[SPACE] Planets in a Binary Star System
 

I have been trying to put together a binary star system and there are a few things I want to know that I cannot find in the book. First, how does the forbidden zone of one star effect the forbidden zone of another star? Does the luminosity of the second star effect the system? And, if two stars are really close, can and will planets form around both of them and how would that work?

Re: [SPACE] Planets in a Binary Star System
 

All of that is in the book, actually, if you read the discussion of forbidden zones closely. Except for temperature and luminosity. There is no simple way to do this. But here's what I worked out:

For a planet of star A:

Figure its temperature based on its orbital distance from star A, and star A's luminosity

Figure its temperature separately based on the distance between stars A and B (which equals the planet's mean orbital distance from star B) and star B's luminosity

Raise both temperatures to the fourth power (that is, square them, and then square them again)

Add the resulting numbers

Take the fourth root (that is, take the square root, and take the square root again)

This will be the blackbody temperature of the planet based on the input from both stars. It won't be much different from that for star A alone, but a really cold planet of star A may get a noticeable boost from star B.

Bill Stoddard

Re: [SPACE] Planets in a Binary Star System
 

You don't need to get complicated about this, because it is the presence of the second star that creates the forbidden zone in the first place. So just follow the rules as they are laid out and this will all get taken care of.

You start with the more massive star, and work out the average distance and the eccentricity of the orbit of the second star. Then you work out the periapsis and apapsis distances (average times (1 - eccentricity), average times (1 + eccentricity)). Then you divide the periapsis distance by three to get the inner edge of each star's forbidden zone, and multiply the apapsis distance by three to get the outer edge of the system's forbidden zone. Generate planets inside the inner edge of the forbidden zone for each star. Generate planets outside the outer edge of the forbidden zone as though they were planets of the primary star, though in fact they will be orbiting the two stars jointly.

In reality yes. But in the system as written this is not taken into account. If you want to adjust the system to be more realistic, follow the procedure that whswhs outlined above.

Note that in cases where a planet receives a significant amount of heat from each of two stars there can be quite a wide variation in its temperature depending on orbital circumstances.

In the GURPS Space system you generate them as though they were orbiting the more massive star outside the outer edge of the forbidden zone. But if the luminosity of the smaller star is appreciable it would be good to take its effect on the temperature into account, as whswhs suggested.

Re: [SPACE] Planets in a Binary Star System
 

This procedure is correct for calculating the average blackbody temperature. If you want to get fancy you can calculate a seasonal range of balckbody temperatures by figuring out the maximum and minimum distances from star B, and doing the calculation twice, once using the maximum distance instead of the A-B distance for a minimum temperature, and once using the minimum distance for a maximum temprature.

Usually the range will be small: I figure about 12C (22°F) for a habitable planet orbiting one of two similar stars just inside the inner edge of the forbidden zone. Most often it will be less than that. In the odd case of a planet that orbits a very dim star from which it gets negligible heat, and that is actually warmed to a liveable temperature by the light of that star's much-more-luminous primary, insolation can vary by a factor of 4, suggesting that an average temperature of 300 K represented a range from a chilly 252 K to a sweltering 356 K.

Re: [SPACE] Planets in a Binary Star System
 

Does this apply regardless of the planets actual distance from star B?

Re: [SPACE] Planets in a Binary Star System
 

At any time the planet's temperature depends on it's actual distance from B at that time. (Give or take lags.)

Over long periods of time the average distance from the planet to B is equal to the [average] distance from A to B, so whswhs's method will give you a fair annual average.

Re: [SPACE] Planets in a Binary Star System
 

Exactly. I did the calculations for a binary star system for a Pyramid article a few years back, and the difference was minimal: the coldest planet was raised only from 25 K to 29 K. If the temperature boost turned out to be substantial, you could always use the minimum and maximum distances to check.

Bill Stoddard

Re: [SPACE] Planets in a Binary Star System
 

Sweet. Thanks guys.

Re: [SPACE] Planets in a Binary Star System
 

If it helps, visualise the forbidden zone of a system as a disk with two circular holes cut in it. Each star is in the middle of one of the holes, and the centre of mass of the pair of stars is at the centre of the disk. The radius of each hole is one-third of the distance between the centres of the holes, and the radius of the disk is three times the distance between the centre.

In either of the holes a planet can follow a nearly-stable, almost-circular orbit around one of the stars while that star orbits the centre of mass of the system. Outside the disk a planet can follow a nearly-stable, almost-circular orbit around the centre of mass of the pair of stars for quite a long time. But in the forbidden zone things are a lot more complicated: most orbits are chaotic and end up either on a collision course or an escape course in geologically short time. The orbits that do last a long time are rather complicated and hard to deal with in Space's simple framework. (eg. Lagrange "points", horseshoe orbits, quasi-satellite orbits, etc.).

Yep, it's an approximation. But Hill Spheres are too complicated.

Re: [SPACE] Planets in a Binary Star System
 

Interesting. I never thought of it like that.