What are the chances that a spacecraft is hit by space junk?

Question

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?

Answer 1

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.

Answer 2

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.

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.