Relativistic rocket means any
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, p ...
that travels close enough to
light speed
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 ...
for
relativistic effects to become significant. The meaning of "significant" is a matter of context, but often a threshold velocity of 30% to 50% of the speed of light (0.3''c'' to 0.5''c'') is used. At 30% c, the difference between relativistic mass and rest mass is only about 5%, while at 50% it is 15%, (at 0.75''c'' the difference is over 50%); so above such speeds special relativity is needed to accurately describe motion, while below this range Newtonian physics and the
Tsiolkovsky rocket equation
Konstantin Eduardovich Tsiolkovsky (russian: Константи́н Эдуа́рдович Циолко́вский , , p=kənstɐnʲˈtʲin ɪdʊˈardəvʲɪtɕ tsɨɐlˈkofskʲɪj , a=Ru-Konstantin Tsiolkovsky.oga; – 19 September 1935) ...
usually give sufficient accuracy.
In this context, a rocket is defined as an object carrying all of its reaction mass, energy, and engines with it.
No known technology can bring a rocket to relativistic speed. Relativistic rockets require huge advances in spacecraft propulsion, energy storage, and engine efficiency which may or may not ever be possible.
Nuclear pulse propulsion
Nuclear pulse propulsion or external pulsed plasma propulsion is a hypothetical method of spacecraft propulsion that uses nuclear explosions for thrust. It originated as Project ''Orion'' with support from DARPA, after a suggestion by Stanislaw ...
could theoretically reach 0.1''c'' using current known technology, but would still require many engineering advances to achieve this. The relativistic gamma factor
at 10% of light velocity is 1.005. A 0.1''c'' speed rocket is thus considered non-relativistic since its motion is still quite accurately described by Newtonian physics alone.
Relativistic rockets are usually seen discussed in the context of
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 ...
, since most would need a lot of space to reach such speed. They are also found in some
thought experiment
A thought experiment is a hypothetical situation in which a hypothesis, theory, or principle is laid out for the purpose of thinking through its consequences.
History
The ancient Greek ''deiknymi'' (), or thought experiment, "was the most anc ...
s such as the
twin paradox
In physics, the twin paradox is a thought experiment in special relativity involving identical twins, one of whom makes a journey into space in a high-speed rocket and returns home to find that the twin who remained on Earth has aged more. Thi ...
.
Relativistic rocket equation
As with the classical rocket equation, one wants to calculate the velocity change
that a rocket can achieve depending on the
exhaust speed and the mass ratio, i. e. the ratio of starting rest mass
and rest mass at the end of the acceleration phase (dry mass)
.
In order to make calculations simpler, we assume that the acceleration is constant (in the rocket's reference frame) during the acceleration phase; still, the result is nonetheless valid if the acceleration varies, as long as exhaust velocity
is constant.
In the nonrelativistic case, one knows from the (classical) Tsiolkovsky rocket equation that
:
Assuming constant acceleration
, the time span
during which the acceleration takes place is
:
In the relativistic case, the equation is still valid if
is the acceleration in the rocket's reference frame and
is the rocket's proper time because at velocity 0 the
relationship between force and acceleration is the same as in the classical case. Solving this equation for the ratio of initial mass to final mass gives
:
where "exp" is the
exponential function
The exponential function is a mathematical function denoted by f(x)=\exp(x) or e^x (where the argument is written as an exponent). Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, ...
. Another related equation gives the mass ratio in terms of the end velocity
relative to the rest frame (i. e. the frame of the rocket before the acceleration phase):
:
For constant acceleration,