Talk:Relativistic rocket

Relativistic Rocket Problem
I will present a credible theoretical design for a relatavistic, or semi-relatavistic rocket here. For now I will use algebra & geometry based newtonian physics to describe such a rocket. A calculas based version of this description may also be presented here in a future improved version of this article.* Improvements to the article may be made by other editors here if the nature  of their work is good, and correct. Let all editors feel free to correct what ever spelling errors, spacing errors, or puntuation errors may be found in this article. Tmayes1965

Please excuse my clumsy editing. This is my first contribution here, and I don't know much about the markup and conventions. I was trying to find the tag for attaching a signature with time and date, but I'll just type them in.


 * 1) Please kill "relatavistic", "relavistic". relativistic please.
 * 2) 2nd paragraph contains two conflicting definitions of "relativistic rocket"

I have now fixed this contradiction.*tim
 * 3) Punctuation is messed up. Please put a space after commas and periods, not before.
 * 4) "wickipedia"?! "cruising velocity"?!!

Article begun by OneRock on 7/23/04.

Somewhere, I have a numerical Fortran solution (or did I write that in Basic) of the general-relativistic rocket problem on a 5 1/4 floppy, which I can no longer access. It ran quite well on my old TRS-80 with no hard drive. I don't think I have the will to solve it again, but I am curious whether anyone else has such a program.

In case you want to duplicate my work, here's what it involves:

First, you must postulate the existence of a propulsion mechanism with specific parameters. My imaginary rocket was propelled by a laser which converts matter and antimatter to a light beam with 100% efficiency. (Onerock 19:40, 28 Jul 2004 (UTC)) I propose this engine as an absolute upper limit on what can plausibly be done without violating widely accepted physical principles.) The program user was asked to specify the mass and thrust of the engine. P.S.: Exploring this site, I see that Eugen Sänger proposed a nuclear photonic rocket long before the discover of the laser.

Second, you must determine the rate at which fuel must be consumed to deliver the required thrust. In the case of the laser drive, thrust is equal to the power of the laser divided by the speed of light. Begin with thrust (force), solve for power, and covert to mass--using E= Mc^2.

Third, you must attach your laser drive engine to a vehicle, and set up the problem of incrimentally calculating velocity after a short time interval. If you do this in a general relativity format, the solution will be valid all the way to relativistic speeds. (See correction below.)

I originally attempted to obtain a classical formula for the result, but I was thwarted by an integral of a form I never encountered in three years of Integral Calculus. Does anyone know how to solve an integral of the following form?

Integral from A to [the integral from A to B of F(x) dx] of G(x) dx.

Sorry I can't be more specific about that integral without tackling the rocket problem anew.

Interestingly, it turns out that such a rocket could take you across the galaxy and back in a few years (on the traveler's clock)---if not for some rather daunting obstacles. First, you would need to start your journey with a matter-anitmatter fuel supply with about as much mass as Earth's Moon. All that mass would come in very handy as a shield against the inevitable collision with a grain of sand which would explode like an atomic bomb. The travelers would have to be frozen in a solid block of ice to withstand the high G-forces. And of course, the Earth might not be here when you return a few years older but hundreds of thousands of Earth-years later.

(Onerock 19:40, 24 Jul 2004 (UTC)) Yesterday, I wrote, impromptu, during my 1-hour daily internet slot (Tuesday thru Saturday at the public library). Today’s message has been written at a more leisurely pace at home.

I hypothesized the 100% efficient matter-antimatter laser-drive engine, not because it is feasible, but because I believe it places an absolute upper limit on what can plausibly be achieved without violating any widely accepted principles of physics. This is not Star Trek; it is real physics. If you want feasible results, you need only reduce the efficiency of the engine and its power to mass ratio. I’m afraid today’s lasers are many orders of magnitude too wimpy to get you to the corner drug store, let alone the far side of the galaxy.

