The old statement that where math is precise it doesn't describe reality, and where math describes reality it is not precise applies here.
That would be important if our officer's were doing the math with pencil and paper. Luckily they will have computers.
You can land on the moon, you can get satellites in orbit, you can dock at the ISS, but these all have months of math double and triple checked and based off of decades of measurements.
The trajectories for all of those scenarios, and more, can be calculated in seconds with modern computers and modern commercially available software, like this one:
http://www.agi.com/products/by-product-type/applications/stk/stk-for-space-missions/There are a lot of things that need to be done to prepare for an ISS rendezvous, having every one hanging around waiting for a supercomputer to finish a 90 day calculation is not one of them.
It's true that there are decades of measurements that go into the models that predict these movements, however those decades are for incremental improvements. For example breaking Earth's gravity field up into 2450 pieces rather than 800 pieces, or making density 80% accurate instead of 78% accurate (yeah, density is the killer, everything else is really straightforward, not density.) Also, a lot of those incremental improvements are for things that need ridiculous levels of accuracy. Shooting down a GPS satellite doesn't need the Earth to be into 2450 pieces, knowing where GPS satellites are precisely enough that they can help with the positions and timings needed for an experiment comparing the speeds of photons and neutrinos, that needs more accuracy.
And even with all of this accumulated data, just check how closely we could predict the crash sites of the last couple satelites that came down.
That's all because even the best models for density aren't all that great, also helped along by the fact that those satellites were out of control and tumbling, making calculating their Cd or Area at any time also tricky. I have been ignoring the inaccuracy of density models in this thread because Steve isn't modeling density, and the vast majority of Aurora combat happens more than 400km above the Earth's surface, so it seems silly to base the accuracy for all long-ranged shooting on that one case.
And on the idea of a guided railgun projectile, I don't buy it. If you can design a sensor that could withstand the acceleration of the shot, it could withstand being hit with a fair portion of that level of energy. We can make (semi) guided munitions for artillery, but none of it will be acheiving anywhere close to the G's of those railguns.
In ten seconds of googling the first reference I found to shooting a rocket out of a gun was the Russians doing it in their T-72 tanks back in 1985. I'm sure it was done in various other situations earlier. In fact I am pretty sure that Gerald Bull successfully shot rockets out of his enormous cannons in Project Harp back in the 60s. His first tries failed as the propellant deformed on firing, but I believe he was able to get the propellant to survive when he slowly filled the tank of (dry) propellant with salt water so that all of the voids in between the propellant grains were filled. Unfortunately I was not able to find any citations to back that up. You are assuming that there have been no electronic or material advancements to partner with the rail gun advancements. You are right that shooting an Excalibur out of one of these railguns would convert it to paste, but we aren't talking about doing that.
It isn't just a little more than the breaking strength of any known material, it is an order of magnitude bigger.
Acceleration doesn't directly compare against "breaking strength" so I don't know what you are talking about here. Also you haven't given any breaking strengths of the material you are talking about, and honestly in my mind "Order of Magnitude Bigger than modern technology" has been my ballpark comparison for every "trans-newtonian" starting tech.
All that said, I actually would approve of lower acceptable muzzle velocities for shrapnel, kinetic, etc, etc warheads. (Or even G requirements if Steve wanted to model Railgun length) These could either be individual tech lines, or simply static multipliers. For example.
Projectile muzzle velocity modifiers:
<list>
<li>Slug: 1.0</li>
<li>Kinetic Missile: 0.8</li>
<li>Shrapnel Missile: 0.7</li>
<li>Conventional Missile: 0.5</li>
<li>Nuclear Missile: 0.3</li>
<li>Laser Rod Missile: 0.2</li>
</list>
