Starlink: Collision risks

[su27k]

A long twitter thread about close approaches between Starlink and other objects:

https://twitter.com/ProfHughLewis/status/1436321009242710022

The important part is this:

In August, @pbdes reported that @SpaceX had made 2219 collision avoidance manoeuvres in the six months to the end of May 2021 [13/n]

If we look at the distribution of the maximum collision probability predicted by SOCRATES for #Starlink conjunctions we can see an average of 77.4 conjunctions per week for the six months to the end of May 2021 (excludes Starlink-on-Starlink) [14/n]

This is equivalent to 2012.3 conjunctions over the  period, on average, which represents about one-third of all the conjunctions < 1 km involving one Starlink. [15/n]

Keeping in mind the limited accuracy of predictions made using public TLEs, it appears as though the number of conjunctions for which the maximum collision probability is > 1-in-100,000 provides an estimate of the number of collision avoidance manoeuvres (+/- 10% or so). [16/n]

Looking at the most recent 3-month period, there were 130.5 conjunctions per week, on average, where the maximum collision probability was predicted to be > 1-in-100,000 (again, about one-third of all conjunctions < 1 km), suggesting a further 1696 manoeuvres. [17/n]

The approach to orbital space safety for #Starlink appears to be quite cautious & is likely enabled by the high specific impulse of the low-thrust propulsion system, which mean that avoidance manoeuvres only have a small effect on overall propellant mass. [18/n]

Combined with some flexibility in the orbits needed to provide the communications service, Starlinks are able to avoid relatively low-risk encounters with debris & other operators. This approach has led to the safety of the system despite the growing system size. [19/n]

This confirms SpaceX is indeed using the very conservative 1 in 100,000 collision probability to determine if they'll perform collision avoidance maneuvers.

[eeergo]

This confirms SpaceX is indeed using the very conservative 1 in 100,000 collision probability to determine if they'll perform collision avoidance maneuvers.

Conservative?

1e-5 probability means that, with just over 1500 satellites currently and 2220 x 2 = 4440 conjunctions/year exceeding that threshold in the first half of this year (during which time more than half of the currently orbiting Starlinks were launched, which means the situation was not in a steady state and the actual number of conjunctions with the current amount of Starlinks should be around 10,000 conjunctions/year), you'd most likely get a catastrophic collision in 10 years, which would likely generate a rapid cascade effect considering the shells are very thin and debris couldn't be tracked fast enough to notify all satellites repeatedly passing through the debris cloud. If they set the bar any lower, they'd be all but guaranteed to initiate that process before 2030.

This doesn't take into account inherent inaccuracies in TLEs CDMs (<1km but unknown how much better) and other tracking of non-Starlink conjunctions. As the tweet shows there are 3000 conjunctions at less than 1 km a week involving at least a Starlink (156,000 a year), and TLEs often have that inaccuracy already built in. Let's remember Starlink "automated" approach relies on TLEs CDMs for their maneuvers, which have uncertainties even if lower than TLEs.

Of course, 1500 satellites is an eigth of the initial megaconstellation's proposed size of 12,000. Then, the 1e-5 collision probability threshold for maneuvering would mean a likely collision in slightly over a year if they didn't maneuver, again without uncertainties smudging the picture. With the full 42,000-strong system, not taking into account competitors or increased number of other satellites in Starlink's orbital regime, the 1e-5 threshold would imply a collision (followed swiftly by a myriad of others, let's remember - there's no room for error here) every trimester.

One wonders what happens with conjunctions with 4e-6 probability though, for which their "conservative" threshold wouldn't apply, and which imply collision likelihood frequencies twice rarer, yet unmitigated - i.e. every 2 years for a "basic" Starlink system, and every 6 months for a complete system.

[envy887]

This confirms SpaceX is indeed using the very conservative 1 in 100,000 collision probability to determine if they'll perform collision avoidance maneuvers.

Conservative?

1e-5 probability means that, with just over 1500 satellites currently and 2220 x 2 = 4440 conjunctions/year exceeding that threshold in the first half of this year (during which time more than half of the currently orbiting Starlinks were launched, which means the situation was not in a steady state and the actual number of conjunctions with the current amount of Starlinks should be around 10,000 conjunctions/year), you'd most likely get a catastrophic collision in 10 years, which would likely generate a rapid cascade effect considering the shells are very thin and debris couldn't be tracked fast enough to notify all satellites repeatedly passing through the debris cloud. If they set the bar any lower, they'd be all but guaranteed to initiate that process before 2030.

This doesn't take into account inherent inaccuracies in TLEs and other tracking of non-Starlink conjunctions. As the tweet shows there are 3000 conjunctions at less than 1 km a week involving at least a Starlink (156,000 a year), and TLEs often have that inaccuracy already built in. Let's remember Starlink "automated" approach relies on TLEs for their maneuvers. So there can be many other approaches which are not registered.

Of course, 1500 satellites is an eigth of the initial megaconstellation's proposed size of 12,000. Then, the 1e-5 collision probability threshold for maneuvering would mean a likely collision in slightly over a year if they didn't maneuver, again without uncertainties smudging the picture. With the full 42,000-strong system, not taking into account competitors or increased number of other satellites in Starlink's orbital regime, the 1e-5 threshold would imply a collision (followed swiftly by a myriad of others, let's remember - there's no room for error here) every trimester.

One wonders what happens with conjunctions with 4e-6 probability though, for which their "conservative" threshold wouldn't apply, and which imply collision likelihood frequencies twice rarer, yet unmitigated - i.e. every 2 years for a "basic" Starlink system, and every 6 months for a complete system.

I think "a rapid cascade effect" is exceptionally unlikely in the event of a collision, for a number of reasons.

Also, the probability for each event is different. You can't assume that events with a probability below the threshold of 1/100,000 are all actually 1/100,000 when they are really in some distribution ranging from 1/100,000 all the way to exactly 0.

[dondar]

This confirms SpaceX is indeed using the very conservative 1 in 100,000 collision probability to determine if they'll perform collision avoidance maneuvers.

Conservative?

1e-5 probability means that, with just over 1500 satellites currently and 2220 x 2 = 4440 conjunctions/year exceeding that threshold in the first half of this year (during which time more than half of the currently orbiting Starlinks were launched, which means the situation was not in a steady state and the actual number of conjunctions with the current amount of Starlinks should be around 10,000 conjunctions/year), you'd most likely get a catastrophic collision in 10 years, which would likely generate a rapid cascade effect considering the shells are very thin and debris couldn't be tracked fast enough to notify all satellites repeatedly passing through the debris cloud. If they set the bar any lower, they'd be all but guaranteed to initiate that process before 2030.

