How Precisely Can a Space Cannon be Targeted?

Question

If I have spaceships that are firing some variety of cannon at each other - MAC, laser, particle cannon, doesn't really matter the type - at extreme range, then even if the gun itself were somehow perfectly precise, the targeting system on which it is mounted is not. If the gun is spinally mounted, the ship will need to turn towards the target, and there's some imprecision there. If the gun is in a turret, there's only so much the aim can be refined with engineering limits.

So my question is: With MODERN technology, how precisely can we aim at a target? Even if I have a gamma-ray laser that can vaporize a target at a range of several light-seconds, and the target can't maneuver in time to evade, it's pointless if I can't HIT the spot I'm aiming at. Having an idea of what we can do with modern tech will give me a lower limit for how accurate a futuristic warship would be.

Answer 1

Depends how long do you need to orient the weapon on the ship to damage it.

If you need the beam to hold for a long time (>1sec), or your using railguns:

I'd be looking at the accuracy of surveying tools like Theodolites. Here's one on eBay than can do 10 seconds of angular accuracy.

That's (10 / 60 / 60)'th of a degree. 0.00277778 degrees. That's about 5cm accuracy at 1km. 1m accuracy at 20km. It could hit a 100m ship at 2,000km.

That's just what the ebay one can do. Assume military grade is twice as accurate. I've found references to encoders able to do 5 seconds of accuracy. So a 100m ship at 4,000km.

If you only need to hit it with a laser for a fraction of a second, or pulses are fine:

We can measure time much more accurately than we can measure angles. So lets measure time instead and use time to measure the angles very precisely.

You can achieve incredible accuracy using rotating mirrors and a static laser fired at precise times to send pulses in exact directions. This is a process we use at my work to build laser scanners for surveying mines / crime scenes / car crashes / etc. You can use it to send gamma ray death beams nanoseconds long.

The process is to start rotating your mirror at a slow, steady speed, put the laser on at low intensity and record exactly when it hits a sensor (inside the gun housing). From that calculate the exact rotation speed and phase of the rotating mirror. If your mirror is doing 1rps, and your computer / sensor / etc is capable of running at 5ghz, you can turn the laser on and off very precisely at the exact angles you need - you can get your laser accurate to 0.000000072 degrees.

That's accurate to 1mm at 1000km. (Could probably do laser eye surgery at 1km). Hit the moons surface within 30cm. 1m accuracy at 1,000,000km. Hit a ship 150m in size in orbit around Mars from Earth orbit.

Answer 2

More accurate than you might think possible

Let's look at a surprising science: photography.

When doing photography of objects that are distant, low light or both you need to have a longer exposure to make the image bright and detailed enough. But anyone these days can tell you that making a picture in a dark room is difficult. You need a steady hand as well. If you've ever worked with telelens cameras to photograph a distant object, you also know the tiniest movement can make the desired object disappear.

Now lets look at one of our most long distant camera. The Hubble telescope. Space is unimaginably big. Pointing it at different stars with a zoom that will give us enough resolution requires an incredibly stable camera. Unfortunately the camera us hurtling through space at huge velocities. For the exposure required you still need some tracking for the most minute changes to keep the camera steady and focused. They even struggled with this at first and made it so it could turn even slower to track more and more distant and low light objects. To quote NASA:

The level of stability and precision that the FGSs provide gives Hubble the ability to remain pointed at a target with no more than 0.007 arcsecond of deviation over extended periods of time. This is the same as holding a laser beam focused on Franklin D. Roosevelt’s head on a dime roughly 200 miles away — which is about the distance from Washington, D.C., to the Empire State Building in New York City — for 24 hours.

If you can point a camera with such small tracking to other stars and planets in other solar systems, you could fire there as well. Mind you, this was made with the end of 1980's technology and since somewhat improved, but if we build something new with today's technology we'll probably make it much better again.