Correction: It is not necessary to apply, or even know, the general relativity formulas. As the time interval, Delta-T, approaches zero, general relativity reduces to special relativity. Consequently, my numerical approach does not rely on such esoteric concepts as curved four-dimensional space.

Apply special-relativity formulas to calculate changes in position, velocity, mass and time for a short time interval, Delta-T. Plug the new values back into the algorithm, and the result after many short intervals should be exactly equal to that predicted by general relativity formulas for the total interval—provided that you chose a small enough Delta-T.

Start with a fairly large Delta-T (perhaps one hour); repeat with smaller values of Delta-T until successive calculations yield the same result within tolerable limits.

Relativistic effects are detectible at much lower velocities if you use double precision math; I’m not sure how much difference that makes. Lower precision with smaller Delta-T’s will probably yield the same result; I’m not sure which method takes more computing time. I used double precision, which yielded an accurate result in a few minutes of TRS-80 computer time for a trip across the galaxy. Today’s PC is a thousand times faster.

Calculations must be kept within a single reference frame. Mix your coordinate systems and the results will be invalid.

From the traveler’s point of view: My hypothetical engine’s thrust is constant; remaining fuel mass decreases at a constant rate; and acceleration increases in inverse proportion to the ship’s total mass with fuel. There is no relativistic mass to consider because the ship and fuel are stationary in the traveler’s coordinates. Due to this simplicity, it is probably easier to calculate the Earth’s position in the traveler’s coordinates, rather than the other way around.

From an Earthling’s point of view: I’m not sure if thrust is increasing or decreasing. Since the relativistic mass of the engine is increasing, we might expect it to produce more light, but the thrust would be diminished in proportion to the red shift of the retreating light source. Conservation of mass-energy requires that the total of kinetic energy plus relativistic mass of the ship (including fuel) decreases by an amount equal to the total energy imparted to the laser beam since the beginning of the trip. I’m pretty sure I didn’t write my old program from this point of view; it’s too confusing.

I recommend that you calculate Earth’s parameters in traveler’s coordinates, but output spaceship parameters in Earth coordinates. With each millisecond on the traveler’s clock, you calculate the time on Earth; then for each hour on Earth, you find the corresponding time on the traveler’s clock and apply special relativity formulas to convert the other parameters. (At least I think that’s sort of the way it’s done. It’s been a very long time since I did it.)

Further comments:

How much acceleration does it take, and for how long, to reach relativistic speeds? Suppose you accelerate at one G in one direction for 355 Earth days. The Newtonian formulas put your speed at just over the speed of light. I’m too lazy to look up the formulas and do the math, but I’d guess general relativity puts your speed at roughly half of light speed.

In case you’re wondering, this laser-drive engine is no kid’s toy. A laser gun having a recoil force of 1000 Newton (i.e. 225 lb.) would consume fuel at a rate of 1000 Newton ¸ c = 1/3 microgram per second. The power of the beam would be 1000 Newton times c = 300 trillion Watt—approximately 100 times the most powerful nuclear power plant on Earth. (Hope I did that correctly in my head.) I wonder if the astronomical phenomenon of gamma-ray bursts might be our passage thru the exhaust of such a space ship in a distant galaxy.

In traveler’s coordinates, the distance across our galaxy decreases as the relative velocity increases. That is why, from the traveler’s point of view, it may take only a few years to cross a distance of 100,000 light-years without traveling faster than light. When the ship is stationary at each end of the journey, the width of the galaxy is 100,000 light-years; mid-way through the trip, the galaxy is only a few light-years across. When Einstein said you can’t travel faster than light, he meant relative to any object in your immediate vicinity. While you are accelerating, even at very modest rates, distant galaxies (both fore and aft) grow nearer or farther at many times the speed of light—without moving! Ain’t language funny!

(Onerock 19:40, 28 Jul 2004 (UTC))I moved my comments re. Twins Paradox to the appropriate forum.

