Thread by @ProfHughLewis

Earlier this week Elon Musk set out his team's expectations for #Starlink satellites over the next 18 months. I thought I would use this month's #SOCRATES analysis to see what the Starlink team should expect in terms of conjunctions & manoeuvres over that period & beyond [1/n]

Before I start, I'd like to offer my thanks to @planet4589 for creating a page on his website with data that enabled me to move forwards with a critical part of the analysis. Thanks also go to @TSKelso for ongoing support and provision of SOCRATES data via @CelesTrak [2/n]

This month we open with the number of conjunctions within 5 km or less predicted for each week from December 2018 to the end of March 2022. Something extraordinary has happened because of #Starlink and the ASAT test in November: a 400% increase in less than 3 years [3/n]

The 1 km conjunction data show a similar increase although it's a little more muted. The last #SOCRATES report from 31 March 2022 predicted 7513 conjunctions within 1 km or less for the first week of April. [4/n]

Work by @COMSPOC suggests that conjunctions involving fragments caused by the intentional destruction of Cosmos 1408 will come in 'squalls' over the next year spacenews.com/russian-asat-d…. We're currently in one of the year's worst. [5/n]

Looking at the predicted conjunctions with a collision probability greater than 1-in-10,000 (a common manoeuvre threshold) we see a similar increase in the count, but now it seems to be dominated by events involving #Starlink & not events involving Cosmos 1408 debris. [6/n]

Here's the predicted count for conjunctions with collision probability greater than 1-in-100,000 (the threshold used by #Starlink for manoeuvres). There is some involvement by Cosmos 1408 debris here but again #Starlink dominates. [7/n]

If we now focus only on conjunctions within 5 km involving #Starlink satellites (but excluding Starlink-on-Starlink events) we continue to see the non-linear trend through time in spite of a modest reduction in the count over the last month (2nd-order poly has R^2 = 0.983). [8/n]

It's a similar story for the conjunctions within 1 km: a small reduction in the count since last month but an ongoing non-linear increase overall (2nd-order poly has R^2 = 0.975). [9/n]

The count for conjunctions with a collision probability greater than 1-in-10,000 & involving #Starlink shows the same trend (remember the number of conjunctions are taken from each #SOCRATES report, which covers predictions for a 7-day period). [10/n]

Here's where we start to get a sense of the operational implications arising from all of these conjunctions, because the autonomous collision avoidance system employed by #Starlink triggers a manoeuvre if the collision probability is greater than 1-in-100,000 [11/n]

The #SOCRATES data suggest about 210 manoeuvres are made every week, or 30 per day. [12/n]

When we add all of the (predicted) manoeuvres, we find that #Starlink passed an important threshold in March: 10,000 collision avoidance manoeuvres. A 3rd-order poly fits the line shown in the graph with R^2 = 1.0 (hence the manoeuvre rate would have a 2nd-order poly fit) [13/n]

Here's where the data from @planet4589 comes in. Jonathan provided me with a count of the number of #Starlink satellites in orbit (amongst other things). This means that I can extend the analysis to look at how the satellite count affect the conjunctions & manoeuvres [14/n]

This is how the number of #Starlink satellites in-orbit (operational & failed) affects the number of conjunctions within 5 km predicted by #SOCRATES (these are only conjunctions involving Starlink & excluding Starlink-on-Starlink) [15/n]

These are the data for the corresponding conjunctions within 1 km [16/n]

And for the conjunctions with collision probability greater than 1-in-100,000 [17/n]

Finally, we get to the relationship between the number of #Starlink satellites in orbit and the collision avoidance manoeuvre rate (shown as the number per day) [18/n]

You may have spotted the trendlines in the last few graphs. We can now use those to make predictions about the number of conjunctions & manoeuvres that might be expected once the number of satellites in orbit reaches 4200 [19/n]

A brief warning before I show you the prediction results: many things could affect the models (trendlines), including fragmentation events, space weather, solar activity, non-Starlink launches, so please approach with caution. Nevertheless, the results are... astounding [20/n]

The model suggests that 4200 #Starlink satellites in orbit would result in 56,200 conjunctions within 5 km per week involving Starlink (but excluding Starlink-on-Starlink). Extrapolating to 32,000 Starlink satellites & we might see 3 million conjunctions per week [21/n]

The 1 km conjunction model suggests that 4200 #Starlink satellites in orbit would result in 1980 conjunctions per week involving Starlink, but more than 100,000 conjunctions per week once the constellation reaches 32,000 satellites [22/n]

And finally, the model suggests that 4200 #Starlink satellites in orbit would require a total of 105 collision avoidance manoeuvres per day. That's roughly equivalent to 1 out of every 40 Starlink satellites manoeuvring on a daily basis, on average. [23/n]

Extrapolating to a #Starlink constellation with 32,000 satellites in orbit suggests 5425 collision avoidance manoeuvres per day (nearly 2 million per year) involving 1 out of 6 satellites in the constellation, on average. [24/n]

The last tweet is why I tend to talk about the 'burden' that is placed on operators and regulators by large constellations of satellites. [25/n]

That's not all. The law of very large numbers will tell you that very low probability events can happen if given enough opportunities. Even with an autonomous system taking action at a relatively low probability level, we might expect to see a #Starlink collision [26/n]

Then, of course, we have 'lethal non-trackable' objects. It's not possible to manoeuvre for things we cannot track. Even if we track them, the number of conjunctions increases to even higher levels, possibly resulting in a change to accepted collision probability levels... [27/n]

...that result in fewer manoeuvres but the neglect of greater risk. [28/n]

That's it for this month's #SOCRATES & #Starlink analysis. Thanks for reading this far. [29/29]