What size could habitable planets in the Castor system be?

[StarCreator]

I'm new to this forum, but I've been reading here a lot over the past several days. I'm planning on starting a sci-fi universe for a gaming group I'm in and for a book that I want to write. I've been doing a lot of research and I want the first planet I'm designing to exist in the Castor system, what I've read(though it may be outdated) says that CastorA has a habitable zone ~6AUs out and CastorB has a habitable zone ~4AUs. My question is how large would/could these planets be? I've done a lot of reading and I understand that it is a function of mass, composition, and spin and the center has to be iron, however I can't really find anything like equations.

I want the planet to have a roughly Earth-like composition, though possibly slightly less metallic, so as to explain the reliance on non-technological things rather than being hyper-advanced. I would also like to know if it is possible for a planet of composition like that to support(earthlike) life and have a surface area twice or maybe three times that of Earth.

Any help would be greatly appreciated, thank you.

 

[DHF]

The Castor System has 6 stars. It might be too unstable to support planets. As Far as land area, you can give it as much or as little land as you want, just determine how much of the surface is covered by water. Mars for example is half the size of Earth but as land area nearly equivalent to Earth because there are no oceans or any other water on Mars.

 

[StarCreator]

From other readings here and elsewhere I would guess that planets might be supportable, as the system is fairly stable, though again I suppose I'm not very knowledgeable. However the closest any of the binary systems ever are to each other is 176AUs, I would think that a planet could thus orbit one binary system and not be drastically effected by the other systems.
Also I'm aware I can make my decisions as I see fit about landmass on the planet, but I am really curious about what the actual size I could make the planet.

Sources:
http://www.solstation.com/stars2/castor6.htm
Celestia
https://www.physicsforums.com/showthread.php?t=705697&highlight=castor

 

[DHF]

Well Anything more then twice the mass of Earth and the atmosphere would start to get funky. As the mass goes up the planet would start to hang onto more hydrogen and have a less Earth like composition.

I would say stick with 1.25 - 1.5 Earth Mass to keep things similar to what we have here. Then again if you are going to change the mineral composition of the planet and make it less metal rich, that might alow you to have a physically larger world with the same or similar mass.

 

[Bandersnatch]

First of all, the closest approach between Aab and Bab components in Castor system is about 70 AU, not ~176 AU( $R_p=a(1-e)$ ). At that distance a planet around either pair would be perturbed by gravitational influence about six times stronger than that of Jupiter on Earth.
This seems sensible as far as stability goes.

For the planet, you want gravity to be roughly that of Earth's.
Gravity depends on mass, which in turn depends on radius and density.
If you assume* the planet to have similar density distribution to Earth, and express all variables in fractions of Earth's, you can simply say:
$R\propto \frac{1}{ρ}$, that is, if you make denisty half as high as Earth's, you can have the planet be twice as large radius-wise as Earth, and still have the same gravity.
And since area is just Pi times radius squared, $A\propto \frac{1}{p^2}$ So, to get twice the area of Earth, you need 1/√2 of its density.

For reference, Earth's density is about 5.5 g/cm^3. Moon is about 3 g/cm^3. Going lower than Moon's might be stretching it.

*it's an assumption that's unlikely to hold under closer scrutiny, but it will give you a ballpark resut that should be accurate enough for your needs. With that in mind, you can always add/deduct maybe 10%-20% to the result and justify it by different mass distribution in the interior.



More importantly, though, Castor is a very young system(100-300 million years). Having life devolp in such time is not very plausible. Consider that Earth was constantly bombarded by meteors and had largely molten crust for the first half a billion years of its existence.

 

[StarCreator]

Thank you bandersnatch, that's very helpful.