They did an n-body simulation based on the known Keplerian orbital elements. That's exactly what you're asking for, right?

Also, the formalism is the standard way astrophysicists understand collisions in gases or galaxies, and it works surprisingly well, especially when there are large numbers of "particles". There may be a few assumptions about the velocity distribution, but usually those are mild and only affect the results by less than an order of magnitude.

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MarkusQ 2 days ago | parent [-]

"N-body simulation" doesn't mean what it's normally taken to mean here.

And the colliding gasses models have the huge assumption of random/thermal motion. These satellites are in carefully designed orbits; they aren't going to magically thermalize if left unmonitored for three days.

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queuebert 2 days ago | parent | next [-]

That's why I mentioned the assumption about the velocity distribution. Sure, the velocities aren't Maxwell-Boltzmann, but that doesn't matter too much for getting a sense of the scale of the issue. The way an astrophysicist thinks (I am one) is that if we make generous assumptions and it turns out to not be a problem, then it definitely isn't a problem. Here they have determined it might be a problem, so further study is warranted. It's also a scientist strategy to publish something slightly wrong to encourage more citations.

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Sanzig 2 days ago | parent | prev | next [-]

Well, sure, they won't be thermally random, but they will be significantly perturbed from their nominal orbits, particularly at the lower orbital altitudes.

Solar flares cause atmospheric upwelling, so drag dramatically increases during a major solar flare. And the scenario envisioned in the paper is basically a Carrington-level event, so this effect would be extreme.

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SiempreViernes 2 days ago | parent | prev [-]

The current "carefully designed orbits" has a starlink sat doing a collision avoidance manuever every 1.8 minutes on average according to their filing for December 1 to May 31 of this year.

	▲	MarkusQ a day ago \| parent [-]
		Interestingly, the report from which they draw that number is one of the few that they cite but do not link to. Here's a link: https://www.scribd.com/document/883045105/SpaceX-Gen1-Gen2-S... It also notes that the collision odds on which SpaceX triggers such maneuvers is 333 times more conservative than the industry standard. Were that not the case (and they were just using the standard criterion) one might naively assume that they would only be doing a maneuver every ten hours or so. But collision probabilities are not linear, they follow a power law distribution so in actuality they would only be doing such maneuvers every few days. It is disingenuous to the point of dishonesty to use SpaceX's abundance of caution (or possibly braggadocios operational flex) as evidence that the risk is greater than it actually is.