes the ecliptic while 21 AU from True Sun, and is above the other three stars it's closest, so the difference between gravity on Tran or Firestealer and True Sun is reduced.
A glaring problem with this model is that Demon is described as a red dwarf. In astronomy, any star still on the main sequence is a dwarf, but this is a blue white Demon, not a red one. Fortunately the description of the system was by Les, the star man, who is notorious for cryptic, evasive, and misleading answers.
I would not try to defend this system for long term stability. I fear it is too tight to have formed a planet with Firestealer so close. If any one can offer an improvement, I'd be interested.
Model summary:
Demon mass 2.36 lum 28.27 Axis 111 orbit 600 years ecc 0.9
True Sun – mass 1.18 lum 1.94
Firestealer mass 0.25 lum 0.0095 axis 5.2 orbit 9.9 years
Tran axis 1.47 lum 0.897 orbit 1.64 years

I don't blame Dr. Pournelle, he's got a good story. I don't think he desk checked his model. Les tells the story as Dr. Pournelle saw it. My offer to blame it on Les was mostly in jest.
“postulate of 90 inclination unnecessary”
If the orbits of Demon and Firestealer are in the same plane, then at peri-astron Demon could be 6 AU from Firestealer (Tran is 5.2 AU), so Firestealer wouldn't stay. It may survive once, if the passage is in sync. I guess we could claim the 600 year orbit of Demon is a multiple of the 9.92 year orbit of Firestealer, and always keeps Firestealer away from Demon (hiding behind True Sun so to speak.)
It takes Demon 11 years to move from 90 degrees relative to True Sun, past peri-astron, to 90 degrees going out. At 90 degrees, Demon is 21 AU away from True Sun, I'd thought Firestealer couldn't out run Demon during that passage.
“Recent interlopers”
My sense is that capture of a passing star is difficult, capture of two exceeded my imagination. How would you script it? Firestealer and Demon were a binary? At encounter with True Sun they exchanged momentum and morphed into a triple system?
Thanks

That's what I meant when I said that I was pretty sure Demon's orbit was too eccentric for the system to be stable - I just didn't run the numbers the way you have.

The reason I say that the 3 stars have to be co-planar is the flip side of why I was guessing that Jerry may have viewed one or both the other stars as recent arrivals and was cool with the whole thing being unstable on a scale of megayears: when he wrote, the prevailing view was that multiple star systems were the product of captures and more complex exchanges. In the early nineties it was shown that they are multiple ab initio, and therefore formed from one dense core - with the angular momentum of the core distributed between them during fragmentation. For 3 or more stars the core has to be an oblate spheroid, verging on a disk, and that dictates co-planarity or something close to it. And also dictates that the system as described just doesn't work. Jerry had no way of checking that, since it wasn't until sometime in the late eighties or nineties that the orbital-mechanical calculations disproving interaction/capture scenarios could be run in an affordable amount of time. It is certainly possible that post-formation encounters could skew the orbital plane of the most distant member - but I don't think it could be enough to get the inclination shift you're looking for without just disrupting the system. As it is, the most common outcome for evolving trinary systems seems to be the ejection of the lowest mass member, leaving a binary. Stable trinaries have pretty circular orbits, I believe.

The unnecessary part comes from the fact that you simply can't get a red dwarf close enough to Tran to produce the required increase in irradiance without the whole thing flying apart. Not even an M0V dwarf has more than ~2% of the luminosity of Tran's primary, and you can't get it close enough on a stable orbit, regardless of inclination, to add 20% to the stellar constant. So either Les lied or didn't pay enough attention in astro class to understand the definitions, and Demon is at least luminosity class III - and the most massive member of the system. Which means that it can stay, and must, stay further out and can be on the same plane. It probably also means that it contributes a fair share of Tran's heat budget throughout its orbit.

I don't know that there's any capture scenario that works [actually, I'm pretty confident that none do], but if I had to go that route I think I'd postulate two binaries, with the fourth star ejected completely from the final system. That's a _really_ complicated dance, no idea who the original partners might have been.

Lego2Gpa wrote:I don't blame Dr. Pournelle, he's got a good story. I don't think he desk checked his model. Les tells the story as Dr. Pournelle saw it. My offer to blame it on Les was mostly in jest.
“postulate of 90 inclination unnecessary”
If the orbits of Demon and Firestealer are in the same plane, then at peri-astron Demon could be 6 AU from Firestealer (Tran is 5.2 AU), so Firestealer wouldn't stay. It may survive once, if the passage is in sync. I guess we could claim the 600 year orbit of Demon is a multiple of the 9.92 year orbit of Firestealer, and always keeps Firestealer away from Demon (hiding behind True Sun so to speak.)
It takes Demon 11 years to move from 90 degrees relative to True Sun, past peri-astron, to 90 degrees going out. At 90 degrees, Demon is 21 AU away from True Sun, I'd thought Firestealer couldn't out run Demon during that passage.
“Recent interlopers”
My sense is that capture of a passing star is difficult, capture of two exceeded my imagination. How would you script it? Firestealer and Demon were a binary? At encounter with True Sun they exchanged momentum and morphed into a triple system?
Thanks

This analysis is beyond my expertise, perhaps even with the appropriate software support. However; this is one of the details that I am eager to accept in order to enjoy the story. A variable star would be more plausible.

This being acknowledged, while Pournelle and Niven are hard Sci Fi writers, they were not averse to taking a few liberties with the laws of physics for dramatic purposes. A little math reveals that the light sail in THE MOTE IN GODS EYE would not have required a massive battery of launching lasers to boost it up to velocity. The fusion powered photon drive on MacArthur could have boosted it up to cruise velocity in only few weeks. Also, a fusion powered photon drive would have only 1/20 th the Specific Impulse of a fusion rocket.