199.250.57.32Onerock 7/29//04

It may be argued that fuel can be collected along the way. Unfortunately, any potential fuel that may be encountered along the way will be coming at you very close to light speed. Collecting fuel will be the furthest thing from your mind, since its momentum would slow you down—besides which, any collision with it would vaporize you. A more feasible way to conserve fuel is to chuck your excess engines into the matter-antimatter reactor when acceleration reaches the max allowable. In that case, most of the mass of the engines may be considered as fuel mass.

I may have found that old 5 1/4" floppy; the label just says “Batch Files”. I’ll see if I can find someone with an operational B-drive to read it. Some of the program is coming back to me, now.

The program should be initiated by user input specifying the following: Mass of the ship, Mass of cargo and crew, Mass of fuel, Mass of one engine, Thrust of one engine, Number of engines, Distance to destination. You may assume 100% efficiency or input a lower figure; calculate fuel consumption accordingly. You may also want to specify a maximum allowable deceleration so you won’t apply the brakes hard enough to crush the frozen bodies of the crew. You may set the initial velocity at zero (relative to the Sun) or get fancy and factor in the Earth’s solar-orbital velocity and the Sun’s galactic-orbital velocity, as well as an escape-velocity correction for the gravity of Earth and Sun. Similar corrections can be made for the gravity at your destination, if you already know what’s there—fat chance.

Use Newtonian formulas to calculate position, mass, time and velocity of the ship (s, m, t, v) after one &delta;T in ship coordinates, which are initially the same as Earth (no-prime) coordinates. a = thrust / (rest mass); v = a&middot;&delta;T;  s = v&middot;&delta;T / 2;  t = t + &delta;T. That gives you position, time and velocity of the 1-prime coordinate system. Note that you are not using relativistic mass to calculate acceleration because you will always calculate acceleration in the ship’s coordinates, not Earth coordinates.

Next use Newtonian formulas to calculate the position, mass, time and velocity of the ship (s', m', t', v') after a second &delta;T in 1-prime coordinates; a' = thrust / (rest mass); v' = a&middot;&delta;T;  s' = v&middot;&delta;T / 2;  t' = t + &delta;T. That gives you the position, time and velocity of the 2-prime (next) coordinate system in 1-prime (present) coordinates.

Using special-relativity, calculate the position, time and velocity of the two-prime (next) coordinate system in Earth (zero-prime) coordinates. I think the velocity formula is v (i.e., velocity of next coordinate system relative to Earth) = (v + v') / (1+ v×v' / c2). I haven’t yet found the position and time formulas. Anybody here know them? I think the answer might be found under the heading of Lorenz transformation http://en.wikipedia.org/wiki/Lorentz_transformation or Poincare transformations http://en.wikipedia.org/wiki/Poincar%E9_group.

You will loop back to calculate a new s', m', t', and v', and repeat the same steps n times to get the position, mass, time and velocity of the ship in Earth coordinates after n &delta;T’s. Before looping back, however, you must determine whether it is time to begin coasting.

You will need to begin coasting and turn the ship around when the remaining fuel is just sufficient to stop the ship at its destination. To calculate the deceleration trajectory, you must run time backwards from touchdown at the destination. In forward time, the arrival fuel mass will decrease, and acceleration will increase until it reaches the max allowable value. From then on, you will convert one engine at a time to fuel, and adjust your thrust, acceleration and fuel consumption accordingly. You will run out of fuel upon arrival.

However, you will be doing these calculations in reverse time; so arrival fuel mass begins at zero and increases, acceleration decreases until one additional engine can be created from fuel mass without exceeding max acceleration. In reverse time, you have negative fuel consumption as you accelerate toward Earth. You begin with the minimum number of engines needed to produce maximum acceleration; you convert fuel mass to engines each time your acceleration decreases below maximum.

Coasting must begin at the point where both velocity and fuel mass accumulated in reverse time relative to the destination are equal to velocity and fuel remaining in forward time relative to Earth. The program should alternate between the departure trajectory from Earth and arrival trajectory at the destination—in leap-frog fashion. Each time the velocity in one direction increases beyond the other, you compare fuel masses; if the arrival fuel mass is greater, then it is past time to begin coasting.

