# Effects of stray bullets in space

A battle takes place on the outskirts of a colonized solar system between attacking and defending forces. Would any stray shots have a chance of hitting a ship or station closer to the center of the system?

Millions of shots are fired, most from railguns or similar weapons. Lasers are used mostly on larger ships, as smaller ships can't handle the heat they output. Nuclear missiles are used but usually hit their target.

There are a few inhabited planets in the solar system, and there is frequent trade and transport between them, large space station factories, and other nearby systems. The entire solar system resembles the Sol system in size.

Is there any chance of railgun rounds or even lasers traveling far enough to be a danger to the stations or ships in the system? What would the effective range of these weapons be?

• Welcome to Worldbuilding, Starpilot! If you have a moment please take the tour and visit the help center to learn more about the site. You may also find Worldbuilding Meta and The Sandbox (both of which require 5 rep to post on) useful. Here is a meta post on the culture and style of Worldbuilding.SE, just to help you understand our scope and methods. Have fun! – FoxElemental Jul 11 '18 at 18:04
• "A chance" is perhaps too vague. There's a chance that everyone here is a super-intelligent frog (except you, of course)...it's just a vanishingly small chance. – user535733 Jul 11 '18 at 18:24
• Those projectiles will become space debris. Their initial speed will (supposedly) pale in comparison to their orbital speed. Even if millions of bullets are fired a random encounter with a spaceship is unlikely. – Alexander Jul 11 '18 at 18:26
• I really want an answer to be this from mass effect: youtu.be/h-UbTNBlVDE (Caution: Language) – PipperChip Jul 12 '18 at 0:00
• The debris resulting from railgun impacts are much more likely to be a problem. – MooseBoys Jul 12 '18 at 0:34

Lasers? No. Lasers need to be focused. They diffuse fairly quickly (on solar distance scales) and the more they diffuse the less damage they cause. I don't believe they'd be dangerous to anything not inside the battle.

Railgun rounds? There's a chance, but it's infinitesimally (read: "only if you say so in your story") low. They'll just burn up in planetary atmospheres, so it's really only ships and bases that are at risk. Unfathomably low risk. Not zero, but really low (as in "millions of rounds wouldn't bring the percentage chance to 0.1% low").

Nuclear missiles (I know you said they almost always hit, but just for completeness). Honestly, the chance of this much-larger-than-a-railgun-round object hitting something is only slightly better than the railgun round itself. But, if they're armed when they go missing... then there's a chance they'd go off in a planetary atmosphere. It would still be written in as inevitable in your story ("Make it happen, Number One!"), but what a light show!

In the long run, I'd say you need to throw out the statistics and use or not use the idea to serve a purpose in your story. When you do, a totally rational comment like, "what were the odds of that!" would be appropriate.

• /use or not use the idea to serve a purpose in your story/ Hear hear! This is the answer. – Willk Jul 11 '18 at 19:42
• Yes, I will definitely need to disregard statistics. I guess if a bunch of everyday stuff happened in my story it wouldn't be very exciting! – Starpilot Jul 11 '18 at 19:55
• "A million-to-one chance succeeds nine times out of ten. Traditionally, one has to say "it's a million-to-one chance, but it might just work!" to invoke this rule. It also has to be exactly a million to one - none of this fiddly "995,351 to 1" business, or whatever other number you might end up with. So while the list of things that people have accomplished with million to one chances is quite impressive, the list of things they have failed to accomplish with odds a few percentage points off in either direction is probably a lot longer and involves a lot more fatalities. – ivanivan Jul 11 '18 at 20:19
• This answer also touches on nukes detonating in an atmosphere. Generally, nukes are MUCH more effective inside of an atmosphere than out, because most of the energy in the initial blast is expressed as X-rays. In space, these X-rays will fry very close objects, disrupt electronics to a medium distance, then quickly follow the square/cube law into little more than background radiation. In an atmosphere, the X-rays turn quickly into thermal energy, which cooks everything and creates a tremendous pressure wave out to a MUCH larger distance. – Ghedipunk Jul 11 '18 at 20:22
• @JBH , yes, even at the top of the atmosphere, though most of the effect would be seen as an EM pulse, rather than a thermal shockwave, because most of the energy would be dumping into the ionosphere. (I get most of my nukes-in-space info from the Atomic Rockets entry on Weapons in Space ) – Ghedipunk Jul 11 '18 at 20:34

