With today’s technology? Well then there aren’t going to be any space battles outside Earth’s orbit, because there isn’t anything outside the Earth’s orbit that is worth fighting over. Oh, China lays claim to Ganymede? We must stop them! Except their claim over Ganymede doesn’t mean anything because they don’t have a spacecraft that can reach the Moon, much less Ganymede.
And even if they did have a spacecraft that could reach the Moon, so what? They’re going to set up a lunar colony, then declare the Moon the 34th province of China? No they’re not, because a lunar colony would cost trillions of dollars and not even the United States has trillions of dollars to pour into a lunar colony.
And even if tomorrow China turns into the implacable enemy of the United States, the best thing that could happen for us would be if China decides to pour trillions of dollars into a lunar colony, because they’re choosing that instead of trillions of dollars worth of nuclear bombs and submarines and tanks and bombers. Our warfighting strategy should be to stand aside and allow them to waste trillions of dollars on a lunar colony rather than trying to stop them.
Aside from that, the most important thing to know about space travel is that the ability of a spacecraft to change its velocity is very very small compared to the velocity of the spacecraft. Forget every notion of pointing the nose of your spaceship toward Ganymede and firing the engines until you get there. Even if you’ve got a Heinlein-style torchship that uses total conversion to generate thrust, you can’t just turn on the engines and blast because you’re not limited by the energy of your reactor, you’re limited by the amount of reaction mass you can carry. The only way to change your velocity is chucking stuff off the back of your canoe as hard as you can.
So any notion of “dogfighting” is nonsensical. Spacecraft won’t dogfight, any more than submarines dogfight. I agree with Bryan’s notion that a space battle will consist of craft detecting each other, and either maneuvering to intercept or avoid, with the recognition that most of the time there’s no question of interception because neither craft has enough delta-v to intercept, even if both cooperated.
And given that if you detect incoming weapons a small change in your trajectory means the weapons miss you, that means during an intercept both craft are going to be making lots of small corrections to make their future trajectories hard to figure. I imagine lots of victories would come, not from hitting the other craft with one of your weapons, but forcing them to expend so much delta-v evading your weapons that they don’t have enough to ever match velocities with a friendly base or spacecraft. And so the enemy astronauts die of starvation, or run out of oxygen, or old age, or whatever, rather than being killed. There’s a lot more empty space out there than stuff.