How quickly can the Starlink spacecraft respond to an impending collision?

update: The word "refused" might be inaccurate:

From the Ars Technica article:

Here's the full statement that SpaceX provided to Ars:

Our Starlink team last exchanged an email with the Aeolus operations team on August 28, when the probability of collision was only in the 2.2e-5 range (or 1 in 50k), well below the 1e-4 (or 1 in 10k) industry standard threshold and 75 times lower than the final estimate. At that point, both SpaceX and ESA determined a maneuver was not necessary. Then, the US Air Force's updates showed the probability increased to 1.69e-3 (or more than 1 in 10k) but a bug in our on-call paging system prevented the Starlink operator from seeing the follow on correspondence on this probability increase—SpaceX is still investigating the issue and will implement corrective actions. However, had the Starlink operator seen the correspondence, we would have coordinated with ESA to determine the best approach with their continuing with their maneuver or our performing a maneuver.

The Forbes article SpaceX Refused To Move A Starlink Satellite At Risk Of Collision With A European Satellite uses strong language in the headline.

The article says:

“Based on this we informed SpaceX, who replied and said that they do not plan to take action,” says Krag, who said SpaceX informed them via email – the first contact that had been made with SpaceX, despite repeated attempts by Krag and his team to get in touch since Starlink launched. “It was at least clear who had to react. So we decided to react because the collision was close to 1 in 1,000, which was ten times higher than our threshold.”

As to why SpaceX refused to move their satellite, that is not entirely clear (the company did not respond to a request for comment). Krag suspected it could be something to do with SpaceX’s electric propulsion system, which “maybe is not reacting so fast” as the chemical propulsion on board Aeolus.

Question: How quickly can the Starlink spacecraft respond to a potential impending collision? Would it for example take a day or two to raise altitude by a kilometer? I've estimated that the total delta-v available from the Starlink's krypton ion thruster is in the ballpark of 190 m/s, but I have no idea of the magnitude of the thrust or how fast they can change their orbits in response to a detected potential collision conjunction.

Just fyi, later in the article it says:

Thus Starlink 44 entered a region of space that Aeolus had occupied first. However, there are no rules in space that require one or another operator to move their satellite when there is a risk of collision. This, says Krag, is something that ESA hopes will be addressed in the near future.

“There are no rules in space,” he says. “Nobody did anything wrong. Space is there for everybody to use. There’s no rule that somebody was first here. Basically on every orbit you can encounter other objects. Space is not organized. And so we believe we need technology to manage this traffic.”

SpaceX has touted the automated collision avoidance systems onboard its Starlink satellites, which are designed to beam high-speed internet around the world. It says that the satellites, each weighing 227 kilograms, are “capable of tracking on-orbit debris and autonomously avoiding collision.” But for this incident, this system does not seem to have been used for some reason.

The risk of collision between the satellites was 1 in 1,000. ESA OPERATIONS/TWITTER

• You don’t need much dV to ensure a miss if you have time. 0.1 m/s achieved over a day is 4km displacement along the orbit. – Bob Jacobsen Sep 3 '19 at 2:23
• @BobJacobsen sounds good; consider writing a "phasing is better than raising"-based answer? The problem is though that I don't know how long it's krypton thrusters would take to even do that. i.stack.imgur.com/PhlRD.jpg (from here (from here)) – uhoh Sep 3 '19 at 3:50
• If the collision avoidance is automated then there is no reason to act. Should the 1 in 1000 chance have turned out to have been likely, presumably the on-board tracking system would have done what was necessary. Hopefully – JCRM Sep 3 '19 at 5:40

Let's do a back-of-the-envelope calculation, carrying only one digit with whatever input data we can find.

The satellites are about 200kg, and various commentators suggest the thrusters can provide about 100mN thrust or so. That's an acceleration of $$0.5\times 10^{-3}$$ m/s/s, or about 2m/s per hour.

Even a small acceleration builds up quadratically, and there are a lot of seconds available. After an hour, that acceleration will have moved the satellite forward (or backward) in its orbit by about 3km, more than large enough to ensure a miss.

The satellite's $$\Delta V$$ is limited, maybe to 500 to 1000 m/s, in which case 2m/s might be a lot to use for a single encounter. But even a day's warning can turn a small $$\Delta V$$ into a wide miss. For example, a 0.1m/s change a day early is a 8km movement forward (or backward) along the orbit. With the acceleration estimated above, that's just a 200 second "burn" (zap?).

Of course, if you don't think these are the right numbers, you're welcome to repeat the connection with any others you'd like. Or you can do the backward calculation: How small does the acceleration have to be so that it takes more than a day to move 1km along the orbit?

$$d = 1/2 a t^2$$ $$a = 2 (10^3)/ (86\times 10^3)^2 = .3 \times 10^{-6} \rm{m/s/s}$$

With a 200kg satellite, that's a thrust of $$60 \mu \rm{N}$$. Commercial Hall thrusters are typically mN, not $$\mu \rm{N}$$, although use of Krypton would cause some loss in thrust.

• just fyi this tweet – uhoh Sep 3 '19 at 23:59
• SpaceX has shared no such details IMO. Those acceleration numbers are not accurate. Even if they were, you cannot assume a linear delta-V addition for a Hall thruster, mind you, this is a nonlinear system. You need to run a basic simulation with the right acceleration numbers to get accumulated delta-V corresponding delta semi-major axis, or cross/along track numbers.. – ASRI_306 Sep 4 '19 at 19:51
• @ASRI_306 Citation, please, for Hall thrusters being a non-linear system? The mass loss is negligible, the thrust is constant at constant power input. – Bob Jacobsen Sep 5 '19 at 0:24
• Thanks for the edit! I came across it by accident, it's always good practice to ping the "complainer" afterward, so they can delete their comment and reverse any possible down voting. OP's don't get automatic notifications when answers are edited. – uhoh Sep 5 '19 at 0:55
• In this answer I estimate Starlink’s total available delta-v of only 190 m/s, requiring 5000 cm^3 of volume and 2.3 kg. On what might your estimate of 500 to 1000 m/s be based? – uhoh Sep 5 '19 at 0:58

Response time was not a factor in this issue.

In a statement sent via email today, SpaceX acknowledged that it would have taken more action if it weren’t for a “bug” in its on-call paging system:

“Our Starlink team last exchanged an email with the Aeolus operations team on August 28, when the probability of collision was only in the 2.2e-5 range (or 1 in 50k), well below the 1e-4 (or 1 in 10k) industry standard threshold and 75 times lower than the final estimate. At that point, both SpaceX and ESA determined a maneuver was not necessary.

“Then, the U.S. Air Force’s updates showed the probability increased to 1.69e-3 (or more than 1 in 10k) but a bug in our on-call paging system prevented the Starlink operator from seeing the follow-on correspondence on this probability increase – SpaceX is still investigating the issue and will implement corrective actions. However, had the Starlink operator seen the correspondence, we would have coordinated with ESA to determine best approach with their continuing with their maneuver or our performing a maneuver.”

• but I'm still interested in an answer to the question. Question: How quickly can the Starlink spacecraft respond to a potential impending collision? Would it for example take a day or two to raise altitude by a kilometer? ...but I have no idea of the magnitude of the thrust or how fast they can change their orbits in response to a detected potential collision conjunction. – uhoh Sep 4 '19 at 9:24