This doesn't take into account inherent inaccuracies in TLEs and other tracking of non-Starlink conjunctions. As the tweet shows there are 3000 conjunctions at less than 1 km a week involving at least a Starlink (156,000 a year), and TLEs often have that inaccuracy already built in. Let's remember Starlink "automated" approach relies on TLEs for their maneuvers. So there can be many other approaches which are not registered.

Of course, 1500 satellites is an eigth of the initial megaconstellation's proposed size of 12,000. Then, the 1e-5 collision probability threshold for maneuvering would mean a likely collision in slightly over a year if they didn't maneuver, again without uncertainties smudging the picture. With the full 42,000-strong system, not taking into account competitors or increased number of other satellites in Starlink's orbital regime, the 1e-5 threshold would imply a collision (followed swiftly by a myriad of others, let's remember - there's no room for error here) every trimester.

One wonders what happens with conjunctions with 4e-6 probability though, for which their "conservative" threshold wouldn't apply, and which imply collision likelihood frequencies twice rarer, yet unmitigated - i.e. every 2 years for a "basic" Starlink system, and every 6 months for a complete system.

so much emotions here.

 "conjunctions" are not a thing within starlink system.
 They are events of possible orbit intersection with other satelites (or for now between rising starlinks from different batches.)
The "fall" in conjuctions reported by Lewis indeed directly correlates with the number of rising starlink in intersecting planes.
SOCRAT counts also satellites in formation as a collision candidates (Because the system is simplified, read STUPID).

The probabilities even for the conjuctions with min 0.1km can be still in the range off 1e-7. And there are many of those.

I will not go into "estimated numbers". Or what even SOCRAT calculates.

Right now Starlink sit strongly under 1% per year for their system. Totally. Please don't comment, especially "doom" without proper numbers or ability to defend scientifically your opinion.

[eeergo]

I think "a rapid cascade effect" is exceptionally unlikely in the event of a collision, for a number of reasons.

Also, the probability for each event is different. You can't assume that events with a probability below the threshold of 1/100,000 are all actually 1/100,000 when they are really in some distribution ranging from 1/100,000 all the way to exactly 0.

Could you list some of those reasons? Common sense would indicate hundreds or thousands of satellites at roughly the same orbital height but mostly differing velocity vectors (except those in the same plane) would be exceptionally vulnerable to a debris field squarely intersecting that height - especially if centered on it.

Regarding the distribution: sure, that's why my numbers are a lower limit simplification, because 1e-5 is the threshold for action. There will be much higher probability conjunctions im the distribution too, but even taking a "monochromatic" probability at 1e-5 you can see the results of not maneuvering, which is why the threshold is not "conservative" at all.

The issue here aren't conjunctions below 1e-5 (hence needing no avoidance maneuvers, even if as shown they will need to lower the threshold if the constellation reaches anywhere close to its planned total size). The issue is the distribution over 1e-5 (and well below 1, to be clear) if left alone, or the part of the distribution just under 1e-5 (and hence necessitating no maneuvers by the current standard). There's also the question of TLE CDM uncertainty which SpaceX uses to determine the probabilities (<1 km but unknown how much better).


EDIT: By the way, realizing people might not have eead the referenced thread and where the 2200 CAMs figure might come from: https://mobile.twitter.com/pbdes/status/1429778141506060289

[Redclaws]

I think "a rapid cascade effect" is exceptionally unlikely in the event of a collision, for a number of reasons.

Also, the probability for each event is different. You can't assume that events with a probability below the threshold of 1/100,000 are all actually 1/100,000 when they are really in some distribution ranging from 1/100,000 all the way to exactly 0.

Could you list some of those reasons? Common sense would indicate hundreds or thousands of satellites at roughly the same orbital height but mostly differing velocity vectors (except those in the same plane) would be exceptionally vulnerable to a debris field squarely intersecting that height - especially if centered on it.

Regarding the distribution: sure, that's why my numbers are a lower limit simplification, because 1e-5 is the threshold for action. There will be much higher probability conjunctions im the distribution too, but even taking a "monochromatic" probability at 1e-5 you can see the results of not maneuvering, which is why the threshold is not "conservative" at all.

The issue here aren't conjunctions below 1e-5 (hence needing no avoidance maneuvers, even if as shown they will need to lower the threshold if the constellation reaches anywhere close to its planned total size). The issue is the distribution over 1e-5 (and well below 1, to be clear) if left alone, or the part of the distribution just under 1e-5 (and hence necessitating no maneuvers by the current standard). There's also the question of TLE uncertainty which SpaceX uses to determine the probabilities (~1 km).

I’m not in a position to dispute the numbers you’re using, but I’d ask you a question.  The relatively simple numbers you’re putting up seem to clearly show doom for this constellation - totally unworkable levels of collisions, etc - so why do the regulators think it’s ok?  It seems reasonably clear the real numbers do not work out as you’re describing - the regulators are competent and can do basic math.  So…

[eeergo]

so much emotions here.

Many.

"conjunctions" are not a thing within starlink system.They are events of possible orbit intersection with other satelites (or for now between rising starlinks from different batches.)

They are as in any satellite. Between different heights and at the same height alike. They are reportedly minimized automatically based on SpaceX tracking -of which we know little or nothing about, but let's take it at face value and say they're not an issue (even if they clearly exist as shown by the SOCRATES data). There are still plenty of conjunctions <1 km with other objects as shown in the Twitter thread, and within those many that SpaceX judges worthy of executing a CAM for (~10000/year currently).

SOCRAT counts also satellites in formation as a collision candidates (Because the system is simplified, read STUPID).

What are you talking about? You're calling SOCRATES stupid?

The probabilities even for the conjuctions with min 0.1km can be still in the range off 1e-7. And there are many of those.

They can. I did not conflate both. I did take however SpaceX's CAM numbers, and they state only events with probability >1e-5 require action, so all those CAMs are over 1e-5. All 2200 of them. Some much higher probably (continuous distribution from 1e-5 all the way to 1). I did some elementary calculations for longer times and/or satellite numbers.

Right now Starlink sit strongly under 1% per year for their system. Totally. Please don't comment, especially "doom" without proper numbers or ability to defend scientifically your opinion.

Excuse me, where are your proper numbers? You just said you'll not go into SOCRATES data? Neither basic multiplication because it's "estimated"? I explicitly showed my work, you're pulling a 1% out of your hat (seriously, where in the world do you deduce that from? By their own admission they did 2200 CAMs in 6 months when Starlink had half the satellites it has now, and now it has 1500 birds...). Where exactly are my extrapolations of their own CAM numbers and probability thresholds wrong?

Talk about emotional responses...

