# Travel in space to Alpha Centuri

## Main Question or Discussion Point

I'm having a bit of a debate on travelling to AC. I was wondering if someone can post calculatons to show how long it would take travelling at 1g accelaration, and how much energy would be needed including any relativistic influences.

Thanks

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DavidSnider
Gold Member
That depends, how long would we be accelerating? Also, what is the mass of the ship?

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JesseM
Also, 1G acceleration in the same direction the whole time so you pass Alpha Centauri at relativistic speed, or 1G acceleration towards AC for half the trip and then 1G acceleration in the opposite direction to "brake" so you arrive at low speed? In the latter case it would take 3.6 years of onboard time (though more time in the Earth's frame), according to the http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html [Broken] page. That page also mentions that if you used the most efficient possible engine that converted fuel mass directly to photons that shot out in the direction of travel, the ratio of fuel mass to payload mass to arrive at AC at low speeds would be 38:1, and unless I'm mistaken the energy expended in the Earth's frame would just be the rest mass energy of the fuel, calculated using E=Mc^2.

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The size of the ship is an issue. It would include travelers and the food required to sustain them. Then their gear, and fuel. Closest I can think of would be a submarine for example. What I'm looking for is what the energy would be compared to a nuke reactor or oil equiv. The time of just 4 years is theoretical only (seems the CBR would cook them), what is the practical limit of speed attainable? Which then affects the time big time.

Nabeshin
The size of the ship is an issue. It would include travelers and the food required to sustain them. Then their gear, and fuel. Closest I can think of would be a submarine for example. What I'm looking for is what the energy would be compared to a nuke reactor or oil equiv. The time of just 4 years is theoretical only (seems the CBR would cook them), what is the practical limit of speed attainable? Which then affects the time big time.
4 years is by no means difficult when considering the radiation of the CMB "cooking" any travelers. Assuming 1g acceleration half the trip and 1g deceleration the other half, you get an effective travel distance of about 12,000 ly before CMB radiation begins to kill off your travelers. If you want a time, this is a journey that takes approximately 18 years, ship time.

Ok, then how much energy would be needed to make the trip?

Using a Los Angeles class sub as an example, we have 7000Mt for the ship, with a crew of say 200, and 2kg food per person per day, comes to a total of just short 10,000Mt not including fuel. At a rate of 38:1 then we would need 380,000Mt just for fuel. And if I read that site right that's fuel that get's converted 100% matter to energy with E=MC^2, correct?

Nabeshin
Obviously it depends on the propulsion method for such a ship.

For your example, assuming 7000Mt ship mass (6*10^12 kg), and 38:1 fuel, I get an lower bound on total energy cost somewhere in the neighborhood of a yottajoule (10^24) for the entire trip.

How many nuke plants?

If I have that correct, that's 400,000,000kg load that needs to be accelarated for 18 years. Converting the fuel into pure energy would be 3.25x10^23 joules. Over 18 years that's a power of 5.6x10^16Watts. A 500kW nuke plant for comparison would mean 11 TRILLION nuke plants. Correct?

Someone emailed me that they would accelarate for one year, getting to 1/10c, then coasting for 44 years and decelarating at AC. Thus 46 year travelling time. So can we calc the energy for that? Seems to me the number of equiv nuke plants would be more than a billion.

Nabeshin
Yes. Cutting down on acceleration does reduce power consumption, to a certain point. However, you suffer diminishing returns as the voyage becomes exponentially longer as you begin to lose the benefits of time dilation. Reducing acceleration from 1g to .1g helps, and to .01g helps a bit more. Beyond this, there's almost no point (you're talking travel times in the centuries by then anyways).

I'm not going to double check your specific numbers, but if you got 3*10^23 that's close enough to a yottajoule, we're in the same ballpark. Good.

Yes, power consumption is a HUGE problem for this kind of travel. If you want more info, I have an article you might want to read.

JesseM
calculating the energy in terms of nuke plants for a 38:1 fuel-to-payload mass ratio is kind of silly from a realistic point of view, because any civilization that can build photon drives that convert mass into photons with optimal efficiency (which would require something like a matter/antimatter drive) is probably going to have much better sources of power than fission-based nuclear power. If you want to assume technology not too far advanced beyond our own, you should probably assume some more feasible propulsion method like an ion drive or nuclear/electric propulsion...here's something I wrote about different propulsion methods on another thread:
This page gives Tsiolkovsky’s equation for the relation between change in velocity, payload mass and initial fuel mass:

