# Why aren't all rocks in space orbiting bigger rocks?

Why do only big rocks (planets) have satellites, and not small ones? Why doesn't cosmic dust orbit rocks that are many times heavier than the dust grains? If dust is still too heavy then what about molecules, atoms, or any particle for that matter? The mass difference should be millions of millions times; isn't it enough for orbiting? The Moon is 1% of the Earth's mass, yet we don't see 1kg rocks orbiting 100kg ones.

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I want to expand a bit on David Zaslavsky's point #1: "A random dust grain probably won't be going at the right velocity to be captured into orbit around a bigger rock (like an asteroid)." Without the assistance of a third body, it's actually impossible for an object to be gravitationally "captured" in an orbit by another: if it wasn't already in orbit before, there's no way for it to start orbiting.

The reason is just conservation of energy. If the object wasn't already in an orbit, then it was moving too fast, given its distance, to be in an orbit. (To put it the other way around, it was too far away, given its speed.) Even if the little guy was moving in just the right direction to come close to the big guy, it won't be captured: it will move in on a hyperbolic path, approach the other object once, and then fly away again, simply because it has too much energy to be captured. The only way to produce an orbit is for a third body to interact with the system and siphon off some energy at the right time.

That can happen, but unless the density of things flying around is high, it's rare. And if the density is high, then subsequent collisions, which will disrupt the orbit, will also be common.

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+1 good to point this out... I glossed over it in the interest of simplicity. –  David Z May 6 '11 at 19:53

The mass difference has practically nothing to do with whether two things can orbit each other. You can have two objects of the same mass in orbit (e.g. binary star systems), or you can have two objects of wildly different masses in orbit (the Earth and a piece of space junk), or anything in between. There are a lot of factors involved, for example:

1. A random dust grain probably won't be going at the right velocity to be captured into orbit around a bigger rock (like an asteroid).

2. When dust grains do orbit asteroids, there will probably be a lot of them, so they're going to collide with each other and lose energy, so they fall out of orbit rather quickly.

3. Planets tend to be pretty isolated, so things can orbit them without getting disturbed by other planets. In contrast, smaller rocks like asteroids are often found in large groups, so a dust grain couldn't orbit just one - it would also be affected significantly by the gravity of other asteroids in the vicinity.

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OK, David, I disagree that you have captured the main point. The OP was asking about small bodies orbiting 100-kilogram bodies. You know that this is impossible and has nothing to do with the 3 details you wrote. The gravitational acceleration coming from 100-kilogram objects is so tiny that the orbital speed would have to be essentially zero for a reasonable radius comparable to 1 AU or similar solar-system-like distances, or smaller. 100 kilograms is $10^{22}$ times lighter than the Earth, so the required orbital velocities for the same $r$ are $10^{11}$ times lower. –  Luboš Motl May 6 '11 at 7:03
The gravitational influence of a 100 kg body 1 AU from the Sun, its Hill Sphere, is about 40 meters; not trivial. However, as Luboš pointed out, a dust particle would need a near-zero relative velocity to orbit it. –  Michael Luciuk May 6 '11 at 11:41
Not only is the sphere of influense very small, and the orbital velocities very small, but the perturbation needed to knock it out of orbit is also very small. Small bodies are affected by solar radiation pressure (and the radiation pressure of reradiated heat), and these tend to push them around. That means the stability of tiny objects orbitting other tiny objects is poor. –  Omega Centauri May 6 '11 at 16:17
@Lubos: no, it's not impossible for something like a 1 kg mass and a 100 kg mass to be in orbit. As you said, it would just require an unreasonably low velocity, which is exactly what point #1 is about. –  David Z May 6 '11 at 19:52
An intriguing picture of small solar systems comes to mind.


Nevertheless, Luboš is correct that for any recognizable system the velocities of capture would be so low as to make the question moot.

As a rough example , equating centripetal gravitational with centrifugal forces, a particle orbiting a 100 kg mass 100 meters away from it would need a velocity order of magnitude of ten microns per second, something that would hardly be observable: the orbit of 628 meters would take 1.7*10^4 hours to complete.

In any case, in real life in our space around the sun it is a many body problem, as David suggests above, so statistical and chaotic behaviours will enter the problem and destroy any small scale regularity. Only in deep outer space outside the sun's field such an orbit might be undisturbed and observed by a patient observer :).