[eeergo]

I think "a rapid cascade effect" is exceptionally unlikely in the event of a collision, for a number of reasons.

Also, the probability for each event is different. You can't assume that events with a probability below the threshold of 1/100,000 are all actually 1/100,000 when they are really in some distribution ranging from 1/100,000 all the way to exactly 0.

Could you list some of those reasons? Common sense would indicate hundreds or thousands of satellites at roughly the same orbital height but mostly differing velocity vectors (except those in the same plane) would be exceptionally vulnerable to a debris field squarely intersecting that height - especially if centered on it.

Regarding the distribution: sure, that's why my numbers are a lower limit simplification, because 1e-5 is the threshold for action. There will be much higher probability conjunctions im the distribution too, but even taking a "monochromatic" probability at 1e-5 you can see the results of not maneuvering, which is why the threshold is not "conservative" at all.

The issue here aren't conjunctions below 1e-5 (hence needing no avoidance maneuvers, even if as shown they will need to lower the threshold if the constellation reaches anywhere close to its planned total size). The issue is the distribution over 1e-5 (and well below 1, to be clear) if left alone, or the part of the distribution just under 1e-5 (and hence necessitating no maneuvers by the current standard). There's also the question of TLE uncertainty which SpaceX uses to determine the probabilities (~1 km).

I’m not in a position to dispute the numbers you’re using, but I’d ask you a question.  The relatively simple numbers you’re putting up seem to clearly show doom for this constellation - totally unworkable levels of collisions, etc - so why do the regulators think it’s ok?  It seems reasonably clear the real numbers do not work out as you’re describing - the regulators are competent and can do basic math.  So…

As you say, it's basic math, and there's no way around it unless you believe in impeccable tracking and constellation control over many decades. Now you want me to read into politicians' minds, and that my friend, is just asking for miracles. But I do know it's not the first time gold rushes happened, either in space or on the ground - rarely because they made long-term sense.


On the other hand, they may be expecting SpaceX to reduce tracking errors with their own 'Space Fences', or lowering the threshold an order of magnitude as Starlink grows, or some software wizardry that hopefully will solve space traffic control congestion in a few years' time because it'll become highly error-free and automated, or any number of 'let's wait and see's.


I was taking issue at calling 1e-5 "conservative" with the numbers of conjunctions, CAMs and satellites already at hand. Not claiming some law of Nature forces this to become doomsday - but current numbers just aren't flattering, and already leave little room for error: human, systematic or otherwise.

[envy887]

I think "a rapid cascade effect" is exceptionally unlikely in the event of a collision, for a number of reasons.

Also, the probability for each event is different. You can't assume that events with a probability below the threshold of 1/100,000 are all actually 1/100,000 when they are really in some distribution ranging from 1/100,000 all the way to exactly 0.

Could you list some of those reasons? Common sense would indicate hundreds or thousands of satellites at roughly the same orbital height but mostly differing velocity vectors (except those in the same plane) would be exceptionally vulnerable to a debris field squarely intersecting that height - especially if centered on it.

After a collision, approximately none of the fragments have exactly the same velocity as the original satellite. The impact is impulsive, which means they are now in new orbits that intersect the original only at most twice per orbit. That means the opportunity to re-collide with another satellite in the shell happens at most twice per 90 minutes.

If they got an infinite number of orbits, they would eventually collide... but they won't have that chance. A few things start happening. For one, most of the fragment will lose energy and velocity, and end up with a lower perigee. That exposes them to more drag, which quickly lowers apogee out of the shell, so they no longer intersect at all. Fragments kicked higher also start to drag. They stick around a little longer, but at the 550 km level drag is pretty high and only the tail end of the distribution gets enough energy to stick around a while.

Also, in a few days, the trackable objects will get added to the catalog, and the rest of the constellation will start maneuvering to avoid them. So the big (most dangerous) fragments only get a few tens of shots at causing more damage. And Starlinks aren't big enough to make a lot of big fragments, perhaps a few tens as well. All these factors reduce the number of debris conjunctions after a collision, which reduces the probability of a cascade.

Regarding the distribution: sure, that's why my numbers are a lower limit simplification, because 1e-5 is the threshold for action. There will be much higher probability conjunctions im the distribution too, but even taking a "monochromatic" probability at 1e-5 you can see the results of not maneuvering, which is why the threshold is not "conservative" at all.

1e-5 is the ceiling. There will be no conjunctions above that, because those always result in maneuvers to place them below the threshold. So there will be some at 1e-6, but none at 1e-4. There will also probably be some at 1e-7, and maybe a few at 1e-8 or 1e-9 (passes within an arbitrary distance aren't necessarily anywhere near the 1e-5 threshold, depending on uncertainty in the orbits and the geometry of the pass). You need the distribution of event probabilities (or at least the mean event probability?) to compute the overall probability of at least 1 collision in a given timeframe.

[envy887]

On the other hand, they may be expecting SpaceX to reduce tracking errors with their own 'Space Fences', or lowering the threshold an order of magnitude as Starlink grows, or some software wizardry that hopefully will solve space traffic control congestion in a few years' time because it'll become highly error-free and automated, or any number of 'let's wait and see's.

SpaceX doesn't need a "Space Fence" for their own satellites. They have highly accurate data from the INS/GPS/star trackers on their satellites and can use this to avoid Starlink fratricide. Starlink on other satellite and Starlink on debris conjunctions are the main concerns, but I'm not sure that anyone realistically expects SpaceX to start tracking everything else in orbit.

[su27k]

This confirms SpaceX is indeed using the very conservative 1 in 100,000 collision probability to determine if they'll perform collision avoidance maneuvers.

Conservative?

1e-5 probability means that, with just over 1500 satellites currently and 2220 x 2 = 4440 conjunctions/year exceeding that threshold in the first half of this year (during which time more than half of the currently orbiting Starlinks were launched, which means the situation was not in a steady state and the actual number of conjunctions with the current amount of Starlinks should be around 10,000 conjunctions/year), you'd most likely get a catastrophic collision in 10 years, which would likely generate a rapid cascade effect considering the shells are very thin and debris couldn't be tracked fast enough to notify all satellites repeatedly passing through the debris cloud. If they set the bar any lower, they'd be all but guaranteed to initiate that process before 2030.

This doesn't take into account inherent inaccuracies in TLEs and other tracking of non-Starlink conjunctions. As the tweet shows there are 3000 conjunctions at less than 1 km a week involving at least a Starlink (156,000 a year), and TLEs often have that inaccuracy already built in. Let's remember Starlink "automated" approach relies on TLEs for their maneuvers. So there can be many other approaches which are not registered.

