Trust me
I make it a habit of not bringing personal identities into internet arguments for a couple reasons, mainly because anyone can claim to be anything on the internet, and also because I don't like appeals to authority. I think that reasoned arguments (and lots of math) are the best way to go about things. However at this point we are really talking about more nebulous claims than can easily be demonstrated, and you've said "trust me" twice, so I suppose I'll return with the "I do this (examination and implementation of force and environment models to accurately propagate space craft and other heavenly bodies) for a living." I'm a software developer for the company I've linked to twice now, and the main developer of one of their propagation products.
it takes longer than you think to come up with the numbers. We have been watching Eris, Sedna, and a number of outer system bodies the size of a small planet and STILL don't have the orbits fixed. In fact Sedna is still a best guess on its path. We could be off by a lot.
You are talking about jumping in from WAY out past these planets and getting accurate data on a body. Gonna take a while....
Calculating Sedna's orbit parameters from Earth is a much harder problem than getting a firing solution on Earth (from, say, Neptune). One of those involves propagating the position of an object 12750 km across a few (say 4) weeks forward in time from measurements taken 4.6E9 km away.
The other involves the propagation of a body 8 times smaller 845 times longer (if you were looking for perihelion position, if you wanted to propagate a whole orbit try 148,200 times longer) from measurements taken almost three times further away.
The longer time is the kicker, as uncertainties in position grow geometrically as you propagate them forward in time.
I'm also not sure how you got that I was trying to shoot at Earth from out past Sedna ("WAY" out past Sedna you said). I have really just been using Neptune because I believe days ago I took an arbitrary firing solution against the Daring that seemed reasonable and extrapolated out where a ship that was that accurate could hit Earth from, and it turned out to be around Neptune. I think that a firing point anywhere in the outer solar system would work equally well as Neptune from a "too far away to do anything about until after the attack" standpoint. And honestly the Neptune case was mostly predicated on speeds the Daring could attain pre-Engine Nerf. When you are attacking something closing at higher speeds the relevant range is smaller. Now that the speeds have been lowered if I reran my numbers I may indeed find a position around Jupiter to be more reasonable, but I think for this discussion that the exact position of the shooter is fairly unimportant.
If you are claiming the math is that easy, and establishing a platform so stable to shoot elementary, then we could shoot our scientific probes of asteroids from orbit. We can't. Not even close. Even if we could come up with a platform that stable the interplanetary medium is not very condusive.
If the math was "normal-speak easy" I wouldn't have a job. What I meant was that it was "easy" in the sense that "it's really hard but we have had thousands of people and millions of computing hours working on it and similar problems in the past 40 years and it's now a solved problem". I also assume that in Aurora their algorithms and computers will be no less effective than ours, and will probably be at least an order of magnitude better.
Our 'piddly little engines' are the best we have to work with. My apologies for not reaching your expectations. And that slug at 40 km/s would take a launcher that would dwarf anything we currently have. But on that thought, you mention that it would hit in days. This is a lot more of a problem than I believe you understand (at least with current technology).
Our 'piddly little engines' are not the best we have to work with in Aurora. According to the schematics we've seen capabilities 100x beyond that of our engines will be commonplace in the early game. Similar to that 40 km/s railgun slug, which is the slowest of the railgun muzzle velocities that Steve has posted. What I have been trying to do is take all of the stated abilities of Aurora tech, and look at what they would accomplish if everything else was similar to modern tech levels.
First problem. Stable platform.
According to NASA fact sites the Hubble telescope has a Pointing Accuracy of 7/1000th of an arcsecond, so platforms in space can align to a target with a great deal of stability. Now granted it's another ball game entirely to maintain stability on an object accelerating on a huge cloud of plasma. I suppose Steve could model accuracy penalties while accelerating, but I think he could also handwave that requirement away. We have a variety of ways already to mitigate instability and jolts for both turrets on naval vessels and more rudimentary science experiments, and it would seem fairly reasonable (to me anyways) to just say, "eh, they have something like that".
Now as far as how long it takes the platform to regain stability after a shot, that depends on the mass of the platform, the offset of the barrel from the center of mass, the abilities of the control system to torque the craft, and a heck of a lot of other things that Steve is not modelling. Seems reasonable to just say that the spaceship is able to damp out it's orientation by the time the next shot is ready.
Remember Newton's Third Law and action / reaction. That slug just created an enormous amount of recoil. Unless the slug was perfectly formed (not likely), suffered no deformation, and the slug was accelerated in a perfectly duplicatable manner each time, you won't get very reproducable results.
You can say literally exactly the same thing about any handgun, rifle, or cannon that has ever existed. It basically amounts to saying “it has to be done carefully” all of the problems you are bringing up are what your millions of scientists are supposed to be figuring out in their cush desk jobs on Terraformed Mars.
We will ignore the fact that the slug won't likely survive launch unless the launcher is hundreds of km long (ok, a dozen km would be doable, but building a 10km object??? in space???). The launcher is going to have to absorb energy imparted on it by that slug. The launcher is going to deform (a lot with this much energy) just as a rifle barrel occilates when firing. The dispertion of the bullet is due to a large part in the inablity of anyone to exactly predict where in the occilation the barrel will be when the bullet exits the barrel. This 40km/s projectile is going to induce SERIOUS occilation on the launcher and whatever it is mounted in.
For a normal unguided kinetic slug going through a coil gun or railgun you don’t have to worry about the G force destroying the slug since the magnetic forces apply to the entire projectile fairly uniformly. It is any fancier components of the slug that are not exactly as magnetic as the rest of the material and accelerating at exactly the same rate as the rest of the slug that will be clobbered, but I agree that for now we’ll have to brush that aside and see how Steve decides to fluff that. As far as the rest of it, you say right there that normal cannons undergo the same flexing, and that is what gives them their inaccuracies. Furthermore I cited earlier that those inaccuracies for a high quality civilian-available hunting rifle were around an arc second. I just make the assumption that with the better materials and technology of the Aurora setting they will be able to maintain and improve on modern accuracy even as the capabilities of their weapons improve. I base this on the entirety of our civilized history, which has shown our weapons becoming longer-ranged, higher powered, and more accurate over time.
Additionally I don’t think that I ever argued that the weapons should be perfectly accurate, on the contrary I think that introducing weapon accuracy in fractions of an arc second or radian as an additional design/research category would be pretty sweet.
I will have to do some more math before I can quantify the sort of effect the interplanetary dust cloud may have on a trajectory, but I would like a citation for that “100,000 particles per cubic centimeter” That is 5 times that of a typical number of gas molecules in a cubic centimeter of atmosphere at 500km above the Earth’s surface.
