Space travel under constant acceleration

Space travel under constant acceleration is a hypothetical method of space travel that involves the use of a propulsion system that generates a constant acceleration rather than the short, impulsive thrusts produced by traditional chemical rockets. For the first half of the journey the propulsion system would constantly accelerate the spacecraft toward its destination, and for the second half of the journey it would constantly decelerate the spaceship. Constant acceleration could be used to achieve relativistic speeds, making it a potential means of achieving human interstellar travel. This mode of travel has yet to be used in practice. Constant acceleration has two main advantages: It is the fastest form of interplanetary and interstellar travel. It creates its own artificial gravity, potentially sparing passengers from the effects of microgravity. Constant-thrust and constant-acceleration trajectories both involve a spacecraft firing its engine continually. In a constant-thrust trajectory, the vehicle's acceleration increases during thrusting period, since the use of fuel decreases the vehicle mass. If, instead of constant thrust, the vehicle has constant acceleration, the engine thrust decreases during the journey. The spacecraft must flip its orientation halfway through the journey and decelerate the rest of the way, if it is required to rendezvous with its destination (as opposed to a flyby). A spaceship using significant constant acceleration will approach the speed of light over interstellar distances, so special relativity effects including time dilation (the difference in time flow between ship time and local time) become important. Hyperbolic motion (relativity) The distance traveled, under constant proper acceleration, from the point of view of Earth as a function of the traveler's time is expressed by the coordinate distance x as a function of proper time τ at constant proper acceleration a. It is given by: where c is the speed of light.