In theory it could require about the same number of rocket launches from the ground as it took to launch the satellites in the first place. You'd just do a single launch with lots and lots of satellites which you gradually move into orbits that hit the Starlink satellites.
The killers don't need to spend weight on payload, and they can be designed for a lifespan of a few weeks, so for example they can carry very small amounts of propellant. They might be small enough that you can't see them until they strike, at which point it might be hard to determine who had launched them. You might think maneuvering thrusters would be visible because they glowed, but resistojets can run at subzero temperatures. It just makes them less efficient.
The saving grace is that as far as I know nobody has such a system flying or ready to fly; the Kosmos 1408 test seems to be the state of the art. And it would probably cause a dramatic takeoff of Kessler syndrome at least in LEO, destroying other satellites as well, eventually everything in LEO. Aside from being a public relations catastrophe, this would dramatically diminish the wartime advantage of spacefaring powers like Russia, China, and the US over non-spacefaring powers like Iran, so those spacefaring powers might be reluctant to use such a weapon if they had it.
You say, "attacking US satellites would probably be an act of war." Well, maybe. But it's just property damage; no human lives are at risk. And SpaceX is theoretically a private company, not officially part of the US military. If damaging the property of private citizens is "an act of war" then just about every country whose citizens own property in Ukraine has a casus belli against Russia now. And in that case Russia also has a casus belli against Germany: https://www.theguardian.com/world/2022/mar/03/germany-seizes...
AFAIK Starlink user terminals aren't designed for stealth, so it would be foolish to expect stealth from them. However, they use millimeter-wave phased arrays with hundreds of elements, so they probably aren't crawling with sidelobes, and in theory their beam divergence would be about a degree with isotropic radiation more than 20dB down from the main beam, so it might be hard to detect until you're passing through the beam. And I'm guessing most anti-radar missiles are currently designed for regular microwaves, not millimeter waves. I don't know anything about Starlink's technical specs, though, and not much about millimeter-wave communications, and nothing about anti-radar missiles.
> In theory it could require about the same number of rocket launches from the ground as it took to launch the satellites in the first place.
You have very dubious reasoning about this. It sounds like you are calculating attacking each satelite with an individually maneuverable free-flying space vehicle. This is clearly not the most optimal way to do it so it is not the right calculation to estimate the minimal number of launches required.
Instead of thinking about smart and expensive satelite killers each with the complexity of a faberge-egg you can pack a missile full of nails and spread them into an expanding cloud with a timed explosive. A shrapnel bomb in orbit if you please. Will one launch suffice to kill all the starlink sats? Maybe, maybe you need two or 3 at different inclinations. You definietly don’t need as many launches as many spacex needed to put their satelites up.
Well, I was trying to make the case that it's not dramatically harder to take Starlink down than it was to put it up. If your barrel bomb full of nails works, that would be even stronger evidence that it's not dramatically harder.
My intuition, though, is that it wouldn't work. Kosmos 1408 became a two-tonne barrel bomb full of nails in November and so far isn't known to have taken down any other satellites.
I don't really understand orbital mechanics, so take the following with a grain of salt.
The Starlink satellites weigh 230-300 kg and orbit at 540-570 km altitude, at which altitude the thermosphere will passively deorbit failed satellites within 5 years. I think a metal object weighing 10 g, such as a nail, would deorbit about 30 times faster, about 2 months, because it weighs 27000 times less but only has about 900 times less surface area. But that's assuming the nail is in orbit in the first place. If you have a barrel bomb in LEO and you blow it up, sending the nails in every direction, most of them will immediately deorbit: those traveling backwards or down will deorbit immediately, while those traveling forwards or up will deorbit 45 minutes later on the other side of the earth.
Only a narrow plane of the shrapnel will stay in orbit at all. If the shrapnel forms a sphere around where the barrel would have been if it hadn't exploded, a plane through its center intersects that sphere in a circle. The nails in this circle will stay in orbit: some are going sideways, some forward and down, others backward and up.
The Minkowski sum of a nail and a Starlink satellite is almost exactly the same size as a Starlink satellite, so we can think of each nail as sweeping out a Starlink-satellite-sized path in its orbit. I don't know how big the satellites are, but they must be on the order of 50 liters to weigh what they do if they're mostly made of metal, which would make them on the order of 40 cm in diameter. So each nail is sweeping out roughly 40 cm x 40 cm x 7000 m/s. So over the course of two months before it deorbits, it sweeps out about 5.9 billion cubic meters (5.9e9).