That concludes one iteration of the program. You should loop back to the beginning and repeat the calculation using a smaller &delta;T—perhaps half as large. When two consecutive iterations yield the same result, withing tolerance limits, you output the resulting trajectory. The output should, at least, describe the duration of the journey in both Earth coordinates and in ship coordinates. It might also tell the time, location and mass at the beginning and end of coasting in both Earth and ship coordinates and the number of engines remaining at touchdown.

The program I am describing is one dimensional. A sensible space traveler would probably go the long way—following an arc well outside the plane of the galaxy’s disk—to hopefully avoid colliding with dark matter.

The program also ignores the effects of gravitational bodies, such as Earth the Sun the galaxy, etc. If you hypothesize a really peppy spacecraft, say ten G’s at liftoff, and you’re only going to Alpha Centauri and back, those gravitational fields will not greatly alter your trajectory. A little more realistically, you will begin with a tremendous mass of fuel (perhaps equal to the Moon’s mass) and very small acceleration; it may take a significant portion of your fuel to overcome the gravity of the Earth and Sun. You may need to spiral once or twice around the Sun before heading into deep space. At the other end of the trip, your fuel mass is greatly reduced, so gravitational fields are insignificant by comparison to your maxxed-out deceleration.

If you wish to make a round trip, you will have to take with you the ability to replenish your matter-antimatter fuel supply at the turn-around point. You’ll probably want to carry only the most basic tools and the information needed to build from there to a functional antimatter production facility. Bear in mind, you’ll be a few years older when you return to Earth, but Earth will be about 200,000 years older, so what’s the point of returning? How many dark ages will have ensued? Will the master race be silicon-based descendants of our computers or will it be an intelligent cockroach? I doubt if either will be friendly to a 21st Century human.

Since any information obtained by such a journey would be unavailable even to the descendants of those who remain behind, who would be willing to pay the bill? Would those making the trip have to pick up the tab before leaving Earth. The more people going, the greater the expense. So a very few people would have to enslave the rest and leave them behind after milking them dry. The cost of this project would make the pyramids of Egypt look like an item on an employee’s expense voucher.

Has anyone read this yet?


 * I've read as much as I can :) Anyway, there was a science fiction story many years back about a space faring race that created highways by collapsing suitable stars into black holes, turning all the resulting energy into laser beams that were bent into loops by the created blackholes.  The idea was that to travel through space one simply dipped a mirror into these beams and got an immediate thrust.  The beam also cleared the path of any debris.  The reason I'm posting this is the fact that your calculations assume that the reaction mass-energy is carried with the ship, but in fact beaming the energy out makes the limit somewhat less useful. njh 05:30, 31 December 2005 (UTC)

Cleanup
This needs lots of cleanup such as spelling, italic variables, consistent symbols for variables, superscripts, and capitalization for starters. Plus it needs to be broken up into sections and otherwise wikified. Gene Nygaard 01:59, 28 January 2006 (UTC)
 * Not just consistent variables but conventional ones, too, and other things like leading zeros. Gene Nygaard 02:01, 28 January 2006 (UTC)

Be more specific about what things you think need changing, and state justification for change"? If you see any actual spelling, puntuation, or grammar errors you are welcome to fix them.?
 * puntuation->punctuation
 * (there are a lot of errors in this article, I just haven't had the time to go through and fix them - perhaps you could run the whole thing through a spell chequer and fix the worst offenders) njh 08:54, 6 February 2006 (UTC)
 * (there are a lot of errors in this article, I just haven't had the time to go through and fix them - perhaps you could run the whole thing through a spell chequer and fix the worst offenders) njh 08:54, 6 February 2006 (UTC)
 * (there are a lot of errors in this article, I just haven't had the time to go through and fix them - perhaps you could run the whole thing through a spell chequer and fix the worst offenders) njh 08:54, 6 February 2006 (UTC)

