What would the physical properties of this planetary system be?

Question

The Idea: A planetary system composed of many interconnected nodes and small bodies in a semi-stable arrangement, with much shorter distances between astronomical bodies than our own Solar System. It's kind of like an orbiting structure made of tinker toys, or the floating mountains in Avatar on an astronomical scale.

Take this, but scale it up. Individual planetoids/rocks in this system should be able to see other bodies, with something like the distance between our Earth and Moon as a common range. So with a much greater density than the asteroid belt, and fewer collisions than a planetary ring. A star still forms in this structure, providing a chance of life evolving on these planetoids.

The Explanation: Our planetary system forms with a significant volume of exotic matter; let's call it Zero-Mat. This particular exotic matter has an interesting property: it repels itself, but increases the gravitation pull of any regular matter near it. It's influence falls off much faster than gravity, say something like 1/r⁴ instead of gravity's 1/r². Thus these exotic particles could attract matter to themselves, but keep that matter from aggregating into larger planets. There may be some mechanism/structure of the exotic matter that allows it to bind together, like an alien form of the nuclear force, if the repellent force is overcome.

The Question: Would this explanation in any way work? Would it allow this proposed system to come into being?

What other ways could this system form?

Answer 1

Exist? Sort of.

It would be possible for something like this system to exist, even without the addition of exotic $\frac{1}{r^4}$ repulsive matter. To scale this up to an asteroid-belt size with "visible" neighbours would be possible as well, as long as you accept that the individual asteroids all have nearly-perfectly uniform angular velocity about the system's star to avoid (major) collisions and gravitational "slingshot" effects that could destabilize the orbits (unless you have an efficient government that can re-zone these about-to-be-ejected-"neighbourhoods" for cold storage, and therefore don't care if you lose a few here and there).

How massive?

First, the Earth-moon distance is about $384\,000\,km$, and for the objects to be visible at typical 1 AU reflected brightness, they would need to be at least 30 arcseconds, which gives us a real diameter of about 60km, equivalent to a spherical volume of about $113\,000\,km^3$, and a mass of $6.2\times 10^{17}\,kg$.

Next, the Earth's orbit is about 940 million km in circumference. If you were to unroll that into a line 940 million km long, and then "stamp" a ring of such planetoids every 384,000km along the ring, you get around 2500 planetoids, "weighing" in at an Earth-scale $1.6 \times 10^{24}\,kg$, given Earth-like density (actually the density would be a lower, but trust me, that wouldn't be helpful, here).

The Earth itself is about $6.0 \times 10^{24}\,kg$, so you could have a few concentric rings and still come up with something relatively of Earth-mass. Of course there's no reason you couldn't make it a bit more or less massive.

Atmosphere? No.

In order to have a human-like life-sustaining atmosphere, the temperature (mean velocity of atmosphere molecules) has to be less than the escape velocity of the planetoid.

The escape velocity, $v_e = \sqrt{\frac{2Gm}{r}} = 38\,m/sec$. (c.f. Earth's $v_e = 11\,200\,m/sec$!)

To sustain liquid water at the surface, the atmosphere would have to have a temperature around 200 K (very approximate value so I don't have to talk about pressure yet). At room temperature (294 K), oxygen molecules fly around at an average of nearly 500 m/s, which is more than ten times the escape velocity. They would be somewhat slower at the 200 K mark, but certainly not by a factor of ten. If I have time later I'll put in the "exact" RMS calculation.

Thus, either the atmosphere would be too cold to support life (at least water-oxygen based life), or the atmosphere would literally fly away.

Pressure and Gravity

Without doing the calculations (yet), I can tell you that the acceleration due to gravity and the air pressure will be far, far less than what we're used to on Earth. The gravity is not a big issue (at least not in the short term, although evolution might be challenged), but the pressure would be quickly fatal to humans, so your species would have to either have evolved to adapt, or your exotic matter would need some kind of "air magnet" properties.