Of course, 1500 satellites is an eigth of the initial megaconstellation's proposed size of 12,000. Then, the 1e-5 collision probability threshold for maneuvering would mean a likely collision in slightly over a year if they didn't maneuver, again without uncertainties smudging the picture. With the full 42,000-strong system, not taking into account competitors or increased number of other satellites in Starlink's orbital regime, the 1e-5 threshold would imply a collision (followed swiftly by a myriad of others, let's remember - there's no room for error here) every trimester.

One wonders what happens with conjunctions with 4e-6 probability though, for which their "conservative" threshold wouldn't apply, and which imply collision likelihood frequencies twice rarer, yet unmitigated - i.e. every 2 years for a "basic" Starlink system, and every 6 months for a complete system.

1. Yes, conservative, because SpaceX said so, and now it was independently confirmed by a space debris expert.

2. You're under the mistaken impression that a collision avoidance threshold of 1e-5 means after the collision avoidance maneuver the probability of collision (Pc) is only reduced to 1e-5, that's not the case, as SpaceX explained in their FCC filing which is quoted here. In most cases, after the collision avoidance maneuver Pc is reduced to be lower than 1e-6. That filing also explained other reasons why what they're doing is conservative, for example they use 10m radius in their modeling of Starlink satellite, which is much larger than the actual satellite.

3. Starlink does not use TLEs for their automated collision avoidance system, this was explained in a FCC filing just a few days ago, see here, what they use is Conjunction Data Messages (CDM) from 18th SPCS.

4. And when 18th SPCS calculates conjunctions and issues CDMs, they most definitely does take inaccuracies in position and speed of tracked satellites into account. This is explained in the Spaceflight Safety Handbook for Satellite Operator, the term you're looking for is "covariance".

5. Dr. Hugh Lewis has stated multiple times that mega constellation like Starlink won't cause collision cascade reaction like you suggested (aka Kessler syndrome), see this tweet for example: https://twitter.com/ProfHughLewis/status/1387532062446456835

So unless you can back up your claims with some real math and simulations, I'm going to insist that "conservative" is the right word to use for the current constellation. Will the threshold need to be adjusted for bigger constellations? I don't know, maybe it will, but given on average each satellite is only doing 3 collision avoidance maneuvers every *year* right now, I don't see a lower threshold will present any difficulties.

[eeergo]

Could you list some of those reasons? Common sense would indicate hundreds or thousands of satellites at roughly the same orbital height but mostly differing velocity vectors (except those in the same plane) would be exceptionally vulnerable to a debris field squarely intersecting that height - especially if centered on it.

After a collision, approximately none of the fragments have exactly the same velocity as the original satellite. The impact is impulsive, which means they are now in new orbits that intersect the original only at most twice per orbit. That means the opportunity to re-collide with another satellite in the shell happens at most twice per 90 minutes.

That isn't the general case. It will depend on the geometry of the collision. Even for forward-scattered collisions, the distributions end up having a strong double-lobed distribution of resulting objects, with some reaching higher apogees, some lower, a scatter of inclinations, but most staying right around the original orbital altitude and inclination (see first attached image from FY-1C's ASAT test, where the collision was highly deboosting since the warhead was extremely slow compared to the satellite's orbital velocity). Then you get precession and orbital perturbations (solar, atmospheric, n-body) that will spread the debris cloud around in a few months' time, which is within the resulting debris' lifetimes in orbit (at the initial height, of course there will be those higher): an example is the spread of the Iridium-Kosmos debris clouds from tight distributions at their initial approximately 90-degree-apart respective orbits, and the homogeneous distribution some months later - see second and third attached images.

If they got an infinite number of orbits, they would eventually collide... but they won't have that chance. A few things start happening. For one, most of the fragment will lose energy and velocity, and end up with a lower perigee. That exposes them to more drag, which quickly lowers apogee out of the shell, so they no longer intersect at all. Fragments kicked higher also start to drag. They stick around a little longer, but at the 550 km level drag is pretty high and only the tail end of the distribution gets enough energy to stick around a while.

Orbital lifetimes for most objects at 550 km are on the order of months to years. Even decaying to lower orbits than the main shell's will take such a cloud uncomfortably close to other lower orbiting satellites, like incidentally the ISS.

Also, in a few days, the trackable objects will get added to the catalog, and the rest of the constellation will start maneuvering to avoid them. So the big (most dangerous) fragments only get a few tens of shots at causing more damage. And Starlinks aren't big enough to make a lot of big fragments, perhaps a few tens as well. All these factors reduce the number of debris conjunctions after a collision, which reduces the probability of a cascade.

I'm afraid this is just completely anumerical. They will take weeks if not months to catalog resulting debris, based on recent experiences with the Indian ASAT or several on-orbit collisions. Satellites won't be able to maneuver clear of the cloud, which will span a large range of altitudes (centered at the operational altitude) and soon start spreading in inclination (which the satellites cannot significantly impulsively change). As you say, then there's the issue of trackability: a small untrackable object under about 10 cm but larger than 1 cm can still cause a lot of damage, yet they are untrackable - and an orbital collision has the peculiarity of creating lots of those. See here: https://conference.sdo.esoc.esa.int/proceedings/neosst1/paper/399 (10% of potentially catastrophically-damaging debris is trackable).
All these issues are valid currently. With an order of magnitude more active satellites *at the same height* this is a substantially non-linearly worsening challenge.

Regarding the distribution: sure, that's why my numbers are a lower limit simplification, because 1e-5 is the threshold for action. There will be much higher probability conjunctions im the distribution too, but even taking a "monochromatic" probability at 1e-5 you can see the results of not maneuvering, which is why the threshold is not "conservative" at all.

1e-5 is the ceiling. There will be no conjunctions above that, because those always result in maneuvers to place them below the threshold. So there will be some at 1e-6, but none at 1e-4. There will also probably be some at 1e-7, and maybe a few at 1e-8 or 1e-9 (passes within an arbitrary distance aren't necessarily anywhere near the 1e-5 threshold, depending on uncertainty in the orbits and the geometry of the pass). You need the distribution of event probabilities (or at least the mean event probability?) to compute the overall probability of at least 1 collision in a given timeframe.

Finally I understand what you're referring to, I think - and I'm afraid you're misunderstanding the dynamics here.
You're assuming SpaceX has kind of a color-coded board with all satellites in green (probability of collision close to 0), and slowly some are becoming progressively redder, until reaching bright red (probability of 1). Once they become orange though, they have the ability to slightly maneuver them so that none gets beyond a certain tone of orange (1e-5) which they set as threshold. That indeed would be the ideal situation. It *may* be for inter-Starlink conjunctions, because they have their own GNSS packages, as you mention in your following post, and that *may* be enough to approach that idealization - we'll have to take their word for it, which is not ideal anyway.