Wow! This is something I have honestly never thought about! But now I will :P

Every object within a solar system has only a few possibilities where it might fly along:

1. Stable orbit around the star:
Well, exactly what it says on the bin. The bullet is on a stable orbit around the star, and may not hit anything within the next ten thousand years.
2. Stable orbit around a planet/ planetary body/ moon:
Nearly the same as above, but unlikely, if the battle was fought in interplanetary space. If the bullet was fired within a stable orbit around a planet, and the velocity of the bullet is not high enough to escape the gravitational field of the said planet, it might work (but I don't believe it).
3. Exiting planetary orbit, reaching stable stellar orbit:
Combination of 1. and 2. The bullet leaves the planetary gravity field and enters an orbit around the system's star.
4. Collision trajectory into a planet/ moon/ asteroid:
Now it is becoming interesting! If the trajectory of the bullet directs it directly onto a planetary body, it may be a danger for everything in orbit around that body.
5. Escape trajectory out of that star system:
The most boring possibility. The bullet leaves the star system and will fly in the dark void between the start, doomed to wait for millennia to meet anything.

Now, how high are the risks for a stray bullet hitting anything in that star system? To be honest, I think that the chance of being hit by a lightning, a comet and a freight train simultaneously would be higher. Remember,

Space is big. Really big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the road to the chemist, but that's just peanuts to space. (The Hitchhiker's Guide to the Galaxy, Douglas Adams)

The chance that some of these stray bullets hit something is, honestly, astronomically small (Pun intended).

But how about lasers and other beam weapons? Most lasers do not keep their focusing for a long time. I remember an experiment where my physics teacher took a laser from the lab, pointed it across the yard and showed us that the beam diameter increased significantly. Your weaponized laser may be more precise, but even they would lose energy on interplanetary distances. Maybe they would heat up a distant spaceship or station, but nothing more.

Tl;dr: Only in a vein of very very very very VERY bad luck would something being hit and receive damage.

• Aren't comets, by definition, in space? -> to find both lightning and a freight train there at all... let alone simultaneously might be ambitious :) – Nikola Radevic Jul 12 '18 at 14:37

Compare with objects in Earth orbit.

Look at a real-time display of stuff in orbit. This represents over 21,000 objects in Earth orbit. This is very, very restricted compared to the size of the solar system. The volume of the solar system compared to earth orbit is on the order of 1E15 times as large.

Given how crowded Earth orbit is, and that the foreign object density is trillions times greater, clearly the collision rate in Earth orbit must be huge in comparison -- yet actual impacts with space debris in earth orbit are rare. They do occur, proving that impacts are possible and will occur given time and chance -- the frequency of impacts is decidely low. It will be many many times smaller for bullets fired from the edge of the solar system.

• 21,000 objects greater than 10cm in size. If you go down to >1 cm that number rises (very very quickly) to 500,000. Additionally, Debris avoidance maneuvers are planned [...] if the probability of collision is greater than 1 in 100,000, a maneuver will be conducted if it will not result in significant impact to mission objectives. If it is greater than 1 in 10,000, a maneuver will be conducted unless it will result in additional risk to the crew. nasa.gov/mission_pages/station/news/orbital_debris.html – Draco18s Jul 12 '18 at 5:26

The number and energy of the objects is lost in the background noise.

ISS already gets hit by stuff; it has armor and emergency procedures in place. With bigger stations and budgets redundant systems should be able to absorb occasional high energy impacts with minimal disruption.

There are about half a million tracked objects near Earth between 1 and 10cm: Holding your space battle in orbit would only about triple the chance of something getting hit by accident.

I saw no answer explicitly using the surface of a sphere for an argument, so here goes:

Hitting a target can be thought of as hitting a shape the size of the target on a sphere with you in the center and a radius of target distance. The probability of hitting said shape while shooting wildly into any direction then is the ratio of target-area vs sphere-surface. Sphere surface is 4*pi*r², but i'll round 4*pi to 10 because it's not going to make much of a difference.

Thus, at 10m distance (in space. no gravity, and you can shoot any direction you want) the probability of hitting a 1m² target (~human or thermal vent of the Death Star) by shooting blindly is 1/1000 ( = 1m²/(10*(10m)² )- not bad. Because of the r² in the denominator, this probability will drop sharply.

