Thread: Would this solar system be stable?

1. Would this solar system be stable?

OK, I'm developing a planetary system around Alpha Centauri B (yes, another fiction-related question), and I want it to have two "Earthlike" planets (a truly Earthlike planet and a Snowball Earth-like planet). The system I've got so far looks like this:

Alpha Centauri B - ~.94 Sol masses
Inner planet - ~.8 Earth masses - .73 AU orbit
with a moon like ours
Outer planet - ~.8 Earth masses - 1 AU orbit
also with a moon like ours.

The inner planet was taken from Solstation's estimate of where a planet orbit ACB would have Earthlike conditions, and the outer planet is just inside the outer radius of the point where CO2 clouds start to form in the atmosphere (I just don't want the headache of worrying about a climate with CO2 clouds).

The thing that worries me is that this is a little closer than Earth and Venus in the solar system - Venus orbits at .72 AU. Intuitively I think it shouldn't make that much of a difference - it's only a matter of .01 AU - but I don't know and that bothers me.

Is it possible to check the stability of this system? Does anyone know how?

Thanks.

PS, there's also a Venus-like .7 Earth mass planet in a .4 AU orbit and a Mars-like planet in a 1.5 AU orbit, but I didn't think that'd make much of a difference.

2. Its needs the geometry checked so as the planets are orbiting at velocities that lend stability to the system..

I see no reason it could not be that way... realistic and scientific logic do not seem to contradict your fiction plan...

Go for it.

3. I tried checking what the planet might be like in a Venus-like orbit (.72 AU). According to this paper the inner edge of the habitable zone is around .95 AU for our sun, which for ACB would be around .7 AU.

Comparing light levels can be determined simply by treating both orbits as spheres and comparing their surface area. Assuming the planet would recieve Earthlike levels of sunlight at .73 AU, it would recieve ~1.028 times Earth's level of sunlight at .72 AU.

This site says temperature increases by the fourth root. Assuming I've done the math right that should come out to 1.007 times Earth's temperature.

Earth's average temperate = 288 K X 1.007 = 290 K = 17 C.

So my planet should be 2 C warmer than Earth, assuming completely equal greenhousing, albedo etc.

Now, comparing that to what I had in mind... The world is supposed to have one ice-free pole, in the northern hemisphere, at the center of a roughly Pacific-sized ocean (the northern hemisphere is almost entirely water above the tropical zones). The south pole is supposed to have an ice cap in the interior of a continent. So I figure I probably want a climate somewhat warmer than Earth, but not too warm - still cold enough that the interior of the south polar subcontinent is cold enough for a big glacier to exist there.

2 degrees warmer sounds about right for that. Differences in greenhouse gasses can take care of the error bars.

I sort of wanted the planet to have a much higher CO2 level than ours (7-900 ppm) because it would make a nice contrast in the development of the civilization there - they wouldn't have to worry about global warming because the relative amount of CO2 they'd have been adding to the atmosphere was much smaller. That would imply a planet that gets less sunlight than Earth for it to have a mildly warmer climate. Oh well, this works too ... I think.

One thing that bugs me is it makes the system a virtual mirror-image of our Venus and Earth (.72 AU inner planet, 1 AU outer planet), just with the Earthlike planet in the place of Venus. Seems like it'd be a pretty big coincidence.

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Originally Posted by Somes J
Alpha Centauri B - ~.94 Sol masses
Inner planet - ~.8 Earth masses - .73 AU orbit
with a moon like ours
Outer planet - ~.8 Earth masses - 1 AU orbit
also with a moon like ours.

...

PS, there's also a Venus-like .7 Earth mass planet in a .4 AU orbit and a Mars-like planet in a 1.5 AU orbit, but I didn't think that'd make much of a difference.
I don't know about stability; but it does seem highly unlikely that two moons with a mass of such a high fraction of the planetary mass would form in one star system.