Relativistic rocket formulas
I've put a bunch of formulas at User:Wwoods/Relativistic rocket formulas. I collected or worked them out several years ago, so I don't have the derivations at hand, but for most of them it shouldn't be to hard to verify them. —wwoods 22:36, 10 February 2006 (UTC)
 * You give some data for a rocket accelerating at constant rate, but it is more relevant, especiall to this article, to correctly apply the rocket equation that takes into account the depletion of propellant during thrust. DonPMitchell (talk) 00:13, 5 July 2008 (UTC)

Additions by Tmayes1965
A long series of paragraphs have been added to this article by the above user, describing the design of a theoretical relativistic rocket. While there are a number of useful points on design considerations that would need to be taken into account, as it stands the additions are much more a prescription for the design on an individual rocket. Sentences such as "It would have a rotating crew habitat" or "There would be an array of high energy lasers, particle beams and some missiles mounted on the starship" are nothing more than crystal ball gazing. Would it make more sense to try and selectively eliminate passages that refer to non-critical design features, move the whole section to a new article on this ""beam core" pion rocket" or just wipe the entire section and try to rebuild a few useful points of consideration, such as the need for sheilding at the bow of the craft? Icelight 01:18, 7 June 2006 (UTC)

Addition/Correction/Question - Andy Stangeland 02 Oct 2006
In the article it mentions that "Gamma rays can be reflected by some materials such as beryllium." This is counter to every other discussion about gamma rays that I've seen. Other sites have said that only theoretical, quantum engineered materials, could deflect a gamma ray. Additionally, I can't find any other resource that says that gamma rays can be deflected. High energy X-rays (lower than gamma rays) can be deflected or refracted at small angles, but the only information I've found on gamma rays said it could be stopped with 2 inches of lead or tungsten. (CRC) Never anything about deflection though.

Nonsense
This whole article is quite a nonsense. It is not useful to derive from the special theory of relativity, since it is obvious from conversation of momentum that a relativic velocity never can be reached by a rocket. From the law of conversation of momentum one easly derives
 * $$ m \ \frac{dv}{dt} + dm \ v_e = 0 $$

for the velocity $$v$$ of the rocket of mass $$m$$ and the velocity $$v_e$$ of the exhaust gases. This leads to


 * $$ dv = v_{e} \frac{dm}{m} $$

and finally by integrating
 * $$ v = v_{e} \ln\left(\frac{m(t=0)}{m(t)}\right). $$

Moreover the relativistic calculation is just wrong, since as an example, there is not a uniform velocity $$v_e$$ of the exhaust gases. The velecity $$v_e$$ is only constant relative to the rocket but not in any frame which is not accelerated. —Preceding unsigned comment added by 84.169.245.54 (talk • contribs) 25 November 2006


 * The relativistic rocket equation is
 * $$ \tanh^{-1}\frac{v(t)}{c} = \frac{v_e}{c} \ln\left(\frac{m_0}{m(t)}\right). $$
 * For $$v \ll c$$, this reduces to the non-relativistic version:
 * $$ v(t) = v_e \ln\left(\frac{m_0}{m(t)}\right). $$


 * The exhaust "velocity", $$v_e$$, is a figure of merit for a rocket, not necessarily the speed of anything.
 * —wwoods 21:33, 26 November 2006 (UTC)


 * Ok, one may define an exhaust velocity just as the ratio of the disired total momentum the space vehicle finally gains to the mass of the propellant. This ratio can indeed be regarded as a figure of merit for a space vehicle and has the dimension of a velocity, but is not the speed of anything. This is in contrast to the classical derivation of the rocket equation, since here $$v_e$$ is in fact the velocity of the exhausted gases measued in the rest frame of the rocket.

Additions by 71.124.2.194
I reverted these additions:


 * It should be noted that any electrical source can be used to have an effective exhaust velocity of nearly $$c$$ using a linear acelerator.

