# Hypothetical Interstellar Spacecraft

• cjackson

#### cjackson

I know of Project Daedalus, Project Icarus, and Project Orion. These basically utilize pulse propulsion. In Daedalus and Icarus helium 3 and deuterium are combusted by a laser to create thrust. And in Orion nuclear bombs explode behind the craft to get it moving. All of these designs only reach a small fraction of lightspeed. Are there any plausible proposals for spacecraft that could reach relativistic speeds and achieve significant time dilation? Will humans be forever confined to the solar system because it's too expensive and impossible from a practical stand point to use antimatter or huge lasers to reach such high subluminal velocities?

I am not familiar with these three projects, but it is not inconceivable to reach relativistic speeds in the future with some specialized propulsion systems.

The usual idea nowadays is to provide a small, but constant, thrust over a very long period of time (e.g. several years) so that the accumulated acceleration is enough to get you to relativistic speeds. This is the idea behind ion propulsion, which provides very small thrust, but is very efficient because the exhaust velocity is very very fast (rather than in a chemical rocket, which provides a lot of thrust, but has slow exhaust velocity so it gets exponentially worse at accelerating you). The basic for the types of propulsion systems where you carry your own fuel is the rocket equation:

$$\Delta v=v_e\ln\left(\frac{m_i}{m_f}\right)$$

Here ##\Delta v## is the velocity gained after expending all your fuel, ##v_e## is the exhaust velocity, and ##m_i,m_f## are the initial and final masses respectively. As you can see, because of the logarithmic function, if you want ##\Delta v## to be a lot larger than ##v_e##, you need your initial mass to be exponentially larger than your final mass, which is not practical. So, with things like ion engines, which have a very high exhaust velocity (up to 50km/s in comparison to a typical rocket engine's exhaust velocities of 2-5km/s) , we can mitigate this problem somewhat.

The problem is that to achieve such high exhaust velocities, one needs to use up a lot of power, and so we can't make ion engines with a lot of thrust because we can't make big enough power sources to give its exhaust such high velocities.

There are of course many other designs currently under consideration. A way to mitigate the fuel requirements would be to basically not carry the fuel with you. These would be like solar sails which try to capture the solar radiative energy, or schemes in which a powerful laser on Earth propels a spacecraft . The problem with these propulsion systems tend to be that photons are horrible momentum carriers since they are mass-less. Photons will basically completely elastically scatter off of your mirror, and impart only a tiny momentum (and thereby a tinier amount of its energy) to your solar sail. For example, a solar photon with energy ##E## has momentum only ##p=E/c##. In this case, it can impart a total momentum of ##2p=2E/c## to your spacecraft (it roughly bounces right back since it). Say you are at Earth where the radiant flux is 1400W/m^2, then the force a 1 square meter large solar panel will generate is only:

$$F \approx 2800W/c\approx 10^-5N$$

Of course, as you get farther from the Sun, your thrust goes down as the second power of distance. But if you had a large enough sail, and you let your spaceship cruise along for a long long time, then you could get up to some pretty high speeds presumably.

Since light is such a horrible momentum carrier, one might want to directly deposit the light energy into the spaceship and somehow create thrust directly from the energy of light. One possible method of doing this (usually considered for how to deflect meteors or other celestial objects from impacts with the Earth) would be by using laser ablation. In laser ablation, you don't let the light reflect off a mirror or something, but instead you use the light to super-heat some material and when this material burns off and ejects into space, it's ejection creates thrust. This is the coolest propulsion method I am aware of, but I'm not sure how feasible it would be for a rocket since you need material that you can use your laser to basically destroy.

Anyways, the final point is that the future is open to possibilities. I'm sure people will come up with different ingenious ideas on how to get us to relativistic speeds. Do not be discouraged!

Are there any plausible proposals for spacecraft that could reach relativistic speeds and achieve significant time dilation?

Not with technologies that might be available in the near future.

The time dilation effect is vanishingly small until you achieve velocities that are a significant fraction of the speed of light - t = t0/ (1-(v^2/c^2)). Thus far, the best we have achieved is Voyager at a whopping 17 km/sec. That is nowhere near a 'significant' fraction of light speed. If you do get up to a significant fraction of light speed, you have an entirely new set of problems to deal with - like getting shot blasted by tiny specks of matter. Needless to say, this would be a stupendously bad way to discover interstellar space rocks. Even at the pedestrian speed of about 17,000 miles per hour [earth orbital speed], engineers worry about collisions with flecks of paint.

I am not familiar with these three projects, but it is not inconceivable to reach relativistic speeds in the future with some specialized propulsion systems.

