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If a rocket flies into space there is a possibility that it will encounter a piece of space garbage; even a small screw can be fatal.

What are the chances that such a collision really takes place? What about such an encounter with the ISS?

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    $\begingroup$ If you apply no lower boundary to the size? Hundreds of impacts expected per hour. Virtually all of them will be barely above atomic scales, but ... no lower boundary supplied! You need to look at the size/risk vs. frequency spectrum. Which is a very big question. FluffyFlareon's answer below is a good start. $\endgroup$
    – PcMan
    Jun 26 at 7:26
  • $\begingroup$ The indisputable answer: it is non-zero, steadily increasing and can reach an irreversible point (if a collision triggers a "Kessler syndrome") $\endgroup$
    – Ng Ph
    Jun 29 at 8:20
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    $\begingroup$ Related story ESA spacecraft dodges large constellation(=Starlink) $\endgroup$
    – Ng Ph
    Jun 29 at 11:01
  • $\begingroup$ I think number of issue have to clarify 1. Controller algorithm may one issue know days have many controlling mechanism have to mention PID, fuzzy logic, Deep learning(neural network) those controlling algorithm not much developed in hardware object detection, object kinematics determination, obstacle detection, sensor accuracy, interfacing issue....etc. 2. As you know universe expand above we expected so object navigation and detection major bottle-neck for that. 3. Time delay major issue in space, know days processor speed of our machine not much faster, command send from controller or comma $\endgroup$ Jul 7 at 12:12
  • $\begingroup$ nd receive from sensor have delay at that moment the space craft collide with object. 4.In hardware point of view the sensor accuracy not much accurate, have tolerance issue, identification and analyzing performance issue. $\endgroup$ Jul 7 at 12:12
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Heh. So it turns out, figuring out the answer to this is precisely what I do for a living.

The glib answer: it depends.

  1. It depends on how big an object you are worried about hitting. Are you worried about damaging wiring harnesses? Are you worried about causing a radiator leak? Punching a hole in the crew module? Annihilating the vehicle altogether? The larger the object, the less likely, in rather dramatic scale.
  2. It depends on what orbit you fly in. Different altitudes and inclinations have drastically different debris populations.
  3. It depends on how big your vehicle is. Bigger vehicles get hit more.
  4. It depends on how long you fly. Stay in orbit 10 years, and you'll get hit with roughly 10 times as much stuff as you would if you stayed for one year.

On ISS, we typically write requirements along these lines:

The [piece of hardware] will not sustain damage from orbital debris that could create a [catastrophic hazard | subcomponent failure | other defined failure] with a probability of 0.xyz over XY years.

What exactly we write depends specifically on the hardware involved, how much we care about it, how much could station suffer if we lost it, etc.

New piece of critical structure? We'd specify a pretty stringent requirement, say, something more than 99% over a decade.

Wire harness for a Wi-Fi antenna for payloads? Maybe not so much, say, 95-98% per year.

A more stringent requirement makes the hardware and (and perhaps more importantly) its certification process more expensive.

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    $\begingroup$ Do you have any sources for this answer? $\endgroup$ Jun 26 at 3:15
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    $\begingroup$ The start of this answer reminds me of a question on scifi asking about growing potatoes after being stored for a long time, and the top answer starts with "I am a PhD Student in potato post-harvest physiology". $\endgroup$
    – pipe
    Jun 26 at 21:45
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    $\begingroup$ @DavidHammen Nothing public I can point to easily. Been doing this for about 8 years though. My last project was the solar arrays they just installed last week and yesterday. References for points 1 and 2 are scattered throughout other answers I've given on this site (maybe when I have more time -- possibly several weeks from now -- I can dig them up and repeat them here). 3 and 4 are just math. I'm deliberately not giving exact numbers we use so I stay away from releasing information that isn't mine to release. $\endgroup$
    – Tristan
    Jun 27 at 2:31
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    $\begingroup$ @Dave In general, we try to write the requirements to span the hardware's expected design life. The meteoroid environment model is constant with time, but the orbital debris environment model includes variations from year to year to try to predict the growth in traffic as well as the effect of the solar cycle on upper atmosphere density. Going for at least 10 years helps us capture most of that variation in an average sense so we aren't reporting out best-case or worst-case values and extrapolating $\endgroup$
    – Tristan
    Jun 28 at 0:58
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    $\begingroup$ @Tristan I understand. I've been in a similar boat with regard to questions I can answer. NASA would classify $\vec F = m \vec a$ as ITAR-restricted if they had their druthers, and the DoD would prefer to classify the same equation as TS/NOFORN. $\endgroup$ Jun 28 at 13:42
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Safety Integrity Level (SIL)

The way that we would conventionally test for and mathematically define the risks involved in space flight, including from debris, would be through SIL levels that describe the number of dangerous events that could acceptably occur in a single hour of space flight. This is very similar to avionics, railroad systems, and autonomous driving.

The number of events per hour is very small, on the order of micro or nano events / hr for the lowest SIL levels, and decreases as the SIL level becomes more hazardous. In other words, MTBF should be very high for failures that are catastrophic and result in loss of life or destruction of expensive property like a shuttle, satellite, probe, or station.