At 1km (10^3 m) the probability is at 1/10 000 000, which is about jackpot-level in a small national lottery. (Here a note about statistics: If you take 10 million independent shots, this does not mean you are guaranteed to hit the target- i you fill out 10 million lottery tickets, you'll make sure that you pick different numbers, independent shots are comparable to buying 10 million lottery tickets and then letting monkeys fill them, you'll get lot's of doubles; -- To compute the probability of hitting a human in space at 1km distance by 10 million independent, random, shots, you have to take the probability of not hitting him with one shot nh = (9 999 999/10 000 000), multiply this with itself by the number of shots snh = (nh^10M) and substract from one h = (1- snh); You then have the probability of hitting that poor guy once or more. That probability is about 2/3. Again, not bad, but you are now shooting 10 million bullets....

At 1AE (distance earth - sun, harshly rounded to 10^12 m) the one-shot probability is 1/10^25, or much more impressively 1/10000000000000000000000000, if you say the target is 1000m² big (instead of 1m²) you are allowed to take three zeros off that (1/10^22). Probability of hitting this station-size target with 10M random shots is 1/10^15 (or about as big as winning a mid-size national lottery twice, in a row, with only one ticket per draw). --- Hitting a specific moon (~ earth moon, 1^12m² target surface) gets your one-shot probability up to 1/10^13, and you 10M-shot probability up to 1/1M ! (Though if a bullet hits a moon, and no one notices... did it hit?)

'Being on the outskirts of the solar system' might mean 10AE distance, bringing the one-shot-station-hit-probability down by another 100 to 1/10^24

Taking gravity into account changes the numbers only slightly (in a civilizatory timeframe, i.e excluding multiple passes of objects on huge orbits)- Shooting away from the sun at less then escape velocity will bend the bullets back, thereby about doubling the bullet density sun-wards. So instead of 1/too_much, you now have 2/too_much.

Lasers are out because the beam gets too wide to damage stuff, and nuclear rockets are not that much different from bullets; Assuming they explode near the unlucky non-target (if not aimed that way why should they, though?), their kill-radius is now the effective target-surface, otherwise the equation is just like with the bullets, but you'll probably not spray 10M nuclear warheads around in an encounter.

One last number fest: Assume there are 10 battles a year, with 10 combatants, each spraying 10M bullets wildly, for 10 years; Further assume there are 1000 stations with 1000m2 target area each, floating 10AE away (never occluding each other for ease of calculation). --- 10^12 bullets at a combined target surface of 10^6 m² in a sphere of 10^27 m² : 1-(( ((1- ((10^6)/(10^27)) ))^(10^12) ) = 1/10^9 - actually not as bad as i'd assumed coming in !

Please heed the note about probabilities given above! While winning the powerball lottery has a 1/10^8 chance, and there have been winners, this is because a lot of people play, and have been for some time. Number of 'players' (stations) and time have already been factored into many of my above values, so they are not directly comparable (Or rather, comparing them you have to keep in mind the givens: the last of my numbers, 1/10^9, is the probability of any station being hit at any time, by any of the bullets shot during 10 years, while the powerball probability of 1/10^8 is the probability of a specific player winning with a specific ticket at a specific draw...)

Lasers aren't particularly dangerous in space outside of space battles. Due to the nature of how they work, they cannot be precisely focused at every distance, which is what makes them so dangerous. A combination of them being less focused at long range and reflection on the few particles that exist in space means that they likely won't cause too much damage to accidental targets. At worst, a capital-ship laser fired in the outer system might accidentally burn out a sensitive sensor or telescope but not much worse.

Solid projectiles, on the other hand, are a bigger issue. In theory, the range for a solid projectile is infinity. Several kilos of heavy metal accelerated to a significant fraction of the speed of light is going to destroy something when it hits and the only way it's slowing down is if it actually hits something. With that said, on a long enough timeframe, the odds of a mass round hitting something is 100%. Most likely, that thing is going to be a black hole or star, neither of which will be impacted by the hit in any meaningful way.

As for effective combat range, there are some technological constraints to this answer. First of all: what's the capability of your ships. You mention a battle at the edge of a system, indicating that FTL is possible. If that's the case and your ships have functionally infinite energy for maneuvering and flying around (think star-wars or star-trek, where orbits are a suggestion) so the answer above remains in terms of collateral damage.
Accuracy of your weapons and thus destructive potential is going to be limited by the maximum acceleration of your ships and their size vs the velocity of your rail weapons. Imagine, if you will, a railgun capable of spitting out rounds at 10% of the speed of light. That lets you put a round in a target at ~30.000 km with a travel time of 1 second. The target has 0.9 seconds to move away from where you're shooting. Assuming an acceleration of 1G, the ship can go a little under 8 meters in any direction, basically guaranteeing a hit on anything larger than an F16. A quick reaction by the pilot (or rather, automated systems) might mean you hit a cargo bay or secondary reactor instead of center-mass, but at 0.1c, that doesn't really matter much, seeing as 100 grams of matter at that speed has kinetic energy in the same ballpark as early atomic warheads.