This equation is a classical one which would need to be modified if delta v were close to the speed of light, but it can give you a sense of the huge amount of fuel needed if you just figure out the mass needed to get to some small fraction of light speed, like 0.01c, where the relativistic correction shouldn't be too big. They give the exhaust velocity for a chemical rocket as 4000 m/sec, and the exhaust velocity for a fission rocket as "12,000 m/sec (for solid-core nuclear thermal with oxygen augmentation), 40,000 m/sec (for nuclear electric propulsion), 100,000 m/sec (for more exotic and theoretical forms)". Using the 40,000 m/sec figure, to accelerate from being at rest wrt Earth to travelling at 0.01c relative to Earth (again, just calculating the answer using Newtonian physics without taking into account relativity, since the time dilation factor is very small at this speed), the equation tells us the mass of the rocket would have to be about e^75 times greater than the mass of the payload, which is about 3.5 * 10^32. If you want the answer in terms of acceleration, this thread gives the equation:

accleration* time = specific impulse * ln(mass ratio)

with each type of rocket having its own specific impulse (wikipedia's relativistic rocket page mentions that specific impulse is the same as exhaust velocity)...rearranging, this should mean the mass ratio needed to accelerate at 1G for some time t would be:

e^(9.8 m/s^2 * t / specific impulse)

If we again use 40,000 m/s for the specific impulse, this becomes:

e^(t * 0.000245/s)

So, to accelerate at 1G for 3 days (259200 seconds) would require a mass ratio of e^63.5, or a total initial rocket mass about 3.8 * 10^27 greater than the payload mass. This page mentions that for an antimatter rocket you might have an exhaust velocity of 10,000,000 m/s, so plugging that into the equation would give the mass ratio as:

e^(t * 0.00000098/s)

This would make 1G acceleration for a few days much more manageable, but to accelerate for 1 year (31536000 seconds) you'd need a mass ratio of e^(30.9), so the rocket would have to be about 26 trillion times more massive than the payload--that's a lot of antimatter!

Yes. Cutting down on acceleration does reduce power consumption, to a certain point. However, you suffer diminishing returns as the voyage becomes exponentially longer as you begin to lose the benefits of time dilation. Reducing acceleration from 1g to .1g helps, and to .01g helps a bit more. Beyond this, there's almost no point (you're talking travel times in the centuries by then anyways).

I'm not going to double check your specific numbers, but if you got 3*10^23 that's close enough to a yottajoule, we're in the same ballpark. Good.

Yes, power consumption is a HUGE problem for this kind of travel. If you want more info, I have an article you might want to read.

This would make 1G acceleration for a few days much more manageable, but to accelerate for 1 year (31536000 seconds) you'd need a mass ratio of e^(30.9), so the rocket would have to be about 26 trillion times more massive than the payload--that's a lot of antimatter!
My goal is to put the energy required into perspective, not an excersize to actually do it. An analogy, like what a trillion dollars looks like since that is so difficult to see. (\$1,000 bills stacked 65 miles high). So to put that energy requirement into nuke plant eqivilent, 1000 for each person on the planet, kinda puts the huge huge massive number into perspective.

Though your number above makes my number puny in comparison. So what's the message here?

Is space travel by ANY civilzation actually physicaly possible? I think not, but that's this primative mind from this perspective. Drake was right.

Yes, power consumption is a HUGE problem for this kind of travel. If you want more info, I have an article you might want to read.
I would like to read it too, please; I've actually been wondering about that for a long time (the theoretical minimum fuel required to move an n kg. mass across a distance x at relativistic speeds with a 100% efficient engine).

-- faye kane, idiot savant

stevebd1
Gold Member
I'm having a bit of a debate on travelling to AC. I was wondering if someone can post calculatons to show how long it would take travelling at 1g accelaration, and how much energy would be needed including any relativistic influences.
You might also find this web page of use which talks about accelerating at 1g to our nearest star using a 100% efficient propulsion system (i.e. matter-antimatter engine) and the fuel required-

http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html [Broken]

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calculating the energy in terms of nuke plants for a 38:1 fuel-to-payload mass ratio is kind of silly from a realistic point of view, because any civilization that can build photon drives that convert mass into photons with optimal efficiency (which would require something like a matter/antimatter drive) is probably going to have much better sources of power than fission-based nuclear power. If you want to assume technology not too far advanced beyond our own, you should probably assume some more feasible propulsion method like an ion drive or nuclear/electric propulsion...here's something I wrote about different propulsion methods on another thread:
I heard that there was some theoretical propulsion method that grabbed the material necessary for fuel from space as you went along. Did I understand that correctly? If so. and making the enormous assumption that such a propulsion system could actually work in practice, wouldn't that solve the fuel weight problem?

jtbell
Mentor
JesseM