The reason for such small velocities is the weakness of the gravitational constant G. The velocity of a stable orbit is proportional to the square root of G. The mass of the orbiting particle does not matter as it is eliminated in equating centripetal and centrifugal forces.

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The reason why we don't see dust particles orbiting comparably tiny rocks within the solar system is just that the rest of the solar system interferes due to how slow such an orbit has to be:

• the presence of other massive bodies perturbs the orbits of dust particles.
• the solar radiation pressure is a significant force for particles smaller than 1µm, also destabilising orbits that slow.
• it's simply really difficult to observe any occurrences of such orbits that do exist (temporarily) within the solar system bounds, both because the systems are tiny, and because they are slow.

There is no reason why such small-scale "planetary" systems can't exist in the interstellar space.

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This is a very late answer, but no answer has been selected yet.

Why do only big rocks (planets) have satellites, and not small ones?

Almost 100 asteroids have satellites, and some of them are rather small. For example, asteroid 54509 YORP has a mass of only 1×1010 to 4×1010 kilograms. That sounds like a lot, but that's a body with a mean radius of only 120 meters. I mentioned 54509 YORP because it appears to be a confirmation of the YORP effect. Radiation pressure made the asteroid spin faster and faster until it split into a couple of pieces. Another proposed source for those satellites of small bodies is collisions. Yet another is capture, but that is rather difficult, particularly for small bodies.

Whether these satellites of small bodies are stable over millions and millions of years is a different question. There are a number of reasons to think that they are not.

• Small bodies have small mass and hence a small gravity field.
There are two key concepts to look at here, the Hill sphere and the Laplace sphere of influence (SOI). The two concepts give different indicators of the stability of the orbit of an object orbiting a small body that in turn is orbiting a larger body. Assuming a circular orbit about some larger body (e.g. the Sun), the Hill sphere is given by $a\left(\frac m {3M} \right)^{1/3}$ while the SOI is given by $a\left(\frac m M \right)^{2/5}$. Here, $a$ is the orbital radius, $m$ is the mass of the smaller body, and $M$ is the mass of the larger body. An object of 106 orbiting the Sun at 3 astronomical units (the asteroid belt) has a Hill sphere of 2.5 km and a SOI of 86 meters. Either way, that's rather small radius over which an even smaller rock can have a stable orbit.

• Small bodies have small mass and hence deviate strongly from being spherical.
The recently visited asteroid 25143 Itokawa and comet 67P/Churyumov-Gerasimenko (both shown below) illustrate this point perfectly. These aren't at all spherical. A better description is a lumpy Russet potato. The non-spherical nature of the gravity fields of these small objects means that the orbit of a body orbiting these small bodies will not be stable. For a marked account of this effect, read the article Bizarre Lunar Orbits from nasa.gov.

25143 Itokawa, image credit JAXA, via Wikipedia commons

! Comet 67P/Churyumov-Gerasimenko, image credit ESA/Rosetta/MPS for OSIRIS Team MPS/UPD/LAM/IAA/SSO/INTA/UPM, via nasa.gov

Why doesn't cosmic dust orbit rocks that are many times heavier than the dust grains? If dust is still too heavy then what about molecules, atoms, or any particle for that matter?

Extremely small particles are ejected from the solar system thanks to solar radiation pressure. Slightly larger (but still very small) particles spiral inward into the Sun thanks to the Poynting-Robertson effect. Slightly larger particles, up to small rock size, will spiral in or out thanks to the Yarkovsky effect. Once the Sun lit 4.6 billion years ago, solar radiation and the solar wind have been clearing the solar system of tiny pieces of stuff. New tiny pieces of junk are continuously created thanks largely to collisions in the asteroid belt. We see the inward-spiralling dust that results from these collisions as the zodiacal light.

The mass difference should be millions of millions times; isn't it enough for orbiting? The Moon is 1% of the Earth's mass, yet we don't see 1kg rocks orbiting 100kg ones.

If you haven't done so already, read the article referenced above on Bizarre Lunar Orbits. What happened to PFS-1 and PFS-2 is truly bizarre.

Understand that and you'll be well on the way to understanding why superclusters can have multiple galaxy groups "orbiting" them, galaxy groups can have multiple galaxies "orbiting" them, galaxies can have multiple stars orbiting them, stars can have planets orbiting them, and planets can have moons orbiting them, but moons cannot have satellites orbiting them. Planets and asteroids are where the hierarchy ends.

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