Space travel under constant acceleration is a hypothetical method of
space travel that involves the use of a
propulsion
Propulsion is the generation of force by any combination of pushing or pulling to modify the translational motion of an object, which is typically a rigid body (or an articulated rigid body) but may also concern a fluid. The term is derived from ...
system that generates a constant
acceleration
In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by ...
rather than the short,
impulsive thrust
Thrust is a reaction force
In physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity (e.g. moving from a state of rest), i.e., to accelerate. Force can al ...
s produced by traditional
chemical rocket
A rocket engine uses stored rocket propellants as the reaction mass for forming a high-speed propulsive jet of fluid, usually high-temperature gas. Rocket engines are reaction engines, producing thrust by ejecting mass rearward, in accordance ...
s. For the first half of the journey the propulsion system would constantly accelerate the
spacecraft
A spacecraft is a vehicle or machine designed to spaceflight, fly in outer space. A type of artificial satellite, spacecraft are used for a variety of purposes, including Telecommunications, communications, Earth observation satellite, Earth ...
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
Interstellar travel is the hypothetical travel of spacecraft from one star system, solitary star, or planetary system to another. Interstellar travel is expected to prove much more difficult than interplanetary spaceflight due to the vast differ ...
. 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
Interstellar travel is the hypothetical travel of spacecraft from one star system, solitary star, or planetary system to another. Interstellar travel is expected to prove much more difficult than interplanetary spaceflight due to the vast differ ...
.
* It creates its own
artificial gravity, potentially sparing passengers from the effects of
microgravity
The term micro-g environment (also μg, often referred to by the term microgravity) is more or less synonymous with the terms '' weightlessness'' and ''zero-g'', but emphasising that g-forces are never exactly zero—just very small (on the ...
.
Constant thrust versus constant acceleration
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).
Interstellar travel

A spaceship using significant constant acceleration will approach the
speed of light
The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit fo ...
over
interstellar distances, so
special relativity
In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates:
# The law ...
effects including
time dilation
In physics and relativity, time dilation is the difference in the elapsed time as measured by two clocks. It is either due to a relative velocity between them ( special relativistic "kinetic" time dilation) or to a difference in gravitational ...
(the difference in time flow between ship time and local time) become important.
[C. Lagoute and E. Davoust (1995) The interstellar traveler, ''Am. J. Phys.'' 63:221–227]
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
In relativity, proper time (from Latin, meaning ''own time'') along a timelike world line is defined as the time as measured by a clock following that line. It is thus independent of coordinates, and is a Lorentz scalar. The proper time interval ...
''τ'' at constant
proper acceleration
In relativity theory, proper acceleration is the physical acceleration (i.e., measurable acceleration as by an accelerometer) experienced by an object. It is thus acceleration relative to a free-fall, or inertial, observer who is momentarily a ...
''a''. It is given by:
:
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:
:
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
Specific impulse (usually abbreviated ) is a measure of how efficiently a reaction mass engine (a rocket using propellant or a jet engine using fuel) creates thrust. For engines whose reaction mass is only the fuel they carry, specific impulse is ...
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
A ramjet, or athodyd (aero thermodynamic duct), is a form of airbreathing jet engine that uses the forward motion of the engine to produce thrust. Since it produces no thrust when stationary (no ram air) ramjet-powered vehicles require an a ...
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
Drag or The Drag may refer to:
Places
* Drag, Norway, a village in Tysfjord municipality, Nordland, Norway
* ''Drág'', the Hungarian name for Dragu Commune in Sălaj County, Romania
* Drag (Austin, Texas), the portion of Guadalupe Street adj ...
. 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
In physics and astronomy, a frame of reference (or reference frame) is an abstract coordinate system whose origin, orientation, and scale are specified by a set of reference points― geometric points whose position is identified both mathem ...
. 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 gravity of Earth, denoted by , is the net acceleration that is imparted to objects due to the combined effect of gravitation (from mass distribution within Earth) and the centrifugal force (from the Earth's rotation).
It is a vector quan ...
), the journey time, as measured on
Earth
Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surf ...
, 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

From the frame of reference of those on the ship the acceleration will not change as the journey goes on. Instead the planetary reference frame will look more and more relativistic. This means that for voyagers on the ship the journey will appear to be much shorter than what planetary observers see.
At a constant acceleration of 1 ''g'', a rocket could travel the diameter of our galaxy in about 12 years ship time, and about 113,000 years planetary time. If the last half of the trip involves deceleration at 1 ''g'', the trip would take about 24 years. If the trip is merely to the nearest star, with deceleration the last half of the way, it would take 3.6 years.
In fiction
''
Tau Zero'', a
hard science fiction
Hard science fiction is a category of science fiction characterized by concern for scientific accuracy and logic. The term was first used in print in 1957 by P. Schuyler Miller in a review of John W. Campbell's ''Islands of Space'' in the Nove ...
novel by
Poul Anderson
Poul William Anderson (November 25, 1926 – July 31, 2001) was an American fantasy and science fiction author who was active from the 1940s until the 21st century. Anderson wrote also historical novels. His awards include seven Hugo Awards and ...
, has a spaceship using a constant acceleration drive.
The spacecraft of
George O. Smith
George Oliver Smith (April 9, 1911 – May 27, 1981) (also known by the pseudonym Wesley Long) was an American science fiction author. He is not to be confused with George H. Smith, another American science fiction author.
Biography
Smith was ...
's
Venus Equilateral stories are all constant acceleration ships. Normal acceleration is 1 ''g'', but in "The External Triangle" it is mentioned that accelerations of up to 5 ''g'' are possible if the crew is drugged with gravanol
[Extract of page 49]
/ref> to counteract the effects of the ''g''-load.
