Recently I finished reading a pair of Science Fiction trilogies by fellow indie writer Michael R. Hicks (namely: The Last War and Redemption), after a co-worker recommend them to me. While I quite enjoyed both trilogies (with the exception of a certain bit regarding the character Jodi in Final Battle), it made me wonder about the portrayal of space battles in Science Fiction, especially with regard to orbital mechanics.
Movement in space is, in essence, very simple. If you want to go in a certain direction, just fire in the opposite direction and you'll keep moving in the desired direction. There is no air to slow you down, so to change your movement, or to slow down, you need to burn again opposite to the direction you're heading ( Newton's First Law). Most Science Fiction stories seem to follow these rules rather well.
But things get more complicated once you start involving gravity, such as when you get close to a planet. I didn't really know about this until I started Kerbal Space Program, but thrusting in a certain direction has a very different effect when you're under the influence of gravity. I could try explaining myself, but NASA did a far better job in the 1980s (requires some knowledge of physics):
The first ten minutes of this video should be enough for a number of observations:
Orbital velocity depends mostly on position and shape of the orbit ( Kepler's Third Law). There's no way to move faster along the same trajectory, so there is no way to catch up to another object if your orbits are equal
Objects in a lower orbit move faster, so if you want to catch up to a spaceship, you need to move yourself into a lower orbit, which usually means slowing down. Many Science Fiction stories have ships accelerating to catch up.
Trying to hit another ship with a missile is harder than it appears. Missiles too are subject to orbital mechanics, and simply having a higher speed will probably just put the missile into a higher orbit. On the other hand, the missile doesn't have to move in sync with the target, so the orbit doesn't need to match, it just needs to hit the target. But even so, the problem is non-trivial.
And that's just one of the simpler problems. Relativity offers a whole new set of challenges when it comes to space combat (the ability to observe enemies over distance is limited by the speed of light, which means you won't spot an enemy ship at 1 light-minute - about 17 million kilometers - distance until a minute later, which means its position is outdated), and that's just the problems our puny human minds can understand today.
But when it comes to Science Fiction, the key to enjoyment is not to take these problems too seriously. If everything works exactly like it does in real life, it wouldn't be science fiction, it would simply be science.
What other real science problems have you encountered in Science Fiction?