However, distance is where it gets interesting. At 60.000 km (still fairly close in terms of space distances, only 1/6th of the distance to the moon), the target has 1.8 seconds to get the hell out. That's twice the time but four times the distance covered. Instead of trying to guess where your target will be within a ~8m radius sphere, you're now looking at a sphere with a radius of ~31m. That F16 sized target you were basically guaranteed to hit last time? not so sure now.

There are two methods of dealing with this issue with regards to rail weapons. The first one is the simpelest and most dangerous to yourself: get close. If you know the maximum acceleration of your target, you know how close you need to be to guarantee a hit with your rail weapons. Get within that distance and you're guaranteed that your shots will hit.
The alternative is much safer for you and a lot less safer for anyone in the vicinity of your target. If distance and acceleration tell you you have a 5% of hitting your target, just fire 20 or 30 rounds in a spread pattern. You might miss with 6, the enemy might dodge another 12, but the rest is going to hit. And that's good enough.

Now all of the above is predicated on the assumption that your ships have functionally infinite delta-V as far as combat situations are concerned. If that's not the case and Hohman transfers and orbital maneuvers are the order of the day, things get interesting. You see, when everyone's on set orbits with no good ways of changing them, then hitting becomes less of a matter of dodging and weaving and more of a matter of gaining positional advantage.
You begin doing things like firing weapons in a specific orbit to force the enemy out of an optimal cruising altitude so they have to expend fuel to maintain or correct their movement. A hit might signal a win, but in this kind of warfare, victory is more likely determined by whoever runs out of delta-V first, mostly because ships at this level of tech have less powerful weapons, giving the enemy enough time to dodge.

The biggest downside of this low-maneuverability combat is that it tends to take place in beneficial orbits. The same place where civilian infrastructure tends to hang out. A volley of railfire in low-earth-orbit might scare an enemy warship into a different orbit, but once the fight's done, those rounds are still there, orbiting and eventually burning up or wrecking a satelite or two.

• I think it is a pretty good point that the popular military spots will be popular civilian spots too, but I would assume most weapons would have escape velocity unless specifically meant to be a long term hassle. – user25818 Jul 12 '18 at 20:47
• Are you sure that the odds of a shot eventually hitting something is really 100%? The universe is expanding, and space is very very very sparse. I haven't done the math, but I would intuitively think the odds may be much lower than 100%, depending on how long the universe lives. Think of it this way: almost any direction you look in space, you see to the edge of visible space, without your line of sight being obstructed by a star. Otherwise the night sky would not be black. – avl_sweden Apr 13 at 19:39

# Lets pull out some math...for funsies.

What we need here is the mean free path equation, which is good for things like "how far can a molecule travel without bumping into any air molecules" to "proving Han Solo wrong about hyperspace jumps."

But it works for us, too.

$\LARGE {\frac {1} {\pi r^2 n_v} }$

$r^2$ here is the radius of our fired slug as it travels through space plus the radius of what we're interested in hitting (space ships) and $n_v$ is the average density of the objects we're interested in hitting (other space ships).1

We'll be generous on both fronts and round the numbers up a little bit2:

• $r^2$ = 2,000 km (approximate radius of the moon)
• $n_v$ = $1.5 * 10^{-37} g/m^3$ (average density of the solar system)

This results in a mean path length of...$5.3 * 10^{29}$ km or $5.618 *10^{16}$ light years. That's approximately 604 thousand times the diameter of the observable universe that the shot would need to travel, on average, in order to hit anything.

But, I can still find enjoyment in stories like these anyway.

1. "Average density of the objects" meaning, their frequency of occurrence in a given volume space. Not their material density.
2. Larger values here result in shorter distances.

Don't think it would cause any problems to people on the planets, as meteors much larger than bullets(even cannonballs) have simply burn'd up in the atmosphere. Space is big, but it could happen(not sure how likely) that some of the bullets hit other ships nearby, depending on how many were fired. As far as lasers are concerned, it would depend on how well focused they are(see this what if xkcd article for more information about that). If a missile missed all the ships, but was programmed to seek something, then either some other ships or some place on one of the planets would have a bad problem if it didn't hit the star or get really confused and run out of the system. Anything that doesn't seek out anything isn't really likely to do anything but get sucked into a planet or the star or just fly off into deep space.

