# Can one predict mass distribution in a solar system given the mass of the star?

I'm trying to write a program to procedurally generate solar systems at a reasonably high level (I'm not interested in doing an n-body dust particle formation simulation).

Is there some sort of distribution that defines where I am most likely to find mass inside a solar system? i.e. should I expect heavier planets further out... or is it completely random?

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Alas, if anyone had a solid answer to this, we'd publish it and become famous exoplanet scientists.

In our own solar system, certainly most of the planetary mass is in the outer planets. The reason that is often cited has to do with the ice line. Beyond a certain distance, water and methane and other such materials are solid rather than gaseous. More solid matter $\Rightarrow$ faster accretion $\Rightarrow$ bigger final products. However, the relative sizes of the outer planets amongst one another is still not so easily determined. If you believe the Nice model, which suggests Uranus and Neptune have swapped orbits, then the outer planet masses were originally monotonically decreasing with distance from the Sun, but there are no quantitative predictions regarding this.

As it turns out, though, there are hundreds of planetary systems out there that look nothing like our Solar system. Radial velocity and transiting surveys have found plenty of "hot Jupiters" - Jupiter-mass and above planets orbiting closer to their stars than Mercury around the Sun. The transiting data obtained with the Kepler mission is given on the Kepler website. Note the large masses at small separations.

On the other hand, with direct imaging, we have found large objects orbiting their stars much further than Neptune orbits the Sun. See for instance Fomalhaut b and HR 8799 c and b.

There may very well be underlying trends, but seeing them amongst all this diversity will require a lot more data. Right now exoplanet science is in its infancy - it is more exploratory than systematic, especially given how hard it is to detect small planets. The only hard restriction is if a proposed arrangement of planets (usually close together and massive) proves to be dynamically unstable on (astronomically) short timescales. Since such systems would not last for very long, we do not expect to see many of them. Of course, calculating such dynamics can be almost as tricky as doing the dust simulation you wanted to avoid.

Ultimately, if you are procedurally generating systems for some visualization/gaming software, no one can fault you for having a little poetic license when it comes to inputting parameters for what these systems may look like.

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It really depends on how high the level you want. Chris already explain clearly about that we dont have any model since we only discover the first exoplanet recently and there only hundreds of planetary system out there, which is not enough for any solid model.

You said that you only want to generate a solar system, so why dont you just throw $N$ planets in your system and look how they evolve in $N+1$ particle simulation (including the star). Make sure they are far away from each other and the size is not comparable with the star so that it will give you a stable solar system. The initial condition can be easily calculated with some knowledge of classical mechanics.

If you want the solar system look more alien, dont use our solar system as model. Instead you should put the larger planet close to the star (hot Jupiter), which is the dominated type of the solar systems we observed so far.

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Careful! Yes the hot Jupiter systems are the most commonly observed, but observation bias is undoubtably at work here. We simply don't know what a "typical" planetary system looks like. –  John Rennie Dec 18 '12 at 7:17
@John You are right. The detection method are mainly the star trajectory perturbation and light intensity variation. So the bias is very strong, for those planet that are big, heavy and close to the star. –  hwlau Dec 19 '12 at 6:29

I know it is an old question, but you may want to take a look at the Titius-Bode law. Especially

Dubrulle and Graner[6][7] have shown that power-law distance rules can be a consequence of collapsing-cloud models of planetary systems possessing two symmetries: rotational invariance (the cloud and its contents are axially symmetric) and scale invariance (the cloud and its contents look the same on all scales), the latter being a feature of many phenomena considered to play a role in planetary formation, such as turbulence.

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