Some initial thoughts on accuracy:
Railgun Size: 200 tons Surface Area: 165.4
, assuming a sphere, has a radius of 3.63m. Length double to 7.2m, call it 10m for some order of magnitude calculations. Unlikely to be 100m long though, but the point remains.
Steve's 4800MJ railgun has a Muzzle velocity of 100,000 m/s, which I like because its a round number.
To hit a target 1,000,000m away, the flight time is 10 seconds. All discussion below assumes the target, an enlarged Daring class ship, is stationary.
The projectile must accelerate from rest to 100,000m/s along a distance of 10m, and then fly for 1,000,000m. Any deviation along the 10m length in the rails will be magnified by 100,000 by the the projectile hits the target. And this is not just limited to the rails, but also the relationship between where the rails are pointing, and where the targeting computer thinks they are pointed, which could be affected by defelction caused by heat, or large accelerations. The quality of the shot could also affect its path: if it does not have a homogenous density, then it might be subject to uneven acceleration. This might affect missiles etc which are not supposed to be solid iron. I am on shaky ground with the maths here though.
The shot can obviously deviate if the target is large enough, but a 100m Daring is 1:10,000 of the 1,000,000m range, so there is only a limited opportunity for shots to deviate and still hit.
Similar logic can be applied to long distance plant bombardment. In theory you can arrive at the edge of the solar system, aim, and launch, then be long gone before the shots arrive at the planet.
However, this assumes that you know with great accuracy the orbit of the planet, which requires you to know its mass, and the mass of the sun. And how fast it perihelion advances. And any influence from other large planets, for example Jupiter. Or any large moons.
Although Aurora doesn’t consider gravity (yet), it would have to be considered in reality, as the target planet might not be directly in line with the sun on our side of the solar system.
Size of earth is 12,742km from wiki, or 10,000km by order of magnitude.
Orbit of Uranus is 3,004,419,704km, again from wiki, or 1,000,000,000km by order of magnitude. So the target is 10 times smaller than the Daring in proportion, or a diameter 1:100,000 of the range. While the shots might have the range, they have a small target to hit.
Solar wind might also have an impact, as would sunlight itself, and any dust or debris in the system.
From
here and
here a modern rifle is accurate to 1 arc minute over 100m, or nearly 3cm over 100m. For order of magnitude calculations, we can round that to 1cm over 100m, or .01m over 100m, or 1:10,000.
All this, and I conclude:
A railgun shooting 1,000,000m to hit a target 100m wide is about the same accuracy as our modern rifles.
A railgun shooting the earth from Uranus is about 10x more difficult than current technology, assuming a straight shot. As soon as the planets are moving, things get much more difficult. In theory if the system has been grav surveyed then you would have this information, but it would need to be accurate to allow a 1:100,000 shot.
All this to say, that really if Steve wants a range limit of railguns and interplanetary bombardment, there is enough (dodgy?) physics to justify it.
Let me know if my maths and physics is off here, as it has been a while since I had to think like this.