Unfortunately, that's not the case for the rest of objects, simply because of the innacuracies of the TLEs and the non-deterministic refinement of tracking. You don't get continuous perfect tracking that allows you to steer clear as soon as the collision probability reaches 1e-5 and not beyond. You get more or less frequent updates with "jumps" in the parameters, and most of those will instantaneously change the collision probability by a lot. Most will stay very low or 0, but some will jump well above 1e-5 immediately, with a distribution that rarely reaches 1 (or 1e-1 for that matter), yet will include lots of 1e-4, 5e-3, 1e-3 and so forth. It's the fundamental difference between a continuous, well-sampled process with low uncertainties, and a discrete, undersampled process with high uncertainties.

Their proverbial color-coded board would be alternating all kinds of colors with each tracking update, and the "magic orange tone" of 1e-5 will be the threshold over which they'll do something about it - but won't be the reddest the board gets, with some points in the board suddenly turning dark orange just after being clear green.

Once you have a collision though, as I mentioned above, all bets are off regarding Starlink-on-Starlink: then Starlink on fragement-of-Starlink conjunctions are no longer GNSS-defined and will be subject to the same limitations.

[eeergo]

This confirms SpaceX is indeed using the very conservative 1 in 100,000 collision probability to determine if they'll perform collision avoidance maneuvers.

Conservative?

1e-5 probability means that, with just over 1500 satellites currently and 2220 x 2 = 4440 conjunctions/year exceeding that threshold in the first half of this year (during which time more than half of the currently orbiting Starlinks were launched, which means the situation was not in a steady state and the actual number of conjunctions with the current amount of Starlinks should be around 10,000 conjunctions/year), you'd most likely get a catastrophic collision in 10 years, which would likely generate a rapid cascade effect considering the shells are very thin and debris couldn't be tracked fast enough to notify all satellites repeatedly passing through the debris cloud. If they set the bar any lower, they'd be all but guaranteed to initiate that process before 2030.

This doesn't take into account inherent inaccuracies in TLEs and other tracking of non-Starlink conjunctions. As the tweet shows there are 3000 conjunctions at less than 1 km a week involving at least a Starlink (156,000 a year), and TLEs often have that inaccuracy already built in. Let's remember Starlink "automated" approach relies on TLEs for their maneuvers. So there can be many other approaches which are not registered.

Of course, 1500 satellites is an eigth of the initial megaconstellation's proposed size of 12,000. Then, the 1e-5 collision probability threshold for maneuvering would mean a likely collision in slightly over a year if they didn't maneuver, again without uncertainties smudging the picture. With the full 42,000-strong system, not taking into account competitors or increased number of other satellites in Starlink's orbital regime, the 1e-5 threshold would imply a collision (followed swiftly by a myriad of others, let's remember - there's no room for error here) every trimester.

One wonders what happens with conjunctions with 4e-6 probability though, for which their "conservative" threshold wouldn't apply, and which imply collision likelihood frequencies twice rarer, yet unmitigated - i.e. every 2 years for a "basic" Starlink system, and every 6 months for a complete system.

1. Yes, conservative, because SpaceX said so, and now it was independently confirmed by a space debris expert.

2. You're under the mistaken impression that a collision avoidance threshold of 1e-5 means after the collision avoidance maneuver the probability of collision (Pc) is only reduced to 1e-5, that's not the case, as SpaceX explained in their FCC filing which is quoted here. In most cases, after the collision avoidance maneuver Pc is reduced to be lower than 1e-6. That filing also explained other reasons why what they're doing is conservative, for example they use 10m radius in their modeling of Starlink satellite, which is much larger than the actual satellite.

3. Starlink does not use TLEs for their automated collision avoidance system, this was explained in a FCC filing just a few days ago, see here, what they use is Conjunction Data Messages (CDM) from 18th SPCS.

4. And when 18th SPCS calculates conjunctions and issues CDMs, they most definitely does take inaccuracies in position and speed of tracked satellites into account. This is explained in the Spaceflight Safety Handbook for Satellite Operator, the term you're looking for is "covariance".

5. Dr. Hugh Lewis has stated multiple times that mega constellation like Starlink won't cause collision cascade reaction like you suggested (aka Kessler syndrome), see this tweet for example: https://twitter.com/ProfHughLewis/status/1387532062446456835

So unless you can back up your claims with some real math and simulations, I'm going to insist that "conservative" is the right word to use for the current constellation. Will the threshold need to be adjusted for bigger constellations? I don't know, maybe it will, but given on average each satellite is only doing 3 collision avoidance maneuvers every *year* right now, I don't see a lower threshold will present any difficulties.

1- Ok then, if they say so we must all shut up and revere them. Experts have been saying all sorts of things regarding Starlink and you've been consistently and openly dissing them. But suddenly one expresses a favorable opinion *for the current situation* (as my numbers showed, 1e-5 will give you 10 years of clean operations for a thousand satellites, even if no maneuvers took place) and they get all authoritative in your view.

2- I'm doing no such thing. I'm noting TLEs have uncertainties on the order of km, and most if not all the POCs>1e-5 need that kind of precision at minimum. Obviously if they perform a maneuver they're going to minimize the POC as much as they can, and with the available uncertainties 1e-6 is the minimum they can be confident they did something (positive) about it. The modelling of satellites as "spherical cows" with diameter equal to the satellite's largest axis is SOP in space debris management, as you can't be certain of the relative attitude at closest approach. Starlink v1.0's array is around 10 m long, so there you go.

3/4- Evidently they take uncertainties into account, through covariance matrices or any other method to do so - yet sizeable uncertainties exist in the first place, and you can't get around them, just mitigate their smearing effect to *statistically* avoid running into more trouble through them than you're running away from. One point I did learn with your remark about CDMs is that these Messages have **lower** uncertainties than run-of-the-mill TLEs, which is reasonable considering no meaningful prediction could be made if your minimum uncertainty is on the km scale. This means that the uncertainty smearing is smaller than I estimated before, and I have corrected that from my previous posts - yet it was an additional factor to the numbers I shared, not a basing assumption: those are still valid, since the hard number of CAMs are the end result of all the CDM-derived analysis.

5- There are plenty of experts that point out how we're already into Kessler dynamics - just that they aren't, and never were going to be, happening in a few hours' time like in Hollywood movies (think Gravity). You're grossly misrepresenting Prof Lewis' words by the way:

https://twitter.com/ProfHughLewis/status/1336584183783837696
https://twitter.com/ProfHughLewis/status/1304426186320347138
https://twitter.com/ProfHughLewis/status/1385535670094008326
https://twitter.com/ProfHughLewis/status/1385537020789989378

He's referring to immediate obliteration of the shell. His last tweet refers to the *current* environment below 600 km. But of course you're looking for slogans, not for nuanced scientific debate, for which you already showed your disdain plenty of times.

