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NonCredibleDefense
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From a purely physical point of view, is that realistic?
If all of its energy is kinetic, it means that the energy must result from it's potential energy+any fuel it is propelled with. Ignoring air-friction and terminal velocity for free falling objects, that means that still the energy of a nuclear weapon is required to bring this thing up into space, or stored as fuel for its propulsion.
So unless the projectile is assembled in space, any rocket bringing it into space will contain at least the energy of a nuclear warhead. Gotta be a very nervous launch, knowing that any failure will result in a fire with the energy of a nuke.
Gravity is your friend. It's more when it's in orbit that you should be careful.
Gravity is not your friend. Getting stuff into LEO is still expensive af. A kinetic projectile dropped from space might have the same energy as a nuke, but it's still going to be a lot more expensive. Additionally, you don't have options on how that energy is released. It's going into the ground and that's that. A nuke (or any other explosive device for that matter) on the other hand can be detonated at a chosen altitude, or as a bunker buster if that's what you want.
The heavier the object, the more it's going to take to push it out of that orbit. If your weapon system is in LEO, you can realistically only drop a rod on a small envelope along the future trajectory of the weapon system. Polar orbits would have the best coverage, but fly over a target outside of polar regions only twice a day. In order to get a wider range of firing solutions, the projectile needs considerable deltaV for orbital changes. And again, gravity fucks you over here because deep within Earth's gravity well, changing the orbit of a massive tungsten rod takes a lot of fuel. Higher up these deltaV costs wouldn't be as prohibitive and you'd have more options for using the weapon, but that would increase the time from launch to impact into the regieme of hours, way too slow for anything.
The best solution would be to have a huge amount of rods in different orbits (akin to the spacejunk that is Starlink) to maximize the chances of at least one being able to fire on a target at any given place at any given time, but because those rods are still heavy af, such a plan is completely unfeasable.
Rods from gods will never happen, at least not around Earth.
High orbits are probably the way to go anyway. Not only will the payload be decently higher, the entry angle will be much steeper and more accurate, much easier hide, and much more capable of hitting anywhere in the world. This trades an hour's delay for a day's delay, but this size of weapon is a strategic weapon anyway.
Why would you need to blow up a city in an hour's notice, but not as soon as possible? If WDMs can be used in this situation (MAD doesn't apply), just use a normal ICBM. 15-30 minutes, possibly much larger booms. The advantage of orbital kinetics is stealth and immunity to countermeasures. A country-wide strike could be arranged with only seconds of warning for the targets, possibly getting ahead of most launch sites, leaving only mobile launchers to deal with.
That of course means a new intelligence war, but whoever gets there first has an unstoppable weapon, which might be important depending on how good interceptor weapons get. Even the idea of feasible hypersonic ICBMs is twisting knickers for a reason.
There are very few situations where that amount of lifting capacity is available for such a niche use. But more has been done for stupider, so something dumb very well could end up flying dangerously.
I have my doubts about that stealth. If it were just the tungsten rod by itself, it could well be coated in black, but the impulse needed to drop a massive projectile out of an orbit (and furthermore into a trajectory that impacts at the target) necessitates a relatively hefty maneuvering unit and that has to radiate heat to be kept operational. Cheaping out on the propulsion could be very costly because a failure in the middle of the deorbit burn would result in the rod coming down in a place you don't want it to.
The only way to hide it would be with decoys, which are already used by ICBM's. Unlike ICBM's, an orbital platform would need those decoys well before it's used because there's no terrain to hide in. A ballistic missile sub is very hard to track, satellites, not so much.
About countermeasures: Becuse the rod can't move by itself, it's stuck on a fixed trajectory after the propulsion stage is discarded. This makes it an easy target for an interceptor missile. You already know where to look so the stealthy rod isn't that hard to find, and then you just have to collide with it. And because the rod is coming down from MEO at the very least, you have ample time to do all this. An impact at such speeds would disintigrate anything and the rod isn't an exception. At the very least it would fracture into multiple less aerodynamic pieces that do much less damage than the sum of their parts.
Deorbit hardware isn't big, just a small solid rocket motor would supply most of the thrust, say 100kg thruster for a 5 ton projectile. The deorbit burn is only 100m/s or so. That's some very sensitive monitoring for what amounts to ISS station keeping burns. Monitoring effectiveness could be increased by only tracking oblong objects, but such a burn on the day side might be near impossible to see anyway. This is for the LEO type the US air force is interested in.
A higher orbit projectile system would be slower but more powerful, and wouldn't need more than 3km/s to deorbit, so 4 ton-ish propulsion section (an eccentric orbit could reduce this significantly, but would narrow possible targets. The long period could allow ion engines, but the downside is big solar panels). At 30,000 km high anywhere in the sky, that's a lot of high-power telescopes tracking a lot of sky for just an exhaust plume.
Decoys would only be useful for the burns, and possibly only for false alarms. If you know a projectile is coming, you probably have a good idea about it's target, so moving to a different bunker could be good enough. In the same way, if an actual threat exists out there, a decoy burn could spur movement.
I don't think decoy satellites are useful here. If you can track these projectiles closely enough to detect plumes or small velocity changes, no amount of decoys will be enough, and orbital warfare is an entirely different ballpark.
About countermeasures, trying to intercept outside of the atmosphere requires a suborbital capable missile (probably fully orbit capable for an intercept from MEO), which will be huge and would require an incredibly precise final stage and a convenient launch location to have any chance of hitting. If you have that capability, you could just hit the projectile before it's used at all, but again, that's orbital warfare.
As for atmospheric countermeasures, a LEO type will spend maybe 20 seconds in atmosphere, mostly covered with a ball of plasma, so tracking could be a non-issue, depending on method. The issue is hitting with enough force to do anything about it. Most interceptor weapons are designed for much weaker, much much slower targets, and anything short of a direct hit will do nothing. A MEO type will be even faster, with less than 10 seconds of plasma and moving over 8 km every second. Good luck hitting that.