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A lot of interplanetary space infrastructure would be focused around Lagrange points, where collision energies would be very low. The threat in this case would come from everything traveling between planets and these regions. These spacecraft would be on a variety of different orbits optimizing for desired time and ∆v costs, and would generally be bound to stop at a planet or some structure. Others would be cyclers, which would be on orbits that allow them to travel quickly through the space between Earth and Venus, but would also take them much further beyond the planets orbits. There would also of course be plenty of stuff in orbit around the planets themselves, but that wouldn't affect interplanetary space.

This is, I think, distinct from a Dyson sphere/swarm situation. That would (generally) be closer to the sun and in more circular orbits, and therefore would also behave more like the traditional LEO collisional cascade (Kessler event? Is there a preferred term for this?).

In this case, even if a collisional cascade began at some point when the planets are relatively close to one another and the space between them is most densely packed, the debris would rapidly dissipate to a huge variety of barely-intersecting orbits around the Sun. The orbits do still intersect though, so the instability would slowly grow.

So my question is a little multifaceted - Could the interplanetary traffic become dense enough or interact enough with densely-populated lagrange regions to initiate a collisional cascade? How long would it take to go from just a slight increase in the background meteoroid threat to something that could shut down interplanetary travel long-term?

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    $\begingroup$ The thing about space is there is a lot of it. Hard to imagine how we could throw up enough hardware to Kessler-ize the solar system. $\endgroup$
    – Woody
    Commented Jul 6 at 19:35
  • $\begingroup$ Can I clarify, are you thinking "general ring of debris", or "debris drifting near really useful points only"? $\endgroup$ Commented Jul 6 at 20:46
  • $\begingroup$ I was thinking more along the lines of "debris near useful points and interrupting traffic" but wasn't sure if that would be possible without a whole ring of debris, because of how much space there is $\endgroup$
    – rhobot
    Commented Jul 6 at 23:23
  • $\begingroup$ The reason it's possible to get a dangerous amount of debris in LEO is that the orbital period is only an hour or so, so you re-encounter the same piece of debris again and again and again. A cycler orbit between Earth and Venus might take months to complete; that's a long time between encounters. $\endgroup$
    – Cadence
    Commented Jul 7 at 10:28
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    $\begingroup$ Didn't someone do exactly this a couple of billion years ago? Between Mars and Jupiter that is. Although it was about 1% of a planet's worth of material it didn't block any of our traffic so far. $\endgroup$
    – asdfex
    Commented Jul 8 at 10:03

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I think not. At least, not without throwing up planetary-scale of mass up there.

Firstly, if we think about Hohmann-style transfers between, eg, between Earth and Venus, then there's a lot of space. This includes cyclers, which essentially use small burns at either end to hop from one such transfer to another (potentially doing "waiting" orbits around the Sun to get back in sync when needed). Each such transfer is an elliptical orbit, and each transfer window corresponds to a different longitude of the ascending node. Together it means that things on such orbit will span the whole region of space between the orbits of Earth and Venus. That's a lot of space for stuff to get lost in. For comparison, the asteroid belt has a mass ~$10^{20}$kg and is essentially completely transparent to probes we send through it. No Kessler syndrome there unless we dismantle Venus and spread it out - but at that point Venus would be a lot less desirable as a destination.

But the OP talks about specific useful points too, like the Lagrange points. The useful Lagrange points are L1 and L2, because they provide valleys through which it's possible to escape planets' gravitational potential well without paying the full energy cost. (This is most easily seen in a co-rotating frame commonly used for 3-body problems, eg this book). These points, however, are unstable. So things placed there will drift out without active station keeping. Let's try and get a rough idea of the scale at which Lagrange points might start getting too crowded.

The JWST is at the Earth-Sun L2 point and does station keeping every ~20 days. Lets say that if it misses a few of those in a row then it completely "exits" the vicinity of the Lagrange point, ie, we can generously give the stability lifetime of objects near Earth-Sun L2 at ~$100$ days. We can also estimate the radius of this vicinity by where the Lagrange point linearized dynamics are a better approximation of the full 3-body dynamics than either of the 2-body systems. This gives us the "radius of vicinity" of L2 as being of the order of half the Hill radius, so in this case ~$700,000$km (which is in fact less than the radius of JWST's "orbit" around L2). Finally, let's say that to make collisions rare we want to make sure that everything around L2 is at least $20$ days from crashing into each other (JWST period between orbital corrections), even if their relative velocities were directly pointing them into each other (which will very rarely be the case). Again, going back to JSWT, we have that the station keeping burns are about $2$m/s per year, which gives us a scale for relative velocities. From this we get each object around L2 ought to be at least $3000$km away from everything else to prevent collisions. Let's further say that each object we put there weights about $1$ tonne.

Putting all these (back-of-the-envelope) guesstimates together, we're safe until we're putting on the order of a hundred thousand tonnes per day into the vicinity of the Earth-Sun L2 point. I'm not claiming that this is an accurate measure by any mean, but it ought to give a rough idea of the scales involved.

EDIT

Here is another approach at guesstimating when the Earth-Sun L2 point might get so crowded that a Kessler syndrome is a problem. Let's start by noting that we don't have a Kessler syndrome with LEO, but it is a risk - so we can take that as our threshold. It's reasonable to assume that the risk of a Kessler syndrome scales with the density of objects and inversely proportional to their orbital period (because the more orbits they do in a given time interval, the more occasion they have to crash into something).

LEO orbits are roughly from 200km to 2000km in altitude, and take about 90min. As above, we can consider "orbits" around L2 to occupy a region of space some 700,000km in radius and orbits take on the order of a month.

This implies that we need ~200 million times more objects around L2 than we currently have in LEO to have the same level of risk. But, as stated above, "orbits" around L2 have a lifetime of only a few months, so we have to keep putting stuff there for the risk level to stay the same. How much? (Very) roughly 2 million times more objects than are currently in LEO per day. This is compatible with the previous guesstimate if each object currently in LEO is 50kg - low for a satellite, big for space junk, and in the right ballpark for something in the middle. Kind of surprised at how closely the answers align considering how different the approaches are.

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  • $\begingroup$ I was trying work out if light pressure was sufficient for breaking the "long term" aspect :) $\endgroup$ Commented Jul 8 at 5:13
  • $\begingroup$ I should think that the timescale at which light pressure matters is orders of magnitude greater than the stability of pseudo-orbits around L1 or L2 in practice $\endgroup$ Commented Jul 8 at 12:28
  • $\begingroup$ Oh you're absolutely right. I was going up a very wrong tree. $\endgroup$ Commented Jul 8 at 18:21

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