This is not true because you have to include the energy source's fuel ...


 * The implication of this is that even a $$c$$ exhaust velocity needs a fuel ratio of 99.9997%; effectively making a 50 ton spaceship require 2 million tons of fuel to have 0.5$$c$$ final velocity. Being able to decelerate also would mean 4x the fuel mass.

The calculation is obviously flawed.

Icek 05:46, 28 December 2006 (UTC)

Pion Engine
The section on pion engines is bogus. The device describe would vaporize in a microsecond under exposure to the levels of radiation described there. Even with chemical rocket engines, a key problem is cooling. Designs for antimatter engines (even ones funded by the infamous NIAC) almost always ignore the simple fact that no form of matter known to man can exist in a solid state when exposed to such enormous radiation flux. DonPMitchell 22:34, 24 October 2007 (UTC)


 * The section on pion drive should be deleted. It is just someone's pseudo-scientific ramblings that belong on their talk page or a blog, not in an encyclopedia.
 * 1. Gamma rays are almost impossible to collimate
 * 2. Beryllium is not a "gamma ray reflector"
 * 3. proton-antiproton collions doesn't just produce pions
 * 4. pumping liquid hyrogen, are you going to pump liquid antihydrogen too?
 * 5. The engine and nozzle and such would evaporate in a nanosecond, when the annililation of bulk quantities of antimatter begins.
 * 6. There is plenty of nonsense about antimatter drives elsewhere in wikipedia

This whole article could be replaced with a summation of the very clear discussion of relativistic rockets in Taylor and Wheeler's book "Spacetime Physics" DonPMitchell (talk) 00:21, 5 July 2008 (UTC)


 * The cooling problems encountered by conventional rockets arise from the contact between the hot expanding propellent and the inside of the engine combustion chamber and nozzle. A pion rocket or antimatter induced heating/fission/fusion engine redirects the products of these reactions using a magnetic nozzle, which cannot be heated. The mass to energy conversions that would occur during the reactions would be intense enough for all the radiation produced to be gamma rays, and very energetic ones since we're talking about proton annihilation and π0 meson decay. As long as the walls of the engine are not impossibly thick or made of too dense metal, the attenuation coefficient will allow most rays to pass right through and exit into space without inducing heat. Obviously this stops being true for the ridiculously large amounts of antimatter -1kg per second, was it ?- and thrust described in the original section, as the gamma rays would be so densely emitted that even the minuscule fraction of them that would interact with the engine materials would melt them.


 * Antimatter induced heating, fission, and fusion engines (or a combination thereof such as the ICAN or AIMSTAR) using pelletized propellent will cause a sudden increase in temperature within the pellet or droplet, leading to gamma ray-producing reactions almost immediately; there will be no time for the reaction mass to thermally radiate the energy input away.


 * Such engines designed for uninterrupted annihilation are the only kind that could have a radiated heat problem. Solid and gas core antimatter rockets are conventional rockets operating at conventional power levels, only using unconventional fuel. They would not generate immoderate amounts of heat. Plasma core antimatter and annihilation powered continuous fusion rockets (such as C. Pellegrino's "valkyrie") have the potential to thermally radiate through whatever contains the reaction mass, but they don't have the time to do so either. Unlike what happens during confined fusion or ionization, the particles are heated suddenly around the annihilation reactions (so much that they fuse in the case of the fusion rocket) and they (along with reaction products, also in the case of the fusion rocket) all exit the engine carrying their heat with them. It's a lot like some extreme form of evaporative cooling.