The usual idea nowadays is to provide a small, but constant, thrust over a very long period of time (e.g. several years) so that the accumulated acceleration is enough to get you to relativistic speeds. This is the idea behind ion propulsion, which provides very small thrust, but is very efficient because the exhaust velocity is very very fast (rather than in a chemical rocket, which provides a lot of thrust, but has slow exhaust velocity so it gets exponentially worse at accelerating you). The basic for the types of propulsion systems where you carry your own fuel is the rocket equation:

$$\Delta v=v_e\ln\left(\frac{m_i}{m_f}\right)$$
Of course, the above equation is only accurate for values of delta v small with respect to c. The relativistic version is

$$\Delta v = c \tanh^{-1} \left (\frac{v_e}{c} \ln \left( \frac{M_i}{M_f} \right ) \right )$$

So for example, if we had a ## v_e## of 0.2 c and a ratio of ## \frac{M_i}{M_f} ## of 100, the first equation says that we should reach a final speed of .92c while the second only allows us to get to 0.726 c.

Now the first equation ignores all relativistic effects, thus to be fair, you would also lose any benefit gained in ship time from time dilation. It would take you 10.9 years ship time to travel 10 light years using this calculation.

With the second calculation, we get the benefit of a time dilation factor of 1.45, and thus the same 10 light year trip would take 9.47 years ship time, almost 1 1/2 years shorter.

But even 0.2c for an exhaust velocity is well beyond anything we can presently come close to, and even it required our fuel supply to be 99 times more massive than the payload to travel 10 light years in 9.47 yrs ship time.

The relativistic version is

$$\Delta v = c \tanh^{-1} \left (\frac{v_e}{c} \ln \left( \frac{M_i}{M_f} \right ) \right )$$

Only if ## v_e## is not the exhaust velocity but the specific momentum dp/dM of the fuel.

The basic for the types of propulsion systems where you carry your own fuel is the rocket equation:

$$\Delta v=v_e\ln\left(\frac{m_i}{m_f}\right)$$
So just add more fuel and you can achieve any velocity you want!

Unfortunately, you can't. A vehicle needs fuel tanks to hold that fuel, and structure to keep everything intact. Adding a bit more fuel is easy: Just top off the tanks. Adding a lot more fuel is not so easy. A lot more fuel means bigger fuel tanks and more structural elements. In practice it's very hard to have ##\frac{m_i}{m_f}## (ratio of initial mass to final mass) greater than 20, which in turn means that it's very hard to have achieve much more than three or four times the exhaust velocity.

There is a loophole, which is that the rocket equation pertains to single stage rockets. Do it just right and each stage can maybe achieve a delta V of three times exhaust velocity. Assuming an exhaust velocity of 200 km/s, all it takes to get close to relativistic speeds (one tenth c) is a 500 stage rocket. No problem! (That was written with tongue firmly embedded in cheek.)

Are there any plausible proposals for spacecraft that could reach relativistic speeds and achieve significant time dilation?
With current technologies, or even realistic dreamed of technologies? No.

Of course, the above equation is only accurate for values of delta v small with respect to c. The relativistic version is

$$\Delta v = c \tanh^{-1} \left (\frac{v_e}{c} \ln \left( \frac{M_i}{M_f} \right ) \right )$$

So for example, if we had a ## v_e## of 0.2 c and a ratio of ## \frac{M_i}{M_f} ## of 100, the first equation says that we should reach a final speed of .92c while the second only allows us to get to 0.726 c.

Now the first equation ignores all relativistic effects, thus to be fair, you would also lose any benefit gained in ship time from time dilation. It would take you 10.9 years ship time to travel 10 light years using this calculation.

With the second calculation, we get the benefit of a time dilation factor of 1.45, and thus the same 10 light year trip would take 9.47 years ship time, almost 1 1/2 years shorter.

But even 0.2c for an exhaust velocity is well beyond anything we can presently come close to, and even it required our fuel supply to be 99 times more massive than the payload to travel 10 light years in 9.47 yrs ship time.

I was mentioning this equation in the context of ion engines. Ion engine exhausts are around 50km/s which is like .00001c. Unless you make your rocket out of fuel only, I didn't see the need to bring up the relativistic effects here...

But that is my fault, because the OP specifically asked for relativistic engines, and I got side tracked into talking about the current prospects...which do not get us anywhere near relativistic speeds.

@D H: Yes, that was the point I was trying to make with the rocket equation. The point was that if you want a velocity that is much higher than your exhaust velocity, then using a rocket might not be the way to go.

I was trying to impress on the OP the difficulty of reaching truly relativistic speeds, without completely just saying "no it can't be done", but I didn't think that came through in my post. That's my fault.

Let me remedy that now.

@OP: Let's do some back of the envelope calculations! Suppose you want to go to Alpha Centauri and back in 2 years of your time. The distance to Alpha Centauri is 4ly, so you need a time dilation factor of roughly 4. This means you need a velocity of:

$$\gamma=4=\frac{1}{\sqrt{1-v^2/c^2}}$$

Solving for v:

$$v\approx .97c$$

So, how much energy would we need to get our spacecraft up to that speed? Let's assume our spacecraft is roughly the size of a space shuttle ~2000tons. And let's not worry about the fuel since we are only doing a back of the envelope calculation. The kinetic energy of this 2000 ton object going at .97c is:

$$E=\gamma mc^2=4*2,000,000kg*c^2\approx 7\cdot10^{23}J$$

This is approximately 170 Terra-tons of TNT equivalent. That's quite a lot of energy!

