Editing Interstellar travel (section)

==== Constant acceleration ====
[[File:Roundtriptimes.png|thumb|upright=1.75|This plot shows a ship capable of 1-[[Gravitational acceleration|g]] (10&nbsp;m/s<sup>2</sup> or about 1.0 ly/y<sup>2</sup>) "felt" or proper-acceleration<ref>{{cite web | title= Clock paradox III | url= http://www.eftaylor.com/pub/spacetime/STP1stEdExercP81to100.pdf | access-date= 2014-08-31 | archive-url= https://web.archive.org/web/20170721192831/http://www.eftaylor.com/pub/spacetime/STP1stEdExercP81to100.pdf | archive-date= 2017-07-21 | url-status= dead }} {{cite book | author1= Taylor, Edwin F. | author2= Wheeler, John Archibald | date= 1966 | title= Spacetime Physics | chapter-url= https://archive.org/details/spacetimephysics0000tayl | chapter-url-access= registration | publisher= W.H. Freeman, San Francisco | isbn= 978-0-7167-0336-5 | chapter= Chapter 1 Exercise 51 | pages= [https://archive.org/details/spacetimephysics0000tayl/page/97 97–98]}}</ref> can go far, except for the problem of accelerating on-board propellant.]]
{{See also|Space travel under constant acceleration}}

Regardless of how it is achieved, a propulsion system that could produce acceleration continuously from departure to arrival would be the fastest method of travel. A constant acceleration journey is one where the propulsion system accelerates the ship at a constant rate for the first half of the journey, and then decelerates for the second half, so that it arrives at the destination stationary relative to where it began. If this were performed with an acceleration similar to that experienced at the Earth's surface, it would have the added advantage of producing artificial "gravity" for the crew. Supplying the energy required, however, would be prohibitively expensive with current technology.<ref>{{Cite book |last=Crowell |first=Benjamin |url=https://open.umn.edu/opentextbooks/textbooks/59 |title=Light and Matter |publisher=Benjamin Crowell |year=2010 |chapter=4 (Force and motion) |access-date=6 May 2023 |archive-date=26 September 2022 |archive-url=https://web.archive.org/web/20220926091944/https://open.umn.edu/opentextbooks/textbooks/59 |url-status=live }}</ref>

From the perspective of a planetary observer, the ship will appear to accelerate steadily at first, but then more gradually as it approaches the speed of light (which it cannot exceed). It will undergo [[hyperbolic motion (relativity)|hyperbolic motion]].<ref>{{cite journal |last1 = Yagasaki|first1 = Kazuyuki|title = Invariant Manifolds And Control Of Hyperbolic Trajectories On Infinite- Or Finite-Time Intervals|journal = Dynamical Systems|date = 2008|volume = 23|issue = 3|pages = 309–331|doi = 10.1080/14689360802263571|s2cid = 123409581}}</ref> The ship will be close to the speed of light after about a year of accelerating and remain at that speed until it brakes for the end of the journey.

From the perspective of an onboard observer, the crew will feel a [[gravitational field]] opposite the engine's acceleration, and the universe ahead will appear to fall in that field, undergoing hyperbolic motion. As part of this, distances between objects in the direction of the ship's motion will gradually contract until the ship begins to decelerate, at which time an onboard observer's experience of the gravitational field will be reversed.

When the ship reaches its destination, if it were to exchange a message with its origin planet, it would find that less time had elapsed on board than had elapsed for the planetary observer, due to [[time dilation]] and [[length contraction]].

The result is an impressively fast journey for the crew.