Relativistic rocket
A relativistic rocket is a hypothetical, driven by the rocket principle spacecraft, the flight speed of the speed of light is so close that significant relativistic effects. From when we speak of significant relativistic effects, depends on the context, but you can say about that the vehicle is at least half the speed of light ( 0.5c ) moves. At 0.5 c have the Lorentz factor γ (gamma ), and with it, time dilation, length contraction and mass factor all the value 1.15. At such higher speeds and relativistic physics is required to describe the motion. When slower missiles Newtonian physics and Tsiolkovsky Rocket Equation are sufficiently good approximations.
- 3.1 To construct a Pionenrakete
General
A rocket is defined by the fact that it carries out its entire reaction mass, energy and engines with it. Vehicles with Bussard ramjet, Awning, maser or laser electric traction are therefore no missiles.
To achieve relativistic speeds, advanced space propulsion methods are needed that are not yet developed enough today. With nuclear pulse propulsion could using today known technology theoretically 0.1 c can be achieved, but these would still numerous technical advancements required. The Lorentz factor γ at 0.1 c is 1.005. A dilation of 1.005, which occurs in 0.1 c is too small to have a significant impact. An interstellar rocket that travels at 0.1 c, is therefore to be regarded as non-relativistic, and their movement can be described sufficiently accurately with almost Newtonian physics.
In general relativistic rocket in the context of interstellar space travel are discussed, mostly because they would need long distances to accelerate to such high speeds. Also in thought experiments like the Twin Paradox they occur.
Relativistic Rocket Equation
As with the classic Rocket Equation is the aim here is to calculate the speed increase DELTA.v, which can achieve a rocket if the specific impulse and the relationship between take-off mass m0 and m1 empty mass are given. The specific impulse has the dimension of a velocity and indicates the pulse which is transmitted by the output of a particular amount of fuel to the rocket divided by the mass of this amount of fuel.
Specific Impulse
The specific impulse is the relativistic missile exit velocity equal to the effective, even though the non-linear relationship between speed and momentum and mass in the conversion of energy to be considered. The two effects cancel each other out. The following applies:
This of course applies only when the rocket no external energy source has (for example, a laser beam from a space station. Thus it would need also transported from the laser pulse to be included in the invoice). If all of the energy for the acceleration of the fuel from an external source is, at the same time without an additional pulse is transmitted, is the relationship between the effective exhaust velocity and specific impulse as follows:
(the Lorentz factor is ).
If there is no external source of power, then interested in the relationship between and the share of fuel mass, which becomes energy. Assuming that there are no losses are
The inverse relation is:
In this table, converted to energy units and the corresponding specific impulse, based on the speed of light, for some fuels (losses not taken into account, unless otherwise specified):
Delta -v
To simplify the calculations, we assume that during the acceleration phase, the acceleration in the reference system of the missile is constant. However, the result also applies to variable acceleration, as long as is constant.
In the nonrelativistic case, the (classical ) results Ziolkowski'sche rocket equation that
Assuming a constant acceleration, the duration of the acceleration phase:
The equation also applies in the relativistic case when the acceleration in the reference frame of the rocket and the on-board time, because at time 0, the relationship between force and acceleration is the same as in the classical case.
Applying the Lorentz transform to the acceleration at, it can be the maximum speed relative to the stationary reference system (that is, to the reference system of the missile prior to the acceleration phase ) to calculate acceleration as a function of co-moving in the reference system and the time in the stationary reference system. The result is
The time in the rest frame is related to the ship's time according to the following equation:
Putting the ship's time in Tsiolkovsky's equation and is given to the resulting time in the stationary system in the expression for, we obtain the desired formula:
The formula for the corresponding rapidity ( the Area hyperbolic tangent of the velocity divided by the speed of light) is simple:
Because you can, in contrast to relativistic velocities simply add rapidities, they are useful to calculate the total value of for multi-stage rockets.
Rocket propulsion by matter -antimatter annihilation
From the above calculations show that a relativistic rocket probably needs to be driven by antimatter. In addition to the photon rocket, the "beam core" Pionenrakete is a conceivable type of antimatter rocket, with the required for Interstellarflüge speed can be achieved of 0.5 c. In a Pionenrakete antimatter in the form of frozen antihydrogen is maintained on the superconducting magnetic bottles. ( Antihydrogen as well as normal hydrogen are diamagnetic and can therefore be held by magnetic fields in the balance. ) By laser of antihydrogen is evaporated at a rate of a few grams per second and ionized. The Pionenantrieb might need a superconducting magnet with a nozzle of 10 Tesla or more.
To construct a Pionenrakete
Robert Frisbee and Ulrich Walter have Pionenrakete examined independently and with similar results. Pions ( also referred to as pi- mesons ) are generated in the pair annihilation of protons with anti protons. In the magnetic " combustion chamber " of a Pionenraketen powerplant, the antiprotons in the form of frozen antihydrogen, brought together with the exact same amount of normal protons. The resulting charged pions have a speed of 0.94 c (ie, β = 0.94 ) and a Lorentz factor γ of 2.93, whereby its life is extended so far that they move 2.6 meters through the nozzle, before they decay to muons. 60% of the loaded pions are either negative or positive, and 40% are neutral. The neutral pions decay immediately to gamma radiation. Gamma rays of that energy may be reflected to any known material, but it is subject to the Compton scattering. By a sign of tungsten occupation and anti-hydrogen tanks can be effectively shielded from the gamma radiation. The charged pions move in helices around the axial electromagnetic field lines in the nozzle and can be focused into a beam which emerges theoretically with 0.94 c. If 1 kg pions were expelled per second, the Pionentriebwerk had lost a thrust of 282 Mega Newton, but in real matter -antimatter reactions are 78 % of the mass energy of the fuel as gamma radiation, and therefore the effective jet velocity drops to only 0.33 c. The diamagnetism can be used to store antihydrogen ice in a superconducting magnetic vacuum bottle. Your temperature should be kept below 1 K to prevent anti-hydrogen sublimated and causes the blood vessel walls Annihilation.
Literature, see: Mirror matter: pioneering antimatter physics, Dr. Robert L Forward, 1986