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 f ...

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 described quantitatively by Newton's third law. When a system expels or accelerates mass in one direction, the accelerated mass will cause a force of equal magnitude but opposite direction to be applied to that ...

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 fly in outer space. A type of artificial satellite, spacecraft are used for a variety of purposes, including communications, Earth observation, meteorology, navigation, space colonization, ...

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 speed Relativistic speed refers to speed at which relativistic effects become significant to the desired accuracy of measurement of the phenomenon being observed. Relativistic effects are those discrepancies between values calculated by models consideri ...

s, 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 diffe ...

. 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

. * 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 ''a''. It is given by: :

x(\tau) = \frac \left(\cosh \frac -1 \right) ,

where ''c'' is the speed of light. Under the same circumstances, the time elapsed on Earth (the

coordinate time In the theory of relativity, it is convenient to express results in terms of a spacetime coordinate system relative to an implied observer. In many (but not all) coordinate systems, an event is specified by one time coordinate and three spat ...

) as a function of the traveler's time is given by: :

t(\tau) = \frac \sinh \frac .

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 The parallelogram of forces is a method for solving (or visualizing) the results of applying two forces to an object. When more than two forces are involved, the geometry is no longer parallelogrammatic, but the same principles apply. Forces, ...

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 ass ...

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 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 math ...

. 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 quantity ...

), 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 sur ...

, 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 ''Tau Zero'' is a hard science fiction novel by American writer Poul Anderson. The novel was based upon the short story "To Outlive Eternity" appearing in ''Galaxy Science Fiction'' in 1967. It was first published in book form in 1970. The book i ...

'', 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 Novemb ...

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 ...

Venus Equilateral The Venus Equilateral series is a set of 13 science fiction short stories by American writer George O. Smith, concerning the Venus Equilateral Relay Station, an interplanetary communications hub located at the Lagrangian point of the Sun-Venus ...

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 gravanolExtract 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), have ...

's novel ''

The Forever War ''The Forever War'' (1974) is a military science fiction novel by American author Joe Haldeman, telling the contemplative story about human soldiers fighting an interstellar war against an alien civilization known as the Taurans. It won the Nebul ...

'' 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 Known Space is the fictional setting of about a dozen science fiction novels and several collections of short stories written by Larry Niven. It has also become a shared universe in the spin-off ''Man-Kzin Wars'' anthologies. The Internet Spe ...

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 E ...

, Earth uses constant acceleration drives in the form of

Bussard ramjet The Bussard ramjet is a theoretical method of spacecraft propulsion proposed in 1960 by the physicist Robert W. Bussard, popularized by Poul Anderson's novel '' Tau Zero'', Larry Niven in his ''Known Space'' series of books, Vernor Vinge in h ...

s 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 consi ...

s. In the non-known space novel ''

A World Out of Time ''A World Out of Time'' is a science fiction novel by Larry Niven and published in 1976. It is set outside the Known Space universe of many of Niven's stories, but is otherwise fairly representative of his 1970s hard science fiction novels. The ...

'', Jerome Branch Corbell (for himself), "takes" 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 ra ...

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 Mary Doria Russell (born August 19, 1950) is an American novelist. Early life and education Russell was born in Elmhurst, Illinois She graduated from Glenbard East High School in Lombard, Illinois, which has registered its chapter of the Nati ...

, 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 ''Revelation Space'' is a 2000 science fiction novel by Welsh author Alastair Reynolds. It was the first novel (but not first published work of fiction) set in Reynolds's eponymous universe. The novel reflects Reynolds's professional background ...

'' series by

Alastair Reynolds Alastair Preston Reynolds (born 13 March 1966) is a Welsh science fiction author. He specialises in hard science fiction and space opera. He spent his early years in Cornwall, moved back to Wales before going to Newcastle University, where he s ...

, 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 c ...

, is capable of constant acceleration at 0.2 ''g'' under full thrust. Clarke's novel "

Imperial Earth ''Imperial Earth'' is a science fiction novel by British writer Arthur C. Clarke, published in 1975 by Gollancz Books. The plot follows the protagonist, Duncan Makenzie, on a trip to Earth from his home on Titan, in large part as a diploma ...

" 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 James S. A. Corey is the pen name used by collaborators Daniel Abraham and Ty Franck, authors of the science fiction series '' The Expanse''. The first and last name are taken from Abraham's and Franck's middle names, respectively, and S. A. a ...

make use of constant acceleration drives, which also provide artificial gravity for the occupants. In '' The Martian'', by Andy Weir, the spaceship ''Hermes'' uses a constant thrust

ion engine An ion thruster, ion drive, or ion engine is a form of electric propulsion used for spacecraft propulsion. It creates thrust by accelerating ions using electricity. An ion thruster ionizes a neutral gas by extracting some electrons out of ...

to transport astronauts between

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 at ...

. 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. He ...

'', 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 rela ...

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 paralla ...

References

{{DEFAULTSORT:Space Travel using Constant Acceleration Interstellar travel Space colonization Special relativity Acceleration