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 drives 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 versus constant acceleration Constant-thrust and constant-acceleration trajectories both involve a spacecraft firing its engine continuously. 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).
Interstellar travel
A spaceship using significant constant acceleration will approach the speed of light over interstellar distances, so special relativity effects including time dilation become important.
Expressions for covered distance and elapsed time
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:
x ( τ ) = c 2 a ( cosh a τ c − 1 ) , {\displaystyle x(\tau )={\frac {c^{2}}{a}}\left(\cosh {\frac {a\ \tau }{c}}-1\right),}
where c is the speed of light. Under the same circumstances, the time elapsed on Earth (the coordinate time) as a function of the traveler's time is given by:
t ( τ ) = c a sinh a τ c . {\displaystyle t(\tau )={\frac {c}{a}}\sinh {\frac {a\ \tau }{c}}.}
Feasibility A limitation of constant acceleration is adequate fuel. Constant acceleration is only feasible with the development of fuels with a much higher specific impulse than presently available. There are two broad approaches to higher specific impulse propulsion:
Higher efficiency fuel (the motor ship approach). Two possibilities for the motor ship approach are nuclear and matter–antimatter based fuels. Drawing propulsion energy from the environment as the ship passes through it (the sailing ship approach). One hypothetical sailing ship approach is discovering something equivalent to the parallelogram of force between wind and water which allows sails to propel a sailing ship. Picking up fuel along the way — the ramjet approach — will lose efficiency as the space craft's speed increases relative to the planetary reference. This happens because the fuel must be accelerated to the spaceship's velocity before its energy can be extracted, and that will cut the fuel efficiency dramatically. A related issue is drag. If the near-light-speed space craft is interacting with matter that is moving slowly in the planetary reference frame, this will cause drag which will bleed off a portion of the engine's acceleration. A second big issue facing ships using constant acceleration for interstellar travel is colliding with matter and radiation while en route. In mid-journey any such impact will be at near light speed, so the result will be dramatic.
Interstellar traveling speeds If a space ship is using constant acceleration over interstellar distances, it will approach the speed of light for the middle part of its journey when viewed from the planetary frame of reference. This means that the effects of relativity will become important. The most important effect is that time will appear to pass at different rates in the ship frame and the planetary frame, and this means that the ship's speed and journey time will appear different in the two frames.
Planetary reference frame From the planetary frame of reference, the ship's speed will appear to be limited by the speed of light — it can approach the speed of light, but never reach it. If a ship is using 1 g constant acceleration, it will appear to get near the speed of light in about a year, and have traveled about half a light year in distance. For the middle of the journey the ship's speed will be roughly the speed of light, and it will slow down again to zero over a year at the end of the journey. As a rule of thumb, for a constant acceleration at 1 g (Earth gravity), the journey time, as measured on Earth, will be the distance in light years to the destination, plus 1 year. This rule of thumb will give answers that are slightly shorter than the exact calculated answer, but reasonably accurate.
Ship reference frame
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