Your question reminds me of this question: Could an astronaut safely shoot the Sun with a gun?

TL;DR No.

Basically, the Delta-V required to change the trajectory is HUGE! Much, much bigger than the feeble amount of energy needed to hit the nearby ships (about 25 times as much as firing a bullet into the Sun from Earth's orbit). Your spent munitions would (in most cases) be on only a slightly different trajectory from the ship there were fired from.

If your ship is in an elliptic orbit, so will its munitions be. If your ship is on a hyperbolic trajectory leading out of the system, so will its munitions be. Only in extremely borderline cases (e.g. a parabolic trajectory) will the trajectory type change, however, it's extremely undesirable to be in such a trajectory in the first place because of the waste of energy to do so. See Eccentricity classifications.

It's unlikely that any ships will be on a trajectory that will intersect (read crash) with a planet or other body, since the Delta-V to into that trajectory is huge, and the Delta-V to get out of that trajectory is equally huge. It would be suicidally stupid to waste so much energy in space, even and especially in a space battle.

It would be a waste of energy to have weapons that could significantly change the trajectories of their munitions, when much lower powered weapons can still destroy or incapacitate an enemy vessel. The guns would also need to be massively reinforced to be able to deliver that much energy in one go without sustaining damage that could cause a critical failure, and believe me, when you're using that much energy you don't want your gun exploding!

Missiles would have to have huge fuel stores (picture launching the Space Shuttle or Falcon Heavy or bigger for every missile). Again, this would be overkill and a waste of energy and resources.

What would happen is that you would end up with a cloud of debris that would gradually spread out since each piece is on a different trajectory. It would become so diffuse that it's unlikely that any piece would hit a future ship passing through the area. The gravity of the planets in the system would slowly change the trajectories over millions of years to either stabilise them, or throw them out of the system. This is similar to the cloud of orbital debris around Earth (which is only a very slight problem at the moment) but much more diffuse. A high Earth orbit is above 35 000 km (more than 40 000 km from the centre of the Earth). The Earth is about 150 000 000 km from the centre of the Sun. That's a ratio of roughly 1:4000. None of the pieces have any chance of hitting a planet for millions of years. There is a very slight chance of a piece hitting a ship in the same area, but no chance at all if the ship is elsewhere in the system.

Lasers dissipate with the inverse square law, just like regular light does. So over astronomical distances, it would be so weak as to have no effect, again unless you were willing to waste enough energy to overcome this, and all the engineering challenges this would entail.

P.S. The effective range would be infinite, if you consider an orbit to be never-ending. Otherwise, limited to the difference between the perihelion and aphelion of the munition's orbit.

• @Gryphon Please be a bit more careful with your edits. Some of your edits are purely a matter of style, and the original author's style is just as good as yours. I noticed you changed all of my Australian spelling to American spelling. I respect that Americans spell differently from Australians. Please be respectful of us and our spelling too. You also introduced some grammatical and punctuation errors into my answer. I've rolled back your edit because none of the changes were beneficial. Thank you for caring! :-) – CJ Dennis Jul 12 '18 at 3:31
• Which raises an interesting point - given sufficiently detailed information from a battle and a sufficiently high-performance spaceship (or drone) it may be possible to intentionally retrieve projectiles fired in a battle after the event. And then launch them at something/someone else to make it look like an accident resulting from the battle. – KerrAvon2055 Jul 12 '18 at 5:44

The primary reason that you would have few issues with the stray rounds striking planets or causing issues, besides the immense distances between objects in space, is the fact that weapons fire would likely be faster than the local escape velocity.

A battle between spacecraft in LEO where projectile velocity is faster than the @ 7 km/sec of Earth escape velocity would see bursts of projectiles flying out into deep space. Interplanetary space battles would need correspondingly higher velocities of the projectiles, since the spacecraft would also be moving at interplanetary velocities.

In the Earth's solar system, the fastest an unpowered object could go while remaining bound by the Sun's gravity is @ 72 Km/sec, and many proposed weapons systems might actually be capable of moving faster. Nuclear propelled "shotgun rounds" can capture 5% of the energy of a nuclear explosion to accelerate pellets to 100km/sec. Nuclear shaped charges and EFP's can move faster yet (See the Atomic Rocket's website for more details).

