Worldbuilding Questions

[Pedant]

Just as a quick one to start with: in S-type binary systems, when the secondary gets nearer to the primary (and the planet), does it mean that the planet heats up more because of the two stars? Is it additive or exponential, do you think?

[gestaltist]

For an S-type system to be habitable, the secondary star would have to be very far away. The added heat is the least of your concerns. It would also disrupt the orbit of your planet. Unless you find some research stating otherwise, I'd go for your secondary being far away enough to have a similar role to Mars or Venus on our Earth - i.e., a mobile, visible (but not all-too-large) celestial object.

[Pedant]

For an S-type system to be habitable, the secondary star would have to be very far away. The added heat is the least of your concerns. It would also disrupt the orbit of your planet. Unless you find some research stating otherwise, I'd go for your secondary being far away enough to have a similar role to Mars or Venus on our Earth - i.e., a mobile, visible (but not all-too-large) celestial object.

Hmm, fair...to be honest, I was trying to base my system off 36 Ophiuchi, both stars of which Zompist said would have a habitable zone of around 0.5 to 1.0 AU, while the stars themselves range in distance between 7 and 169 AU. (I was planning on those numbers being slightly more average for Surya and Mitra--temporary names--say around 12 and 73 AU.)
Still, that does bring up the question of angular diameter. Does anyone have any ideas? I can't seem to get my head around the equations...

[mèþru]

I think Artifexian did a relevant episode at some point. If not, one of his episodes on complex star systems might still have useful links.

[zompist]

Still, that does bring up the question of angular diameter. Does anyone have any ideas? I can't seem to get my head around the equations...

This bit is easy. Suppose the star is about the size of the sun. (It's actually smaller, but not by that much.) Its diameter d is then 1.391×10^6 km. The circumference of a circle of 7 AU is D = 43.9 AU or 6.58×10^9 km. So the angular diameter is d/D = 0.0002114. Multiply by 360 to get .076 degrees; multiply by 60 to get 4.57 arc-minutes. (Cross-check at Wolfram Alpha)

By comparison the Sun is 30 arc-minutes, while Jupiter at its closest to us (4 AU) is less than 1 arc-minute.

[Zaarin]

Wikipedia is unhelpful in not stating the separation of 36 Ophiuchi A and B, but it does mention that an orbit of greater than 1.5 AU would be unstable. So you might get away with 0.5 to 1.0 AU, but I wouldn't want to guarantee that long term. On the plus side, 36 Ophiuchi C is certainly far enough away from A + B to host a stable planetary system.

[Pedant]

Wikipedia is unhelpful in not stating the separation of 36 Ophiuchi A and B, but it does mention that an orbit of greater than 1.5 AU would be unstable. So you might get away with 0.5 to 1.0 AU, but I wouldn't want to guarantee that long term. On the plus side, 36 Ophiuchi C is certainly far enough away from A + B to host a stable planetary system.

Thanks very much, Zompist and Zaarin!
Also, adjustments made! Now Surya and Mitra have an average separation of 63 AU, and a maximum proximity of 30 AU--which gives plenty of space for reasonably-sized solar systems to form around both stars. And then there's the third star, which I'm putting out at 500 AU again--but making it a K-star as well (is this reasonable?). With any luck, the Ajjamans won't have far to go to find planets to colonize (or, possibly, aliens to meet with...).
One more question: anyone know how to calculate absolute magnitude if you don't have apparent magnitude, only luminosity and mass and the like?

[Zaarin]

Also, adjustments made! Now Surya and Mitra have an average separation of 63 AU, and a maximum proximity of 30 AU--which gives plenty of space for reasonably-sized solar systems to form around both stars. And then there's the third star, which I'm putting out at 500 AU again--but making it a K-star as well (is this reasonable?). With any luck, the Ajjamans won't have far to go to find planets to colonize (or, possibly, aliens to meet with...).

Perfectly reasonable for all three to be K stars--NB that's also the case of your prototype, 36 Ophiuchi. (I did something somewhat similar for my sci-fi story, except I went with a double planet--which had the twist that the technologically superior species suspected the existence of the other species hundreds of years before first contact, from the time the first telescopes were invented.)

One more question: anyone know how to calculate absolute magnitude if you don't have apparent magnitude, only luminosity and mass and the like?

Wikipedia offers this formula. Just don't ask me how to solve or even read it. :p

[bbbosborne]

Now Surya and Mitra have an average separation of 63 AU, and a maximum proximity of 30 AU--which gives plenty of space for reasonably-sized solar systems to form around both stars. And then there's the third star, which I'm putting out at 500 AU again

isn't the average separation between the two stars in an S-type system supposed to be at least twice as much (120-600 AU)? the third star seems fine, so im wondering, is there a system that idk about that surya and mitra fall under?