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Originally Posted by fagricipni
I don't know about stability; but it does seem highly unlikely that two moons with a mass of such a high fraction of the planetary mass would form in one star system.
A coincidence, but not awfully unlikely. Out of the 9 planets of Solar System, 2 have massive moons: Earth with mass fraction of 1/81, and Pluto, with mass fraction of 1/9. 2 out of 4 planets having massive moons would not be improbable.

More of a coincidence would be if both moons are Moon-sized. They would be more likely to be different in size... like, one Europa-sized and another Mercury-sized. But coincidences do happen in Solar System... Mars just happens to have both rotational period only 40 minutes longer than Earth and axial tilt just 2 degrees bigger.

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Centauri A would likely perturb your Mars analog more than Jupiter perturbs our Mars, solved by not having any planets farther from Centauri B than Snowball Earth or use Centauri A as your setting with some what longer radius of the planets.
The Moon coincidence is easily solved by having Snowball Earth's moon about half as far away and about half the diameter, so they will appear much the same. Neil
Last edited by neilzero; 2010-Nov-13 at 02:07 PM.

7. Originally Posted by neilzero
Centauri A would likely perturb your Mars analog more than Jupiter perturbs our Mars, solved by not having any planets farther from Centauri B than Snowball Earth or use Centauri A as your setting with some what longer radius of the planets.
Solstation has a link to a paper suggesting orbits could be stable out to 2-3 AU for Alpha Centauri, and also suggests a general one-fifth distance rule which would suggest a 2 AU limit (Alpha Centauri A and B are very close in mass so it should be reasonably applicable). I figure 1.5 AU is probably safe.

One thing that bothers me is the moon of the inner planet - I tried simulating it with Gravity Simulator and it was disturbingly wobbly. On the other hand this paper suggests the stable zone should be ~.48 times the Hill radius, which is around 1 million km, which suggests it should be OK out to 480,000 km.

To be safe I'd like to put it inside the inner third of the Hill sphere (330,000 km) but the problem is it'd be an older planet than Earth so if anything the moon should be farther out. It might help to make it smaller - according to this a half-sized moon would be closer to the Earth, and that would be nice in other ways as it would let me keep a more Earthlike day/night cycle. Unfortunately I have no idea how to calculate the effect that would have on the recession rate ... perhaps I should start another thread for that.

8. I have run a simulation of your system with masses and distances as stated above. I assumed that the planets have near circular orbits and are all in the same plane + or - a couple of degrees.

I added Alpha Cen A with mass 1.1 solar masses, semimajor axis 17.57 AU and eccentricity 0.518. I assumed it to be in the same plane as the planets. The simulation ran for 100ky.

The planets's orbits are quite stable most of the time but take a "kick" each time AlphaCen A goes through its perifocus. This gives short term increases/decreases in period (a few days +/-). Eccentricity also varies by a small amount and all the planets' orbits precess rapidy. But overall there does not seem to be any long term damage to the orbits over the 100ky period.

I also tried it with the plane of the planet's orbits starting at 45 degrees to the orbital plane of the two stars - great example of the Kozai effect!. There are huge cyclic exchanges between eccentricity and inclination for all the planets but at different cycle tmes. Amazingly there are no actual collisions/close encounters during the 100ky and periods remain quite stable while eccentricity goes up to 0.6 or more. These planets are definitely not habitable.

9. Solstation gives an average distance of 23.7 AU, ISBD gives 23.6. Cool though.

I'm still working on Planet II's moon. If I put it within 245,000 km it recieves proportionately more gravitational force from the planet and less from the sun than our moon (treating gravity as scaling by r^2), so I figure an orbit of 200,000 km or so should be stable.

That would give huge tides (not quite 7X as high as ours) but that can be alleviated by making the moon smaller. A moon a quarter or a fifth the mass of our moon would give similar tides to what we experience at that distance. I assume the obliquity stabilization effect of our moon is a factor of tidal force, and scales by r^3?

The evolution of such a moon system over time would be a bit of a headache though. It would probably have to be a relatively recent capture (last couple of billion years).

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