 * My point is, the cooling problem does not exist but these rockets would irradiate everything. 82.65.175.49 (talk) 10:09, 5 February 2012 (UTC)


 * Ok, i rewrote some of the article, removed the dead first reference, and added some new ones which authors were mentioned in the article. Also removed the bogus "1kg of antimatter for X Newtons of thrust" part, the redundant description of magnetic containment, and that link to the vacuum flask(!) article. It still needs to be written in an organized way by a real expert, but at least it should be accurate now. 82.251.149.7 (talk) 23:51, 5 February 2012 (UTC)

Bogus or not, the pion section should be rewritten to make it clear that this is a highly hypothetical concept. Currently it reads as if it were an existing, working technology. Nobody even knows if pion engines are possible.--114.181.225.100 (talk) 23:10, 25 March 2017 (UTC)

Fuel
It may be worth noting that the only onboard fuel that would be required would the amount necessary to get to a noticeably relativistic velocity. After that point, the radiation energy from the forward direction (from stars or even from cosmic background radiation) would be blue-shifted to the point where it would be providing all the energy needed for further acceleration. 68.39.154.196 (talk) 15:18, 4 October 2008 (UTC)

No. Absorbing such radiation would slow the spacecraft down, due to conservation of momentum. The blue shift comes from its speed in the first place. You don't get something for nothing. 131.111.185.8 (talk) 16:01, 21 January 2011 (UTC)


 * This article is really bad. Apparently none of the editors understand the difference between rocket fuel and rocket propellant. Confusing the two is rampant here. Fuel is the energy source; propellant is the "stuff" (atoms, electrons, photons) which a rocket expels in order to gain momentum. It also does, imho, a really bad job of separating the useful physical properties (of the various parts of the system) from parameters used (mostly in comparisons by hobbyists, I'd guess) to compare properties. Ve & Isp for instance. I understand that the clowns who established the field used these and that they are so entrenched in the field's literature that they need to be discussed, but I also think that most kids, after taking high school physics, are NOT familiar with them while they are quiet familiar with the concepts of mass, velocity, acceleration, and momentum. I suggest that the introductory discussion confine itself to concepts which most readers will be familiar with before jumping to other, and unnecessary, concepts.67.140.181.214 (talk) 18:39, 22 March 2018 (UTC)

Table on specific impulse needs references
Where do the values in the table about specific impulse come from? In particular, I can find no research article in which it was calculated that electron-positron annihilation with a "hemispherical absorbing shield" results in a 0.25c specific impulse. Also note that the values for eta and I_sp/c as reported in the table have apparently no connection with the formula for I_sp given in terms of eta, as given in the article just before the table appears. [For example, the table says that for the pion engine, eta is 0.56. However, if you plug eta = 0.56 into the equation given for I_sp, you would get I_sp = 0.898c. What is going on? If the I_sp is reduced due to "energy losses," this needs to be explicitly and clearly stated.]

Please give references for the data in the table.

Also, at the moment Reference (1) is nothing but a broken link.

Nullinfinity (talk) 22:49, 23 June 2009 (UTC)

Specific Impulse
I_sp is defined as:

I_sp = g0 * v_e

Where g0 is acceleration due to gravity at earth's surface. This doesn't significantly affect the derivation, but either each I_sp has to be replaced with a v_e or every v_e needs to be multiplied by g0. — Preceding unsigned comment added by 129.22.124.89 (talk) 00:25, 5 July 2014 (UTC)

External links modified
Hello fellow Wikipedians,

I have just added archive links to 2 one external links on Relativistic rocket. Please take a moment to review my edit. If necessary, add after the link to keep me from modifying it. Alternatively, you can add to keep me off the page altogether. I made the following changes:
 * Attempted to fix sourcing for http://scientium.com/diagon_alley/commentary/bowden_essays/sotm/starship/rockets.htm
 * Added archive https://web.archive.org/20120118144444/http://thefutureofthings.com:80/articles/33/new-antimatter-engine-design.html to http://thefutureofthings.com/articles/33/new-antimatter-engine-design.html

When you have finished reviewing my changes, please set the checked parameter below to true to let others know.

