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Of course...I did have Physics in college but is was a while ago. I understand friction has a lot to do with how a bullet behaves on Earth and in Space there is no friction. So I believe that the bullet would add its speed to the speed of the spacecraft and not slow down till it actually hit something possibley flying for a very very long time at that speed. Could make it actually very dangerous anywhere near any battle zone or you could get hit by a projectile fired days, weeks , months or even years earlier. Physics says once an object starts moving it tends to keep moving. But what about in an atmosphere where there was indeed friction such as close to a sun or to a planet.
Velocities do add in space just as they do on Earth. However on Earth drag forces (friction in the air for example) act quickly to slow something like a bullet. If nearing the speed of light it gets more complicated since you need to use relativistic physics rather than Gallilean or Newtonian physics.
Gravity is different from friction. Gravity is the attractive force between two bodies with mass. A bullet will experience a force towards a massive object. In the case of a planet or star that force could be significant enough to deviate its path. This can all happen with zero friction.
Your questions are a bit vague. If this hasn't answered your questions you will need to be more specific.
like playing ping pong on a moving train. The speed on the ball is only relevant to the observer.
Currently you're travelling at 107,300 km/h (or if you prefer 67,062 miles per hour) orbiting the sun, which itself is orbiting the center of our galaxy at dizzying speeds.
Edit: The Solar System is traveling at an average speed of 828,000 km/h (230 km/s) or 514,000 mph (143 mi/s) within its trajectory around the galactic center, which is about one 1300th of the speed of light—a speed at which an object could circumnavigate the Earth's equator in 2 minutes and 54 seconds. (google)
But then again once you actually leave that object its effect on you starts to diminish. We are tied to the earth by gravity so what it does we do. But the factor that does not allow it to diminish in this case is the lack of friction in space. What is there was indeed friction and you where actually able to move that fast wihtout burning up which I do not think is possible. But if you where what would happen if you fired a bullet. The bullet would slow down quickly because of the effects of friction and you would infact end up shooting your self.
Let me elaborate. Whatever speed you're doing in space is irrelevant. If you set your reference from (or coordinate system if you think of it that way) as centered on yourself, then you are stationary (by definition). If you fire a bullet in some direction, that bullet will leave you at a constant speed, you'll never run into it. However if you're under some form of acceleration such as continuously thrusting in the same direction as that bullet, then yes you could end up running into that bullet. Exactly when would depend on how much that acceleration is and the speed of the bullet.
The point is, you have to be accelerating towards the bullet if you are to run into it again.
http://en.wikipedia.org/wiki/Grumman_F-11_Tiger
I think that's what the OP was envisioning.
Of course, it doesn't happen in Elite 4. But afaik, your ship's velocity doesn't gets added to your cannon shells. Or the difference is very slight. Missiles / Mines though, seem to benefit?
AFAICT the speeds at which you are during combat (a couple hundred m/s) are relatively low compared to any projectiles, including missiles, so you don't run into any of those issues or projectiles. If you ask such questions on the official forums, especially during European working hours, chances are you may even get a response from someone who really knows.
My guess would be that projectile calculations for the guns and cannons are vastly simplified (projectiles move at an absolute fixed speed in a straight line from their origin to their "maximum range"), while propelled rockets act under the same rules as all ships, with a fixed "top speed" inside the frame of reference provided by the instance; that would imply that any "excess speed" from being fired from a moving shiup would bleed away rather quickly.
Shooting a gun while moving at supersonic speeds is a funny proposition since nothing will move supersonic without continued acceleration for very long, and in fact, a lot of projectile weapons will fire rounds at subsonic speeds. That won't matter in space since the whole concept of a speed of sound breaks down at the low medium densities out there.