What would be a good engagement distance for space ships, assuming it took place in the sol system

Question

(Edited due to oversights and ridiculous numbers) So I was curious about this. I know similar questions have been asked but they all have specific parameters that are different from mine.

All ships are equipped with dark matter engines, allowing them to accelerate faster then what should be possible given the limitations of the human body, at around 2500gs for sublight when all power is to the engines, and around 250gs of acceleration when combat systems are being used. There are also maneuvering thrusters with a max of around 200gs accelerationfor them.

So basically all ships are equipped with laser weapons no matter the size. The power will differ but they all have lasers. 2: smaller ships (gunships, corvettes) will have mass drivers that fire rounds at about .3c. Larger ships like destroyers and cruisers (apart from heavy cruisers) use Railguns that fire rounds at around 2200gs Heavy cruisers, carriers and Battleships will use Gauss cannons to fire rounds at about 2500gs

Small ships will have kinetic and energy point defense weapons. Kinetic ones fire rounds at 1300gs

Large ships will have heavy autocannons and converted mass drivers as point defenses along with energy weapons. Autocannons fire at 1500gs base velocity and mass drivers at 2000gs

All ships have some form of torpedo, most ships use torpedoes that have a base acceleration of around 2100gs and a burnout time of 3 minutes. They are radar guided. Carriers and battleships will often use larger warheads that have an acceleration of 2500gs and a burnout time of 3.5 minutes

Carriers carry gunships and corvettes, along with landing craft. Ship armor and shields is normally good enough especially for larger ships that engagements can be drawn out, for smaller ships capital class weapons will usually destroy them relatively fast. All targeting is done with AI, target acquisition and the discharging of weapons is done by humans but tracking and leading is done by targeting AI most of the time. Some ships have their whole weapon system completely controlled by AI while others split the responsibility. I’m also curious about how they would fare against more.... realistic ships IE ships that are less advanced, IE more realistic ships that are bounded by basic physics and human biology (can’t accelerate too fast, stuff like that) assuming that things like shielding and armor stay consistent for simplicity.

Answer 1

Let's assume, for convenience, that the diameter of the laser is about the diameter of the target ship. If ships of any type can perform evasive maneuvers at, say, 2000 gravities, then the distance at which a weapon can reasonably reliably hit is the distance at which the travel time of the weapon to the target ship is less than than the time it takes for the target ship to move one ship-length. At longer distances, the ship has enough time to move out of the way of the beam by randomly accelerating / decelerating.

So, at 2000 g (19,620 m/s²) a ship would move about 98.1 meters in 0.10 sec. and about 220.8 meters in 0.15 sec. since acceleration compounds. (For comparison, an Iowa class battleship used in WW2 is about 270 meters long.) A laser beam moves at the speed of light, unsurprisingly, so your engagement distance for lasers might only be at around ~0.15 light second, which is about 45,000 kilometers. The solid projectile weapons (railguns, autocannon, mass drivers, etc.) fare even more poorly since their projectiles are much, much slower and have a much smaller size than the laser beam, they are easier to dodge.

(But wait, you say, what if I make the laser's beam width bigger? Well, that increases the chances of hitting the target but also weakens the beam since its energy is spread out over a larger area. How much? Quite a lot; good ol' πr² tells us that if you double the diameter of the beam, you get 1/4 the intensity and if you triple the diameter of the beam, the beam is at 1/9th the intensity.)

The torpedoes simply have no effect except at point blank range. 2000 g is, as mentioned earlier, about 19,620 m/s², so any ship easily outruns the acceleration of the 8,500 m/s² torpedoes.