Ignoring gravity (as the roads are travelling quite fast), the rods move on straight-line trajectories between deflector stations, and these trajectories must never intersect the planet. If we continue these trajectories past the deflector station, they also never intersect the planet (consider the circumscribed circle around the deflector stations). It is thus not possible to hit the planet with one station "skipping a turn". This is also quite obvious if you look at the graphics your Claude generated. While it would be possible for your deflector stations to do extra deflection, this isn't what is specified here.

The momentum changes on the rods are also substantial even without firing, so your stations will knock themselves out of orbit, and would need active manoeuvring or to be very heavy and operate as cursed statites held up by deflection (which will need some complex control changes as the number of rods varies).

I also don't think the rods can reasonably reach 0.01c on 2 rocket fuel, but this is a relatively minor concern.

i don't have any deep knowledge of physic....

tacking earth as example.....

Orbital speed is 7.8km/s just to reach any orbit in vaccum
in 500km heigh orbit the orbital speed is still around 7.2 km/s
in 30.000km heigh the orbital speed is still 3.4 km/s
As long as the speed will not exceed escape velocity of 11.2km/s we have a reasonable orbit.
so 30000 km/s is reasonable well above the escape velocity so we need to have a lot and quite strong deflectors to keep the rods in an orbit

In the end i think its about applied forces and the energy available/needed to have this working, albeit realistically not so much...

But Nauvis is sure not exactly earth...

in sense of game and SF i would say make much such stations and they have to be very very costly to produce (like 100 accumulators and much more solar panels to generate the energy which is needed to have working Satellites which will bend the paths of the rods. and a serious cooling time to have the used station in place again through action/reaction process of applying the deflection (one set for maintaing the ring, one set for impact deflection)

Probably also have some more energy available as with reactors/fusion / fuel cells and what not to pick from Factorio (Aquilo)
As such a deflection will need the energy in a very very short time it would be reasunable to use also highspeed capacitors and supercondutors

Also pickable energy in orbit with a magnetic field would be some thethers

So you can probably stretch out the research for all this....
as everything is high speed some little change will lead to huge differences, maybe there is also (infinite) reasearch for impact accuracy (first stage is about 100 tiles off, so the better the more exactly ?

Could be also mores stages as on your roadmap.....
first one for the simple boiler plate rods-from-god using just gravity impact energy.
secound stage then the storage ring using fulgorian and more

ok the geometry one actually got me ngl. you're right, if a station just doesn't deflect, the rod stays outside the ring and goes into a wider orbit, not down. so it doesn't hit anything, it
just leaves. the biters get menaced by a rock that left lol. so yeah "a shot is a skipped turn" is cope, I'll fix the wording. the firing station has to actually kick the rod down, which btw is
exactly the energy-burst thing the other comment was talking about (supercaps dumping everything at once). funny that you both landed on the same fix from different directions.

the recoil point I genuinely love. of course bending a rod at 0.01c shoves the station back. so the "ring" is really a bunch of statites holding themselves up by constantly throwing tungsten,
and the balance shifts every time you add or fire a rod. that's cursed and I kind of want to keep it as a lore thing — let a ring run out of power and it slowly falls out of the sky.

the expensive-stations-with-real-power direction I like a lot. right now a station is "one rocket" which is way too cheap. splitting ring-keeping vs the impact kick, capacitor banks, a dumb
gravity-drop tier before the proper ring, accuracy research so early shots miss by 100 tiles... that's basically a whole tech tree and it's going in the notes. won't get to all of it soon but
it's the direction.

(the 0.01c on two fuel thing — yeah fair, but I also carry a fusion reactor in my backpack in this game so I stopped fighting that battle a while ago)

anyway this is the good stuff. mod literally started as a petty revenge thing because a Rampant nest burned down my factory, and now people are doing actual orbital mechanics to tell me my
revenge doesn't work. love it.

If I may. From a physics standpoint, you’re right.
But you’ve forgotten one important fact - this is a game, not reality.
We literally have a fusion reactor that weighs a whole bunch of kilograms, and we just stick it in our armor so it generates endless energy for us, lol.
But yeah, the mod definitely needs to be rebalanced, since all the recipes are pretty simple and the effect is insanely destructive.