SIL Description Acceptable failure rate Acceptable MTBF
SIL 4 Catastrophic: eminent loss of life and complete destruction of shuttle/station; situation unreasonably uncontrollable 10-9 events/hr 109 hrs, or 114,000 years of space flight
SIL 3 Hazardous: possible loss of life and spacecraft; a very difficult situation to control 10-7 events/hr 107 hrs, or 1,140 years of space flight
SIL 2 Major: reduction in safety margins; perhaps leading to non-fatal injuries or damage to important mission systems unrelated to survivability 10-5 events/hr 105 hrs, or 11.4 years of space flight

Note that these are the ideal statistics and aren't reflective of real-world practice. Also, the number represent the aggregate time of space flight across all relevant spacecraft. Imagine testing an entire fleet of 5000 self-driving vehicles, each driving on highways and city streets for 1000 hrs for a total of 5,000,000 hrs, and you measure how many times that one of the cars was placed into a "catastrophic" situation that led to fatality or "hazardous" situation that could've led to fatality. Say the numbers are 1 and 4 for a full 5 incidents. Then the average failure rate would be 5 events/5,000,000 hrs of drive time, or 10-5 events/hr. This would probably not be considered successful based on aviation standards, but automotive manufacturers and regulators might interpret these figures acceptable. In space flight, designers and the aeronautic institutions that employ them are pretty conservative, so these wouldn't be "good enough" – the technical term is an "intolerable risk" as opposed to an "acceptable risk".

Obviously, some objects that are unmanned are treated differently from manned spacecraft, and probes, satellites, space stations, etc. will have different risk metrics. The above is a general outline.

Managing Risk

So if these SIL metrics need to be met for a mission to be satisfactorily safe, what can be done, when random debris is floating around in near-Earth orbit? The key is to:

  • reduce the probability of dangerous events occurring;
  • as well as manage faults, failures, and disasters when they occur.

The US DoD has catalogued 27,000 pieces of debris in near-Earth orbit hurtling at speeds of about 17,500 mph around the planet; NASA's statistical analysis of sensor readings approximate that 23,000 of these are the size of a softball (d = 9.7 cm) or larger, and thus definitely large enough to cause a catastrophic event. In addition there are an estimated:

  • 23,000 pieces > 10 cm (d), softball sized
  • 500,000 pieces > 1 cm (d), marble sized
  • 100,000,000 pieces > 0.1 cm (d), width of mechanical pencil graphite

The marble sized ones and anything smaller can't be reliably tracked.

enter image description here

The paths of these more massive debris are analyzed (diagram above), and given a conservatively large margin of error to make the likelihood of a collision decrease to 10-9 events/hr or thereabouts. This is probably based on statistical tests (diagram above), such as Monte Carlo simulations (or something comparable but computationally faster). In the unlikely event that one of the 23,000-27,000 large tracked objects strays too far from its predicted trajectory while monitoring it (diagram above) and comes possibly dangerously close to the spacecraft, NASA initiates a Debris Avoidance Procedure, possibly involving both automated and manual roles of maneuvering the spacecraft to safety, which is part of long-standing guidelines at NASA as a means to limit SIL 4 events from occurring to an acceptable failure rate / probability.

As for the smaller debris, contemporary ships are equipped with shielding and ideally redundant protection (diagram) and redundant critical systems and hardware in case small debris damages the principal shields or mission-critical components or subsystems. Redundancy greatly reduces the probability of failure and greatly increases the MTBF. These shields work for debris smaller than 1 cm.

Mid-sized debris risks probability difficult to measure?

That leaves the 1 cm – 10 cm debris, the most deadly debris. These are large enough to breach shielding and yet are small enough to be untraceable.

In order to find the probability of a collision with these, we'd need to use historical data of how many hours all of spacecraft has flown versus how many collisions with these kinds of debris have happened. Unfortunately, the number of collisions is statistically insignificant. The other problem is that the number of pieces of debris has not remained static. For instance, in 2009, a commercial spacecraft carrying Iridium crashed into a latent Russian satellite, resulting in thousands of new pieces of debris. So the number of debris has not stayed static, making the probability calculations dependent on chronological time humanity's explored or used near-Earth space. This renders computations challenging:

  • small number of collisions, essentially statistically insignificant
  • time-varying amounts of dangerous 1 cm – 10 cm debris

Compare this to our example of testing a fleet of self-driving cars. We can easily (theoretically) scale this to tens of millions of hours testing and dozens of accidents. The probability of crashing is more or less static or at least mean-reverting across all of the cars because hazards of crashing are not continuously increasing or decreasing unless some variable – like snowfall – perverts the data, with disproportionate amounts of accidents occurring during snowy conditions and sensors failing to detect snow-covered signs.

There may be no satisfactory range of numbers to quantify the probability without substantial historical data of collisions, near collisions, number of hours of space flight time conducted since the beginning of space exploration, and approximate number of 1 cm – 10 cm debris across the entire timeline of space flight, use, and exploration. NASA might know all of this data. Even then, our detection of 10+ cm objects has improved, our spacecraft is (probably) more reliable now, so any (hypothetical) past collisions were more likely than they would be today, introducing yet another set of variables to make things even more unfeasible to compute, since these probabilities would rely on historic data that's skewed toward obsolete technology of the past.

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    $\begingroup$ What does SIL stand for? $\endgroup$ Jun 26 at 2:54
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    $\begingroup$ sorry, yeah, that means safety integrity level $\endgroup$ Jun 26 at 2:58
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    $\begingroup$ Do you have any sources for this answer? What is the source for the table, and for the figure? $\endgroup$ Jun 26 at 3:13
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    $\begingroup$ So is a "SIL level" a safety integrity level level? What's the highest level level of safety integrity level level? Can we take it to a new level level? Do you need a PIN number for this? $\endgroup$ Jun 26 at 3:29
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    $\begingroup$ @OrganicMarble The description looks similar to IEC 61508, which defines 4 SILs, and is something like the bible for safety-critical and safety-related systems. $\endgroup$ Jun 26 at 11:13

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