GHS Physics Class Extra Credit

Im posting this for my Physics extra assignment, but to kill two birds with one stone, I have a few questions. To start, a friend and I are drafting rules for a hard science, table top, space based naval combat game. I come to consult this board on the “Hard Science” aspect of the game. The ships will be moving on vectors through three dimensional space; we already have a system to properly convey this. During the movement phase, vectors will be plotted and the ships engines will burn for a set period of time to accelerate to the speed desired. We are taking into account the mass of the ship to determine inertia holding it back while accelerating. This brings me to my first question; what is the fastest speed that modern rocket engines can propel a space vehicle and how long (on a maximum burn) would it take to reach such a speed (please include the approx. mass of the vehicle)? Secondly, we are, of course, taking out gravity as well as air resistance, which brings me to my next question. Parabolic motion is natural of projectiles on Earth (or any other gravity bearing thing out there), but how do projectiles behave in low to high orbit? My guess would be that they would have a less of a curve the farther they were from the planet. Is this correct? If so, at about how far away from an earth-sized planet would a projectile cease to follow any orbital pattern? Lastly, what are some theoretical technologies you could see being used on spacecraft three-hundred years from now? Fictional but with scientific possibilities ideas are welcome! Please comment, I need comments for the grade!

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