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What density of satellites in LEO is permissible before a single collision has a reasonable chance of triggering the catastrophic destruction of everything in orbit? How many orders of magnitude are we below this level presently--is this a practical concern that limits our ability to utilize space in the long run?

(The reason a single collision could result in near-complete destruction is that when satellites collide, or are badly damaged, they release many pieces of debris that may badly damage other satellites and cause further collisions. If the probability of collision with debris (before deorbiting) times the number of pieces of debris produced by collision is greater than one you end up in a supercritical regime as with viral pandemics and nuclear meltdowns/explosions.)

Rex Kerr
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What you're describing was popularized some years ago by Donald Kessler at NASA. It has since been termed "Kessler Syndrome".

In short, a collision could feasibly set off a cascading chain reaction of collisions. Note that the time scales for this aren't necessarily on the order of minutes or even hours... collisions may just start happening at an ever increasing rate.

As to what that density actually is, there is no hard number. Depending on which study you read, we may even be at this critical point now. Here's a recent one by the man himself (PDF Warning).

  • Is there a study you can link to? There's plenty known about how to use neutron absorbers etc. to control reactions; presumably there are analogous calculations in such studies? (There are new launches all the time, adding orbiters faster than old ones being deorbited, so quite some number of people with billions of dollars collectively don't yet think we're at the critical point, or deem the chance of a trigger to be very low.) – Rex Kerr Aug 02 '13 at 17:53
  • I have read studies like that (which I cannot find open sources for/can't remember), but in general I don't think it is as well-understood. One reason is the description of "spatial density" in the first place... the nature of orbits makes it difficult to even come up with a description. For instance, what is a "region" in space? Is it just an altitude band? If so, how do you account for varying inclinations or relative phase angles? –  Aug 02 '13 at 17:59
  • You integrate? I'd expect that the expected number of impactors released by a collision would be the trickiest part to nail down. If one knew that, the distribution in inclination/phase angle after collision ought to be comparatively straightforward. Sure, you'd only get a mean field approximation but if you're worried about order of magnitude that should be ample. Anyway, the Kessler paper covers what I was hoping to find! – Rex Kerr Aug 02 '13 at 18:07
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    But integrating over, for instance, inclination is misleading at best, since there are certain regimes (sun-synchronous, for instance) that are orders of magnitude more populous than others. –  Aug 02 '13 at 18:10
  • It's a triple integral: the flux from the expected distribution of fragments (1) produced from everything that's there (2) through the cross-section of everything that's there (3). I grant that time could make it very complex as debris paths enter different regimes (well-isolated initially to highly diffused from debris-debris collsions at long times). I had only been thinking of rapid cascades, but I do see how you could be in the middle of a slow one and not even know it. – Rex Kerr Aug 02 '13 at 18:17
  • The link to that study is broken now; can we have a title or an updated link? – DJG Jun 16 '21 at 02:24