6- You're free to consider it as conservative as you want, the numbers are what they are. Plus: nyet, those numbers of 3 per satellite-year are for around 800 satellites. You don't have data to say how many they're performing now with 1500, although it's probably around 10. Still, that sounds like a small number until you realize that's a statistical process we're talking about, and the absolute numbers are big, ensuring probability will take advantage of any mistake: around ten thousand a year with a 10th of the initial constellation built up, and a non-linear increase Prof Lewis is showing in SOCRATES data. A complete minimal (12000) system will have millions of conjunctions a year and similar orders of magnitudes of CAMs. If we consider smooth nominal operations forever, everything is and will be fine obviously - here we're talking about uncertainties, mistakes or oversights, and their consequences.

As for the simulations: please do so yourself before asking others to develop dissertation-grade work for you. I'm taking real-world number disclosed by SpaceX themselves and showing what they mean mathematically for different degrees of extrapolation. You're misconstruing an expert's words stripping them of their nuances and twisting the concluding message in order to advance your agenda, as you've done before most notoriously with Dr McDowell's points

[su27k]

1- Ok then, if they say so we must all shut up and revere them. Experts have been saying all sorts of things regarding Starlink and you've been consistently and openly dissing them. But suddenly one expresses a favorable opinion *for the current situation* (as my numbers showed, 1e-5 will give you 10 years of clean operations for a thousand satellites, even if no maneuvers took place) and they get all authoritative in your view.

If an expert says things contradicting what SpaceX says, then there's a different of opinion and we will need further analysis to see who's right. But if both expert and SpaceX says the same thing, then there's much higher likelihood of them being right, high enough to override some opinion from someone who clearly doesn't know how collision avoidance works in the first place.

And yes, I very much like to see expert "expresses a favorable opinion" for Starlink, especially one who has less favorable opinion before, but has now changed his opinion based on fact, which is what everybody should be doing. Nobody is stopping you from quoting other expert who has less favorable opinion, if you can find them.

2- I'm doing no such thing. I'm noting TLEs have uncertainties on the order of km, and most if not all the POCs>1e-5 need that kind of precision at minimum. Obviously if they perform a maneuver they're going to minimize the POC as much as they can, and with the available uncertainties 1e-6 is the minimum they can be confident they did something (positive) about it.

Ok, then you admit by using SpaceX's current collision avoidance strategy, they're no where near a collision every 10 years as you suggested?  In fact their safety projection is orders of magnitude better a collision every 10 years, that's what I call conservative.

The modelling of satellites as "spherical cows" with diameter equal to the satellite's largest axis is SOP in space debris management, as you can't be certain of the relative attitude at closest approach. Starlink v1.0's array is around 10 m long, so there you go.

And this SOP is conservative in case of Starlink because the solar array is very small in a sphere of 10 meters. It's only 3.2 meters wide, if you model it as a cylinder of 10 meters, its volume is only 80 m^3, it only occupies 2% of the total 4189 m^3 of a 10m sphere.

5- There are plenty of experts that point out how we're already into Kessler dynamics - just that they aren't, and never were going to be, happening in a few hours' time like in Hollywood movies (think Gravity).

"happening in a few hours' time like in Hollywood movies" is exactly what you're describing in your original comment: "which would likely generate a rapid cascade effect considering the shells are very thin and debris couldn't be tracked fast enough to notify all satellites repeatedly passing through the debris cloud.".

Usually for LEO objects we get TLEs in a few hours after launch, so by saying it happens so fast that we wouldn't have time to track it, you're literally suggesting it's like Gravity the movie.

You're grossly misrepresenting Prof Lewis' words by the way:

https://twitter.com/ProfHughLewis/status/1336584183783837696
https://twitter.com/ProfHughLewis/status/1304426186320347138
https://twitter.com/ProfHughLewis/status/1385535670094008326
https://twitter.com/ProfHughLewis/status/1385537020789989378

He's referring to immediate obliteration of the shell. His last tweet refers to the *current* environment below 600 km. But of course you're looking for slogans, not for nuanced scientific debate, for which you already showed your disdain plenty of times.

No, I didn't mispresenting his words, none of the tweets you quoted contradicts what I said, which is in his opinion, Starlink won't cause rapid cascade collisions like you described in your original comment, he literally said exactly this here:

https://twitter.com/ProfHughLewis/status/1380655591094374403
https://twitter.com/ProfHughLewis/status/1380658489421402115

6- You're free to consider it as conservative as you want, the numbers are what they are. Plus: nyet, those numbers of 3 per satellite-year are for around 800 satellites. You don't have data to say how many they're performing now with 1500, although it's probably around 10.

The twitter thread actually touched this later on:

https://twitter.com/ProfHughLewis/status/1436334166447173640

So with 1,500 satellites, they have about 130 conjunctions with Pc > 1 in 100,000 per week, that's 6,760 per year or 4.5 collision avoidance maneuver per year per satellite, so not much different from what I said.

Still, that sounds like a small number until you realize that's a statistical process we're talking about, and the absolute numbers are big, ensuring probability will take advantage of any mistake: around ten thousand a year with a 10th of the initial constellation built up, and a non-linear increase Prof Lewis is showing in SOCRATES data. A complete minimal (12000) system will have millions of conjunctions a year and similar orders of magnitudes of CAMs. If we consider smooth nominal operations forever, everything is and will be fine obviously - here we're talking about uncertainties, mistakes or oversights, and their consequences.

Actually I don't see why there would be a non-linear increase of conjunctions. There's no reason that conjunctions between Starlink and non-Starlink satellites would increase non-linearly if you only increase # of Starlink satellites while keeping # of non-Starlink satellites unchanged.

It appears non-linear in Dr. Hugh Lewis' chart because he's using dates as x-axis, so his curve is affected the launch cadence SpaceX is using, and this cadence itself is increasing non-linearly, for example there're 13 launches between 12/1/2020 to 5/31/2021, but only 9 between 6/1/2020 to 11/30/2020, this difference would be able to explain the non-linear trend he's seeing.

As for the simulations: please do so yourself before asking others to develop dissertation-grade work for you. I'm taking real-world number disclosed by SpaceX themselves and showing what they mean mathematically for different degrees of extrapolation. You're misconstruing an expert's words stripping them of their nuances and twisting the concluding message in order to advance your agenda, as you've done before most notoriously with Dr McDowell's points

I'm not the person who said Starlink will have a runaway collision cascade in 10 years, that's all on you, you said it you'll need to prove it.