Spacecraft in Joe Haldeman
Joe William Haldeman (born June 9, 1943) is an American science fiction author. He is best known for his novel '' The Forever War'' (1974). That novel and other works, including '' The Hemingway Hoax'' (1991) and '' Forever Peace'' (1997), hav ...
's novel '' The Forever War'' make extensive use of constant acceleration; they require elaborate safety equipment to keep their occupants alive at high acceleration (up to 25 ''g''), and accelerate at 1 ''g'' even when "at rest" to provide humans with a comfortable level of gravity.
In the Known Space universe, constructed by Larry Niven
Laurence van Cott Niven (; born April 30, 1938) is an American science fiction writer. His best-known works are '' Ringworld'' (1970), which received Hugo, Locus, Ditmar, and Nebula awards, and, with Jerry Pournelle, '' The Mote in God's ...
, Earth uses constant acceleration drives in the form of Bussard ramjets to help colonize the nearest planetary system
A planetary system is a set of gravitationally bound non-stellar objects in or out of orbit around a star or star system. Generally speaking, systems with one or more planets constitute a planetary system, although such systems may also consis ...
s. In the non-known space novel '' A World Out of Time'', Jerome Branch Corbell (for himself), "takes" a ramjet
A ramjet, or athodyd (aero thermodynamic duct), is a form of airbreathing jet engine that uses the forward motion of the engine to produce thrust. Since it produces no thrust when stationary (no ram air) ramjet-powered vehicles require an a ...
to the Galactic Center
The Galactic Center or Galactic Centre is the rotational center, the barycenter, of the Milky Way galaxy. Its central massive object is a supermassive black hole of about 4 million solar masses, which is called Sagittarius A*, a compact ...
and back in 150 years ships time (most of it in cold sleep), but 3 million years passes on Earth.
In '' The Sparrow'', by Mary Doria Russell, interstellar travel is achieved by converting a small asteroid into a constant acceleration spacecraft. Force is applied by ion engines fed with material mined from the asteroid itself.
In the '' Revelation Space'' series by Alastair Reynolds, interstellar commerce depends upon "lighthugger" starships which can accelerate indefinitely at 1 ''g'', with superseded antimatter powered constant acceleration drives. The effects of relativistic travel are an important plot point in several stories, informing the psychologies and politics of the lighthuggers' "ultranaut" crews for example.
In the novel '' 2061: Odyssey Three'' by Arthur C. Clarke
Sir Arthur Charles Clarke (16 December 191719 March 2008) was an English science-fiction writer, science writer, futurist, inventor, undersea explorer, and television series host.
He co-wrote the screenplay for the 1968 film '' 2001: A Spac ...
, the spaceship ''Universe'', using a muon-catalyzed fusion rocket
A fusion rocket is a theoretical design for a rocket driven by fusion propulsion that could provide efficient and sustained acceleration in space without the need to carry a large fuel supply. The design requires fusion power technology beyond cu ...
, is capable of constant acceleration at 0.2 ''g'' under full thrust. Clarke's novel " Imperial Earth" features an "asymptotic drive", which utilises a microscopic black hole and hydrogen propellant, to achieve a similar acceleration travelling from Titan
Titan most often refers to:
* Titan (moon), the largest moon of Saturn
* Titans, a race of deities in Greek mythology
Titan or Titans may also refer to:
Arts and entertainment
Fictional entities
Fictional locations
* Titan in fiction, fictiona ...
to Earth.
The UET and Hidden Worlds spaceships of F.M. Busby's Rissa Kerguelen saga utilize a constant acceleration drive that can accelerate at 1 ''g'' or even a little more.
Ships in the '' Expanse'' series by James S. A. Corey make use of constant acceleration drives, which also provide artificial gravity for the occupants.
In '' The Martian'', by Andy Weir
Andrew Taylor Weir (born June 16, 1972) is an American novelist and former computer programmer. His 2011 novel '' The Martian'' was adapted into the 2015 film of the same name directed by Ridley Scott. He received the John W. Campbell Award for ...
, the spaceship ''Hermes'' uses a constant thrust ion engine to transport astronauts between Earth
Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surf ...
and Mars
Mars is the fourth planet from the Sun and the second-smallest planet in the Solar System, only being larger than Mercury. In the English language, Mars is named for the Roman god of war. Mars is a terrestrial planet with a thin atmos ...
. In ''Project Hail Mary
''Project Hail Mary'' is a 2021 science fiction novel by American novelist Andy Weir. Set in the near future, it centers on junior high (middle) school-teacher-turned- astronaut Ryland Grace, who wakes up from a coma afflicted with amnesia. ...
'', also by Weir
A weir or low head dam is a barrier across the width of a river that alters the flow characteristics of water and usually results in a change in the height of the river level. Weirs are also used to control the flow of water for outlets of l ...
, the protagonist's spaceship uses a constant 1.5 ''g'' acceleration spin drive to travel between the Solar System
The Solar System Capitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Solar ...
, Tau Ceti
Tau Ceti, Latinized from τ Ceti, is a single star in the constellation Cetus that is spectrally similar to the Sun, although it has only about 78% of the Sun's mass. At a distance of just under from the Solar System, it is a relat ...
and 40 Eridani
40 Eridani is a triple star system in the constellation of Eridanus, abbreviated 40 Eri. It has the Bayer designation Omicron2 Eridani, which is Latinized from ο2 Eridani and abbreviated Omicron2 Eri or ο2 Eri. Based on parallax ...
.
References
{{DEFAULTSORT:Space Travel using Constant Acceleration
Interstellar travel
Space colonization
Special relativity
Acceleration