Last edited:
IThe kinetic energy of this 2000 ton object going at .97c is:
$$E=\gamma mc^2=4*2,000,000kg*c^2\approx 7\cdot10^{23}J$$

For comparison, world-wide energy production in 2008 was about ##5\cdot10^{21}## Joules. So we're talking about the entire power output of all humanity for centuries.

Having grown up with "the promise" of Space Travel that has all but completely stalled, I find this subject rather depressing. Considering how little it costs to keep labs going on Antarctica and how difficult it can be to fund even those, on good days I doubt a man will walk on Mars by 2114. On bad days I wonder if a man will again walk on our Moon by then. Confined to our Solar System? I have grave doubts we will get beyond the stony planets for 500 years. That said, "forever" is a very long time.

What "promise"? There has been no "promise" since the end of the Apollo program. Don't confuse sci-fi movies or pop-sci articles with reality.

With the exception of those who dabble in the perpetually low Technology Readiness Level (TRL) concepts, everyone working in the field knows full well how slow progress has been and will continue to be. While NASA and other organizations do invest monies in futuristic ideas, the vast majority don't pan out. Pop-sci articles focus on those futuristic ideas, ignoring that most of those ideas just don't work.

What "promise"? There has been no "promise" since the end of the Apollo program. Don't confuse sci-fi movies or pop-sci articles with reality.

With the exception of those who dabble in the perpetually low Technology Readiness Level (TRL) concepts, everyone working in the field knows full well how slow progress has been and will continue to be. While NASA and other organizations do invest monies in futuristic ideas, the vast majority don't pan out. Pop-sci articles focus on those futuristic ideas, ignoring that most of those ideas just don't work.

Perhaps I'm older than you as I grew up reading about Viking, Aerobee-Hi, Vanguard and Atlas and watching early attempts on TV. I saw JFKs "we choose to do these and the other things because they are hard" speech, Live. It may not be exactly scientific but it felt like a promise to a kid growing up with such rapid progress... that's why I put it in quotation marks, since I recognize now it was just a pattern brought on by mistaking Cold War pissing contests for heroic exploration. Back then, I bought the hype, studied, and machined amateur rockets and test stands to prepare for a career. Then, I went to college to study Engineering and grew up.

I mentioned nothing about Pop Sci and in fact my pessimism is grounded in the Science of just how difficult the multitude of problems that face us actually are, as well as most Nations' miniscule commitment to exploration and pure science. Don't chastise me or even attempt to categorize me with that "sci fi" and "pop-sci" whitewash. I may be entertained by it from time to time, but I do know the difference and I think my post is realistic if not overly optimistic.

Your "promise" did exist back in the 1950s and 60s. There were serious proposals to have a permanent manned presence on the Moon, to build nuclear rockets to send astronauts to Mars, even to start building space colonies.

There were three key obstacles to those plans: budget realities, President Nixon, and Congress. While Nixon pretty much had to allow the Apollo Moon landings to go forward, he didn't like the Apollo program for the simple reason that the Apollo program was a Democratic idea. Congress went along with the redirection and eventual cancellation of the Apollo program because NASA was becoming a big drain on the budget, with spending peaking at about 5% of the federal budget in 1966. Those extravagant plans didn't mix well with budgetary or political realities.

Your "promise" did exist back in the 1950s and 60s. There were serious proposals to have a permanent manned presence on the Moon, to build nuclear rockets to send astronauts to Mars, even to start building space colonies.

There were three key obstacles to those plans: budget realities, President Nixon, and Congress. While Nixon pretty much had to allow the Apollo Moon landings to go forward, he didn't like the Apollo program for the simple reason that the Apollo program was a Democratic idea. Congress went along with the redirection and eventual cancellation of the Apollo program because NASA was becoming a big drain on the budget, with spending peaking at about 5% of the federal budget in 1966. Those extravagant plans didn't mix well with budgetary or political realities.

Exactly. I'm painfully aware of the small mindedness that essentially ended The Grand Dream. I was not aware that NASA reached a whopping 5% but I imagine that's a bit difficult to label and extract an exact number other than just "NASA" since the networking that came into being was so far reaching and completely unprecedented.

Someone, maybe Arthur C. Clarke (and maybe others) tried to compile a truly complete list of all the offshoot benefits from the Space Program and it becomes so far and wide that it is extremely hard for the average person to see the connection... possibly even harder to find politicians who can see it, let alone explain it to their constituents.

As far as I can tell, unless there is some major breakthrough by some country, presently China comes to mind, that feels threatening to some other Super Power, or until and unless some surprise asteroid takes out half of a city, what politicians who control budgets see as "realities" will remain small-minded and sadly, Earthbound.

PS The latter will remain true in the USA until and unless people start voting for people that have brains and can lead instead of some Good Ol' Boy they would feel comfortable with at a bar.