And I'm not misconstruing anything, you're the one who's trying to make 1+1=3 even when expert said 1+1=2.

[envy887]

Could you list some of those reasons? Common sense would indicate hundreds or thousands of satellites at roughly the same orbital height but mostly differing velocity vectors (except those in the same plane) would be exceptionally vulnerable to a debris field squarely intersecting that height - especially if centered on it.

After a collision, approximately none of the fragments have exactly the same velocity as the original satellite. The impact is impulsive, which means they are now in new orbits that intersect the original only at most twice per orbit. That means the opportunity to re-collide with another satellite in the shell happens at most twice per 90 minutes.

That isn't the general case. It will depend on the geometry of the collision. Even for forward-scattered collisions, the distributions end up having a strong double-lobed distribution of resulting objects, with some reaching higher apogees, some lower, a scatter of inclinations, but most staying right around the original orbital altitude and inclination (see first attached image from FY-1C's ASAT test, where the collision was highly deboosting since the warhead was extremely slow compared to the satellite's orbital velocity). Then you get precession and orbital perturbations (solar, atmospheric, n-body) that will spread the debris cloud around in a few months' time, which is within the resulting debris' lifetimes in orbit (at the initial height, of course there will be those higher): an example is the spread of the Iridium-Kosmos debris clouds from tight distributions at their initial approximately 90-degree-apart respective orbits, and the homogeneous distribution some months later - see second and third attached images.

It is the general case, and your plots show it. The constellation shell is (effectively) a spherical surface. Anything intersecting but not continuously on that surface can only ever collide at the intersection points. Anything not on and not intersecting the surface cannot collide at all, even if it's orbiting nearby in an ominous-looking and brightly colored "cloud".

An object with a different period is not on that spherical surface. An object with a different apogee or perigee is not on that surface. On the Gabbard plot, only objects exactly at the intersection of the horizontal and slanted lines are in the shell. Most objects are not at that intersection.

Drag means that even objects in nearly circular orbits pass through the shell surface quickly. The overall lifetime is irrelevant - only the time spent at a particular altitude band matters. An object in a 549 km circular orbit cannot ever collide with the 550 km circular shell, even though it may have a lot of 1 km passes. So as soon as those objects decay only a few km they aren't a threat to the operational satellites. 1 km of decay happens in hours or a few days, depending on the object's ballistic coefficient, and also on solar activity.

The vast majority objects are going to be intersecting, but not in, the shell. That means at most 2 opportunities for a collision per orbit. With only 16 orbits per day, those aren't going to add up very fast - even if it take several weeks to update the catalog and several months to decay to non-intersection.

If you want to estimate the number of significant intersecting objects generated, the probability of collision per orbit, and the mean time to decay to non-intersection, we can estimate the time to recollision. Say that's 100 fragments, a 1e-7 probability of collision per orbit, and a mean of 3 months to decay to non-intersection, then the probably of a recollision is about 16 orbits/day*30 days/mo*3 mo*100 fragments *1e-7 collisions/orbit = ~1.5%.

Finally I understand what you're referring to, I think - and I'm afraid you're misunderstanding the dynamics here.
You're assuming SpaceX has kind of a color-coded board with all satellites in green (probability of collision close to 0), and slowly some are becoming progressively redder, until reaching bright red (probability of 1). Once they become orange though, they have the ability to slightly maneuver them so that none gets beyond a certain tone of orange (1e-5) which they set as threshold. That indeed would be the ideal situation. It *may* be for inter-Starlink conjunctions, because they have their own GNSS packages, as you mention in your following post, and that *may* be enough to approach that idealization - we'll have to take their word for it, which is not ideal anyway.

Unfortunately, that's not the case for the rest of objects, simply because of the innacuracies of the TLEs and the non-deterministic refinement of tracking. You don't get continuous perfect tracking that allows you to steer clear as soon as the collision probability reaches 1e-5 and not beyond. You get more or less frequent updates with "jumps" in the parameters, and most of those will instantaneously change the collision probability by a lot. Most will stay very low or 0, but some will jump well above 1e-5 immediately, with a distribution that rarely reaches 1 (or 1e-1 for that matter), yet will include lots of 1e-4, 5e-3, 1e-3 and so forth. It's the fundamental difference between a continuous, well-sampled process with low uncertainties, and a discrete, undersampled process with high uncertainties.

The uncertainties are the only reason the probability of collision is not always either exactly 0 or exactly 1. The probability reflects the uncertainties. Conjunctions are predicted several days out. If the uncertainties are still high as the conjunction approaches, they will maneuver so that the prediction (including the uncertainties) drops below threshold.

This progression of the predicted probability of collision and associated uncertainties isn't continuous, but it's definitely a progression.

[ulm_atms]

Whoa guys, you are getting very worked up here.

1.  I believe that the regulators/SpaceX are trying their best.  This is the first "MEGA constellation" ever put up and at an eye popping pace too.
2.  Well you got to start somewhere and at a minimum, SpaceX seems to be taking this whole thing collision avoidance issue seriously.  They seem to be constantly working/tweaking it as new data/observations come in.  I'm not sure who they could really ask as #1 means they really don't have anyone TO ask as they are first even attempting something of this size.
3.  They specifically made their sats to de-orbit quickly(lowered the orbits of shells) in case of failure/issues and to fully burn up before they hit the ground.  Who else is doing that? (Here is looking at you OneWeb...your sats won't decay for a LONG time where you are placing them currently.....)

I guess what I am trying to say is give them time guys.  You have 1/2 the forum declaring doom and the other 1/2 declaring a rosy future.  Reality is probably some where in between like always.  At least we can be grateful SpaceX seems to be taking every effort to balance an "efficient" but safe rollout.  The FCC/Space Command seems to be ok with what they are doing anyways....which is why I am not in the worse case side.  If they were sending out "Warning!, Warning!, Warning!  That is going to end badly because SpaceX won't listen to us!!!" I would be much more concerned.

Do the numbers say there will be an impact/collision at some point...sure...but it's how hard you try to avoid that situation and steps taken to keep that from happening in the first place that matters most at this juncture.  Once again, no one has done something of this size before....they(SpaceX, FCC, Space Command) have to start somewhere IMO.

[abaddon]

Whoa guys, you are getting very worked up here.[...]
I guess what I am trying to say is give them time guys.

You are summarizing the general feeling of most of the posters on this thread and site.  However, there are some who vehemently and voluminously disagree.

I think it'd be better to have a thread where discourse on the dangers of large-scale LEO constellations can be discussed that is not quite so single-operator (SpaceX) focused, but instead includes >all< constellations (Starlink, OneWeb, Kuiper, Telesat).  Similar to the current thread in the Commercial space forum where the topic is limited to impacts specific to Astronomy.