Even objects moving at less than solar escape velocity would pass the vast majority of planets, asteroids and so on, and zoom out on highly elliptical orbits like those of comets. We are talking long term comets which take thousands of years to return to their origin points (and even than they might persist in their orbits for billions of years before possibly intersecting another object).

But the Gun Captains on space warships are a pretty tough lot, and would minimize even that

• I can't believe it's taken this long for someone to cite Sir Isaac Newton as the Deadliest SOB in Space. :) – Shadur Jul 12 '18 at 7:05

Laser beams are very straight but they do slowly diverge. If aimed at a distant planet, the beam will probably be spread over millions of square kilometers and will be very weak, barely even detectable.

Railgun slugs will burn up in the atmosphere of an Earth-like planet, so only spaceships, space stations and people on planets without atmospheres will be vulnerable. Since they will be carrying just as much energy as when they were fired, they can potentially do damage, but the vast majority of slugs will hit uninhabited rocks that no-one cares about, so we're talking about rare events where a single hole is made through a station, possibly killing someone but not destroying the whole place.

Nuclear missiles contain conventional explosives which have to be detonated with the correct timing to make the fissile material go supercritical. If the missile simply smashes into something it is likely to explode but it will not be a nuclear explosion, it will be as a dirty bomb. Treat it as a regular missile.

Regular missiles are probably the most dangerous, since they may be partly designed for atmospheric use and might not burn up in the atmosphere. This greatly increases the number of potential victims, and a stray missile from space could kill a lot of people on Earth.

All that said, there has not been even one recorded case in history of anyone being killed by a meteorite, and meteorites will remain significantly more common than stray shots from a space battle.

At "the outskirts of the solar system", there is, as everyone has written, no real big deal.

What about in orbit around an inhabited planet, though?

Even there, the problem will not be the bullets, missiles, railgun slugs, or whatever, since there's only one of them per bullet.

The problem instead will be the debris that other people have mentioned in passing.

The bullets will be fired from something moving at orbital speed, to something else moving at orbital speed. The bullets won't be significantly faster or slower than orbital speed, because once you're moving at a good few miles (or kilometres) a second there's really no point using a lot of energy to go much faster.

If you're in orbit around an inhabited planet, this could be devastating.

By destroying a single satellite, the Chinese in 2007 added over 3,000 pieces of trackable debris into orbit around Earth, as well as a cloud of countless smaller particles. At orbital velocities, paintflecks strike with the same kinetic energy as a rifle bullet. A 4in (10cm) object would impart kinetic energy equivalent to 25 sticks of dynamite.

If the battle is in low orbit, and explosively destroys a significant proportion of two fleets and all the shrapnel from their missiles, then within 15 minutes (or whatever the low orbit period for that planet is) the planet will be surrounded by a cloud of debris: satellites, space stations etc which are hit by those will be shredded, each one adding a few thousand more particles to the cloud as it is hit. The particles in the cloud would also intercollide, creating more and more fragments in a runaway reaction.

But how likely are they to be hit?

For an estimation of the risk: currently, collision avoidance maneuvers are performed a "couple of times a year" on the ISS (I'll call this "once every 200 days": anyone got more specific stats?) and are performed if the chance of collision is higher than 1 in 100,000. There are about half a million pieces of debris being tracked.

So naively, to get a probable hit once a day you'd need 200 * 100,000 * 500,000 = 10M particles. Statistics isn't linear, so multiplying by 100,000 doesn't change that 1:100,000 into a 1:1, but it's good enough for our purposes.

To get a probably hit once an hour, which is what you'd need to have a good chance of hitting anything that launched, you'd need about a quarter billion trackable particles to blockade the planet.

This would make launches completely infeasible and wipe out all satellites and space stations at that level. Whatever level the battle happened at, it would likely destroy everything below it and an almost equal distance above it, through elliptical orbits and orbital degradation. Anything happening at a significantly higher levels much, as if the orbits were that elliptical then the debris would collide with the planet. So if the battle happened in low orbit, geostationary sats would be mostly safe, for example.

You'd need rather more particles as your orbital radius increased, though, as every doubling of the altitude would cube the volume.

This leads to an obvious military approach of "dusting" planets with a few billion particles each to prevent them launching against you, when you attack their solar system. At that point, you then have air superiority, and all the planets have to do what you want or you drop bigger rocks on them.