--but making it a K-star as well (is this reasonable?)

yeah, there's no limitation to what type of stars inhabit a system

[Pedant]

Isn't the average separation between the two stars in an S-type system supposed to be at least twice as much (120-600 AU)? the third star seems fine, so im wondering, is there a system that idk about that surya and mitra fall under?

Strictly speaking, no...I was going off something from Wikipedia. Alpha Centauri's twin suns (not counting Proxima) are technically even closer, going as near as 11 AU. Nevertheless, both are deemed to have stable habitable zones, because the figure given was that a planet couldn't cross be further away from the primary than a fifth of the secondary's distance from said primary. This little bit makes it all the easier to set up the system.
(Incidentally, Surya should apparently be about as bright as the sun from Jupiter from the surface of Ajjamah, while Mitra would be about as bright as a full moon. Maybe I need some adjustment if it’s not to turn out to be a rather dark world...)

[k1234567890y]

I am currently making a triple star system with two of them being main sequence stars with habitable planets, one is a G-type star(G2V) and the other is a K-type star(K1V), well, one of them with a habitable moon instead of a habitable planet.

The distance between the two main sequence stars with habitable planets is around 225 AU.

The third member of the system is a white dwarf, with its distance to the center of mass being 1,556 AU.

[bbbosborne]

Isn't the average separation between the two stars in an S-type system supposed to be at least twice as much (120-600 AU)? the third star seems fine, so im wondering, is there a system that idk about that surya and mitra fall under?

Strictly speaking, no...I was going off something from Wikipedia. Alpha Centauri's twin suns (not counting Proxima) are technically even closer, going as near as 11 AU.

isn't alpha centauri in a binary system though? with proxima, i guess it's an s-type system but their separation is apparently 13000 AU. i guess i stand corrected on my previous message. so if a 3rd star orbits around a binary pair, it's still an s-type system?

[k1234567890y]

Isn't the average separation between the two stars in an S-type system supposed to be at least twice as much (120-600 AU)? the third star seems fine, so im wondering, is there a system that idk about that surya and mitra fall under?

Strictly speaking, no...I was going off something from Wikipedia. Alpha Centauri's twin suns (not counting Proxima) are technically even closer, going as near as 11 AU.

isn't alpha centauri in a binary system though? with proxima, i guess it's an s-type system but their separation is apparently 13000 AU. i guess i stand corrected on my previous message. so if a 3rd star orbits around a binary pair, it's still an s-type system?

yes, I think, the distinction between s-type and p-type is for planets it seems...

Proxima Centauri itself has a p-type orbit, but the planets of Alpha Centauri stars can still be of the s-type.

[gach]

Just as a quick one to start with: in S-type binary systems, when the secondary gets nearer to the primary (and the planet), does it mean that the planet heats up more because of the two stars? Is it additive or exponential, do you think?

It seems that you've already figured an answer to this, but a direct answer is probably still welcome. The energy input from the stars is proportional to the incoming radiative flux, which follows the inverse square law. That's a direct consequence of how radially expanding flux spreads out in 3D space. The flux from different sources behaves independently and is thus additive.

What this means is that if you have two equally bright sources with distances r₁ = 1 and r₂ = 10 (i.e. the second one is 10 time further than the other), the energy fluxes from them will be proportional to F₁ ~ 1/r₁² = 1 and F₂ ~ 1/r₂² = 0.01. The more distant source is thus only 1% of the apparent brightness of the nearer. In magnitudes this means a difference of 5 mag in the apparent brightness. In contrast, the difference between the apparent magnitudes of the Sun and the full moon is 14 mag, corresponding to a factor of 400000 between their brightness.

In the context of a binary star, a more distant component appearing only 1% as bright as the nearer one won't give you a feeling of warmth but it's plenty bright enough to turn the night into day. Think for example how bright the sky is a few minutes before a total solar eclipse or at sunset when most of the Sun is below the horizon (the latter one being, of course, hugely dependent on the atmospheric extinction at horizon). So such a star won't fry you alive. On the other hand, if the stars have very eccentric orbits and this is only the closest distance the other component ever comes to you, we are speaking of an energy flux varying between 1% and negligible. That's the sort of amplitude that can easily kick in climate cycle of some sort in the time scale of the binary orbit.

If you've settled to a binary system with similar mass stars that have habitable zones around 0.5 AU to 1 AU and the closest separation of 30 AU, we can calculate the same ballpark estimates using, say, a factor of 50 for the minimum distances. In this case the more distant star will only ever appear 0.04% as bright as your main sun, or 8.5 mag dimmer. That sort of brightness restricts its possible effects to the planetary climate a lot, although visually it will still be way brighter than the full moon.

[Pedant]

This actually does rather fit what I was going for...something a tad like Maraille, I guess, where there's light but not a second day. (Still two shadows, though; I really like the mythological possibilities available from that.)