How long does Kessler Syndrome last?

Question

I realise this about as useful as asking "how long is a piece of string?" but bear with and I will attempt to set parameters.

OK, so there has been an apocaplyse and now, at the time of my question, a century later, mankind has been reduced to a strictly ground-based existence. Many of the old timers have remembered the stories they heard growing up about how mankind used to have planes and spaceships etc, but frankly a lot of the younger folk either don't care or just flat out disbelieve. There is still old tech everywhere, some broken, some working and commonly used.

(INSERT EDIT HERE) Before the apocalypse the society had approximately 5 trillion inhabitants. Most on-world, some off-world. So, a lot more satellites than 'our' Earth currently has in 2020, plus there were also many O'Neill Cylinders, an Orbital Ring, many hundreds of space elevator towers leading to the Orbital Ring, and a fledgling Dyson Swarm growing near the Sun. Most of the stuff in low Earth orbit started colliding when humans stopped controlling it. A little at first, but then it quickly grew until it became full on Kessler Syndrome. Most of the stuff in high Earth orbit is untouched. (2nd EDIT here) Quick note to mention that my space elevators are not based on hard science, that this is very much a sci-fi-fantasy story, that there is magic based tech involved, and the towers do not have the usual 'tether-ball' arrangement that hard science demands. They are literally only towers 100kms high. About half of them attach to the Orbital ring, but the rest are just launch/ land platforms + accomodation. Also, I fully expect Kessler Syndrome to last more than a century, and my story reflects this. Although I have not got the expertise to back this up, (hence the question), my story requires it so I am very glad if we can prove that KS will actually still be happening a century after this mysterious apocolypse.

The question I want to know is, would the Kessler Syndrome still be in place and happening a century later, or would it have burned itself out by now?

I realise I am short on details, so huge apologies on that regard, but nevertheless wondering if anyone has any ideas?

Answer 1

Kessler Syndrome will start at the most occupied orbital heights with the most crossing satellite paths. This is currently low earth orbit at a few hundreds of kilometers height. Once Kessler Syndrome starts, real world space elevators would be snapped and destroy the orbital ring with their debris. I cannot say what will happen to your towers: This depends on how massive your towers are, and whether they are hit by parts that are still several tons in mass. If the towers are massive enough, they will remain standing, and help in clearing the height levels that they span. If the towers are not massive enough some/all of them will be destroyed, and the part above the impact will crash down in a pretty catastrophic manner.

How long does it take for the Kessler Syndrome to stop? Well, that's a function of height: The further up you get, the lower the atmospheric drag will become and the slower the orbits of the debris will decay. Unfortunately, atmospheric pressure is an exponential function of height and orbital decay itself is a self-accelerating effect. So, while a satellite at 150km height will only for about one orbit (roughly 90min), the ISS at 400km would live for a low amount of years if it were not reboosted regularly. Sorry, I couldn't find any precise numbers quickly, I can only give a qualitative overview. As far as I know, anything above 1000km stays in orbit at least a century.

Satellites with elliptical orbits will tend to propagate the Kessler Syndrome across the height levels: They will collide with debris at a low altitude, but their own debris will be too fast for that height level and rise along the ellipse to greater heights where they can collide with higher satellites.

Geosynchronous orbits are never cleared from debris, the remains of your orbital ring will basically stay forever where the ring was. Unless the orbital ring was held together by the space elevators, in this case it will fly off into deep space.

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So, if you want your Kessler Syndrome to be over within a century, you must strictly avoid any satellites between about 1000km and 30000km height. The orbit of the orbital ring (above geostationary orbit) will be filled by the debris of that ring, but since it all starts in the same orbit, it will form a thin planetary ring that is easy to avoid when you want to fly into deep space.

You can justify this restrictions by the presence of the space elevators: A space elevator is basically a thin cable that will be snapped pretty much by anything that hits it at orbital velocity. To ensure the safety of these, you need to avoid having any satellites/debris that might cross their paths. So, you either put your satellites into a low orbit that decays quickly and can be shown not to come close to a space elevator within their lifetime, or you make the satellites geostationary so they don't have velocity relative to the space elevators.

Answer 2

100 years of Kessler Syndrome is too low

The math is clearly hard, but this is a serious issue, and has been studied by Lawrence Livermore National Laboratory.

Assuming no new launches, with a starting date of May 4 2009, the number of 10 cm or more objects rises from about 14K to 50K over a hundred year period. We of course, have launched many satellites since 2009, so the current situation is even worse; the situation described in the question is far worse.

This study was based on computer modelling that included orbital mechanics, atmospheric variations, and solar cycles - averaged against multiple simulations runs.

This paper does not predict how long Kessler Syndrome would last, but it does say that the current debris field would continue to become more crowded for over 100 years even without any more launches in the future.

With your increased space presence as a basis, the situation can only last longer. My understanding is the primary factor re: the duration of the Kessler system is the total mass in orbit subject to collision breakup. While O'Neill cylinders would certainly be tough enough to survive small impacts. The total mass in the proposed situation is far in excess of the amount considered in this paper.

Answer 3

Another factor here: You have a pretty high tech society, what steps are they taking to remove the junk?

Track a piece of junk in a low orbit, engage with a high power laser pulse as it passes overhead. The objective isn't destruction, but simply vaporizing a bit of material--the puff of gas goes down, the object goes up. Now it's in a more elliptical orbit, periapsis is lower, drag brings it down sooner.

Once you have cleared some orbits you can launch spacecraft into the safe zones--they contain mirrors and lenses to redirect the laser. Now you can engage additional debris head-on which will be more effective. (From the ground you could get a near head-on shot against stuff in low orbit but you would be going through an awful lot of atmosphere, aim would be a problem and dissipation would be much worse.)

You will have to work with care clearing the higher orbits to avoid bringing debris down on the craft in low orbit.

The limit of this approach is how small debris you can track.