If we approximate the Starlink volume as a 30 km thick sphere beginning 540 km above earth's surface, its inside radius is about 6911 km and outside radius about 6941 km. That has a volume of 1.8e19 cubic meters. So a random nail has a chance of about 1 in 3 billion of killing a particular Starlink satellite, of which there are almost 2000, so about 1 in 1.5 million of killing any of them.
From one point of view that suggests that a barrel of nails could work; you just need several million nails to kill any satellites (thus, tens of tonnes, which is feasible) and several billion nails to kill them all (which is not).
Smart and expensive killer satellites are likely to be much more cost-effective. Faberge eggs are far too simple, though; your killer satellites need to be more like the complexity of a feature phone. A feature phone controlling a Bernz-O-Matic valve, though.
I think the more general point here is that, because LEO is a place, people tend to think of it as being kind of like Central Park or Spain, giving them misleading intuitions about what kinds of interactions to expect. A good starting point for your intuition pump is to remember that the surface area of LEO is basically the same as the surface area of Earth. It's slightly larger, because the radius is larger, but the radius is only about 8% larger in this case.
Now consider that we're talking about, in this case, satellites distributed over 30 km of altitude (thickness). This gives you a volume that's roughly ten times the volume of the Earth's oceans. (You can throw in the crust too if you find it helpful.) So instead of thinking about shrapnel from a barrel bomb trying to hit a microwave oven in Central Park, think about trying to hit a microwave oven somewhere in the oceans of ten Earth-sized planets. Even with a 7-km-per-second supertorpedo with two months of fuel, it's not going to be easy without guidance.
Space, in short, is big.
I'd like to blame stupid movies like Star Wars and Gravity for this, but I think it's just the kind of cognitive error the humans are unavoidably prone to. It's easy to get results that are off by nine orders of magnitude like this when you just rely on your untutored intuition.
The other counterintuitive thing about LEO is that, though for hypervelocity collisions it's a three-dimensional space, for things like rendezvous or getting from your launch trajectory to your desired orbit, it's a six-dimensional space of orbital elements. For understanding the results of a barrel bomb in orbit, it may be more useful to think of the nails as being distributed across a small ball of this six-dimensional space in the six-dimensional point occupied by the barrel, rather than gradually spreading out in a complicated way in three-dimensional space. The humans are not good at intuitively reasoning about six-dimensional spaces either.
The killers don't need to spend weight on payload, and they can be designed for a lifespan of a few weeks, so for example they can carry very small amounts of propellant. They might be small enough that you can't see them until they strike, at which point it might be hard to determine who had launched them. You might think maneuvering thrusters would be visible because they glowed, but resistojets can run at subzero temperatures. It just makes them less efficient.
The saving grace is that as far as I know nobody has such a system flying or ready to fly; the Kosmos 1408 test seems to be the state of the art. And it would probably cause a dramatic takeoff of Kessler syndrome at least in LEO, destroying other satellites as well, eventually everything in LEO. Aside from being a public relations catastrophe, this would dramatically diminish the wartime advantage of spacefaring powers like Russia, China, and the US over non-spacefaring powers like Iran, so those spacefaring powers might be reluctant to use such a weapon if they had it.
You say, "attacking US satellites would probably be an act of war." Well, maybe. But it's just property damage; no human lives are at risk. And SpaceX is theoretically a private company, not officially part of the US military. If damaging the property of private citizens is "an act of war" then just about every country whose citizens own property in Ukraine has a casus belli against Russia now. And in that case Russia also has a casus belli against Germany: https://www.theguardian.com/world/2022/mar/03/germany-seizes...
AFAIK Starlink user terminals aren't designed for stealth, so it would be foolish to expect stealth from them. However, they use millimeter-wave phased arrays with hundreds of elements, so they probably aren't crawling with sidelobes, and in theory their beam divergence would be about a degree with isotropic radiation more than 20dB down from the main beam, so it might be hard to detect until you're passing through the beam. And I'm guessing most anti-radar missiles are currently designed for regular microwaves, not millimeter waves. I don't know anything about Starlink's technical specs, though, and not much about millimeter-wave communications, and nothing about anti-radar missiles.