Cheers. —cyberbot II  Talk to my owner :Online 01:22, 19 October 2015 (UTC)


 * Fixed one link:.
 * The scientium source was used to back largely inrrelevant information, and does not appear to have been a wp:reliable source. Removed: . - DVdm (talk) 07:12, 19 October 2015 (UTC)

"By applying the Lorentz transformation on the acceleration"
The article mentions a Lorentz transformation, but those are not valid for an accelerating frame. The proper time arclength gives the same t' = (1/a)sinh(at) relation on a hyperbolic motion worldline, however. Should this be changed? -AkariAkaori (talk) 08:03, 21 April 2017 (UTC)
 * I have removed the "on the acceleration" part (which I already had changed to "to the acceleration" in my copy edit), but the transformation can be applied because the non-rocket frame is inertial. The standard Lorentz transformation (with c=1) between the rest frame $$(x',t')$$ and the "instantaneously comoving inertial" frame the rocket $$(x,t)$$ at rocket time t is given by:
 * $$dt' = \gamma(t) \ ( dt + v(t) \ dx )$$
 * $$dx' = \gamma(t) \ ( dx + v(t) \ dt )$$
 * No problem. DVdm (talk) 08:25, 21 April 2017 (UTC)


 * I just noticed above the Lorentz transformation part to derive $$\Delta v = c \tanh \left(\frac {I_{sp}}{c} \ln \frac{m_0}{m_1} \right).$$ it is already stated that $$\frac{\Delta v}{c} = \tanh\left[\frac{at}{c}\right]$$ (which would already give us delta-v without needing to find rest time), are these part of the same train of thought or should they be in different subsections like the different derivations for the classical rocket equation are? AkariAkaori (talk) 07:41, 22 April 2017 (UTC)


 * No idea. I hadn't seen that article Tsiolkovsky rocket equation before. - DVdm (talk) 08:47, 22 April 2017 (UTC)


 * Please note that Delta-V/c = tanh((Ve/C)(ln(m0/m1)) is given (derived) in the UCR article The Relativistic Rocket which as of 25/1/2018 is easily found on the web (and has persisted for over 10 yrs).

Difficult
This article's lead claims:"Achieving relativistic velocities is difficult, requiring advanced forms of spacecraft propulsion that have not yet been adequately developed." Plainly speaking: this is false. First, we need to carefully frame the issue. While "atom smashers" are able to accelerate massive objects (H, Pb, & Xe (LHC); H, Al, Au, Cu, U (RHIC)) to near light speed (protons were accelerated to 0.99999999c at the LHC) with a GREAT deal of difficulty there is no recorded event in which any macroscopic object has been accelerated to near light speed. Nor is the attainment of such velocity possible with any known or reasonably straightforward improvements of known technology; that is it is not "difficult" it is (currently) impossible. Claiming is is "difficult" is false and misleading because in fact it may never be accomplished. (This is using the reasonable constraints that a rocket vehicle carries its own fuel (energy) and propellant.) "have not yet been adequately developed" is another misleading, but factually correct statement. In fact, there are very good {evidence based) reasons to believe attaining relativistic velocities with rockets in the kilogram to kilotonne range is not possible; no evidence contradicts this. I am changing this profoundly misleading sentence to:"There is no known technology capable of accelerating a rocket to relativistic velocities. Relativistic rockets require enormous advances in spacecraft propulsion, energy storage, and engine efficiency which may or may not ever be possible."71.31.150.130 (talk) 15:40, 25 January 2018 (UTC)


 * I agree with the edit. An extra book source would be welcome. - DVdm (talk) 15:51, 25 January 2018 (UTC)


 * This is not quite accurate. There are many theoretically possible designs that would allow such engines, and there has been some research into photonic thrusters, which (due to their 'exhaust' velocity literally being the speed of light), can absolutely be used to accelerate to relativistic speeds assuming a large enough energy supply. Current photonic thrusters have been able to exert forces on the order of millinewtons with power inputs of a few kilowatts and so it is entirely feasible that with enough resources this idea could be scaled up to practical sizes. 131.227.33.141 (talk) 18:39, 7 March 2018 (UTC)