[mandrewa]

On the other hand, they may be expecting SpaceX to reduce tracking errors with their own 'Space Fences', or lowering the threshold an order of magnitude as Starlink grows, or some software wizardry that hopefully will solve space traffic control congestion in a few years' time because it'll become highly error-free and automated, or any number of 'let's wait and see's.

SpaceX doesn't need a "Space Fence" for their own satellites. They have highly accurate data from the INS/GPS/star trackers on their satellites and can use this to avoid Starlink fratricide. Starlink on other satellite and Starlink on debris conjunctions are the main concerns, but I'm not sure that anyone realistically expects SpaceX to start tracking everything else in orbit.

And hopefully we are going to set things up so that every constellation has the accurate location and orbit of every other functioning satellite in every other constellation in the sky (and I hope OneWeb and Starlink are doing this right now) with any status changes being updated almost immediately.

So that none of these functional satellites are a risk to each other.

The problem then becomes the probability of collision with the uncontrolled satellites or the debris there from whose locations and velocities are not known so precisely and which cannot be changed.

[eeergo]

It is the general case, and your plots show it. The constellation shell is (effectively) a spherical surface. Anything intersecting but not continuously on that surface can only ever collide at the intersection points. Anything not on and not intersecting the surface cannot collide at all, even if it's orbiting nearby in an ominous-looking and brightly colored "cloud".

An object with a different period is not on that spherical surface. An object with a different apogee or perigee is not on that surface. On the Gabbard plot, only objects exactly at the intersection of the horizontal and slanted lines are in the shell. Most objects are not at that intersection.

Drag means that even objects in nearly circular orbits pass through the shell surface quickly. The overall lifetime is irrelevant - only the time spent at a particular altitude band matters. An object in a 549 km circular orbit cannot ever collide with the 550 km circular shell, even though it may have a lot of 1 km passes. So as soon as those objects decay only a few km they aren't a threat to the operational satellites. 1 km of decay happens in hours or a few days, depending on the object's ballistic coefficient, and also on solar activity.

The vast majority objects are going to be intersecting, but not in, the shell. That means at most 2 opportunities for a collision per orbit. With only 16 orbits per day, those aren't going to add up very fast - even if it take several weeks to update the catalog and several months to decay to non-intersection.

If you want to estimate the number of significant intersecting objects generated, the probability of collision per orbit, and the mean time to decay to non-intersection, we can estimate the time to recollision. Say that's 100 fragments, a 1e-7 probability of collision per orbit, and a mean of 3 months to decay to non-intersection, then the probably of a recollision is about 16 orbits/day*30 days/mo*3 mo*100 fragments *1e-7 collisions/orbit = ~1.5%.

Evidently I agree that the pieces in the debris cloud susceptible to collide against another satellite only intersect at two points in their orbit with that satellite, at most - apologies if I made it sound like that basic concept wasn't clear. But we're not dealing with just one satellite! There's several thousands of them at the same altitude, with slightly or completely different orbits, that precess at different rates than the debris field objects, and are affected differently by perturbations. Many have larger eccentricities than the parent body (and those which do not are then in the same circular shell as the parent body, for the most part, so can potentially affect other satellites at the same altitude all around their orbit - and those are not just a few, as you can see from the plot) and will take days or weeks to decay out of that regime (at 550 km you don't fall 1 km in a few hours), during which time cataloguing them will still be ongoing, which means little chance for CAMs. It's true each piece will only pass roughly 16 times a day through range of altitudes the constellation is at, but there are thousands of satellites and a large distribution of hundreds of thousands, if not millions, of objects capable of inflicting catastrophic damage intersecting the "shell", which adds up to (10^-2 seconds x 10^5 objects) much longer times, in the order of hours.

Regarding your numbers, I believe those are unrealistically optimistic don't you think? Most orbital collisions involve thousands of trackable debris (plus remember the huge gap between trackable >10 cm and not overly harmful <1 cm), not 100. Also, lumping all fragments into the umbrella "1e-7 POC" seems a bit arbitrary, doesn't it?

The uncertainties are the only reason the probability of collision is not always either exactly 0 or exactly 1. The probability reflects the uncertainties. Conjunctions are predicted several days out. If the uncertainties are still high as the conjunction approaches, they will maneuver so that the prediction (including the uncertainties) drops below threshold.

This progression of the predicted probability of collision and associated uncertainties isn't continuous, but it's definitely a progression.

Sure, but you're sidestepping from your false statement: you had just claimed 1e-5 was the upper limit for collision probability that a conjuction would ever reach during that discontinuous progression.

1e-5 is the ceiling. There will be no conjunctions above that

As you can see from the tweet kindly quoted by su27k above (ProfHughLewis/status/1436334166447173640, which I'd earlier overlooked), that's not the case - there are as many conjunctions with 1e-5 as maximum POC as there are with 1e-3 and 1e-4, excluding Starlink-on-Starlink, which supposedly (but then again, maybe not) avoid going beyond 1e-5 with their more accurate internal GNSS tracking. They will be lowered as soon as they are discovered and the actual physical conjunction will not take place, if that's what you mean - but my initial point was that 1e-5 was not conservative if looking at what long-term POCs it would give rise to if chosen any tighter. To repeat myself from my previous post: "If we consider smooth nominal operations forever, everything is and will be fine obviously - here we're talking about misjudged uncertainties, mistakes or oversights, and their consequences."

[eeergo]

Whoa guys, you are getting very worked up here.[...]
I guess what I am trying to say is give them time guys.

You are summarizing the general feeling of most of the posters on this thread and site.  However, there are some who vehemently and voluminously disagree.

I think it'd be better to have a thread where discourse on the dangers of large-scale LEO constellations can be discussed that is not quite so single-operator (SpaceX) focused, but instead includes >all< constellations (Starlink, OneWeb, Kuiper, Telesat).  Similar to the current thread in the Commercial space forum where the topic is limited to impacts specific to Astronomy.

Such a thread exists for something much less generic (impacts to astronomy), yet most participants in the "nothing to worry about" camp firmly made all points gravitate around SpaceX/Starlink, and accuse critics of being anti-SpaceX/Musk/capitalism/whatever, even when most critiques are agnostic about the megaconstellation under discussion - although obviously Starlink being the largest by far, it's difficult to avoid mentioning it. In fact, remarkedly vehement disdain for "scientist elitism" sent the thread to moderation purgatory for a long while.

Regarding "give them time", that was the predominant discourse about mostly any environmental problem when it was still developing and was easy to tackle, even if excessively well-researched and understood as such. Solutions to evident issues cannot just rely on the goodwill of profiting parties under the belief that "they'll sort it out".