What would it take to sustain a 1g acceleration over a 75 year period?

[SLD]

That is if you had a space station somewhere outside of say Jupiter’s orbit, and you built a huge rocket ship and simply set it on a course away from the sun, towards a far away star, with a simple acceleration of 1g, what speeds would you achieve and how long could you sustain such an acceleration realistically?

I guess it would depend on the fuel type. But if you could sustain a 1g acceleration for a long period of time you’d reach relativistic speeds after several hours. 3600 seconds x 9.8m/s/s.

Leaving earth orbit on chemical rockets we achieve an acceleration of 3g’s for several minutes on rockets that are larger compared to humans. So maybe in space we could build a rocket that is several kilometers long, mostly fuel, but a sizable living space, And accelerate it at 1g towards a star and reach it within a lifetime without an issue. Of course at some point we will need to reverse course and slow it down at 1g to reach orbit So we don’t fly by.

I once read that given a continuous 1g acceleration, you could explore the universe within a lifetime, due to relativistic time and space dilation. 1 g solves the problem of gravity. But is such an idea utterly unrealistic because one could never build such a rocket? Would some kind of nuclear powered rocket work? It seems to me that a nuclear explosion type rocket, assuming you could control it, would give you far more than a 1g acceleration And you couldn’t sustain life inside such a protected capsule. You’d pull too many g’s. Maybe there’s a middle ground, but all I keep reading about are projects that give us a much slower, but very long, sustained acceleration, e.g. light sails.

of course why sustain the acceleration after reaching speeds of, say, over .9c? Due to relativity, you aren’t likely to go much faster. And will you still feel the acceleration as 1g once relativistic effects really begin to kick in? I guess I’m still confused about the impact of special relativity on the travelers v. those who remain earthbound.

 

[lpetrich]

The acceleration is
\( a = \frac{\dot m}{m} v_e \)

where m is the mass of the spacecraft, m-dot the rate of mass loss as exhaust and waste heat (remember E = m*c²), and v_e is the effective exhaust velocity or specific impulse:
\( v_e = \frac{\dot p}{\dot m} \)

for momentum p. It is easy to integrate this equation:
\( u = \int a \, dt = v_e \log \frac{m_0}{m} \)

where m₀ is the initial mass, and u is sometimes called the "rapidity" in relativitistic kinematics. The actual velocity v is
\( v = c \tanh \frac{u}{c} \)

For perfect efficiency, v_e = c, and u = 77 c. The initial-to-final mass ratio is 4*10³³.

Thus, doing so is totally impractical.

 

[Loren Pechtel]

It's months to relativistic speed, not hours.

 

[barbos]

of course why sustain the acceleration after reaching speeds of, say, over .9c? Due to relativity, you aren’t likely to go much faster.

From outside observer perspective you are not. But from your point of view you ARE.
It just looks like space contraction to you. So in order to reach some place 1000 light years away in your life time you need to keep acceleration on full as long as possible.

 

[Bomb#20]

I guess it would depend on the fuel type. But if you could sustain a 1g acceleration for a long period of time you’d reach relativistic speeds after several hours. 3600 seconds x 9.8m/s/s.

That makes 36000 m/s after an hour. That makes 36000 km/s -- 12% of c -- after a thousand hours. I'm guessing you were mixing meters up with kilometers.

I once read that given a continuous 1g acceleration, you could explore the universe within a lifetime, due to relativistic time and space dilation. 1 g solves the problem of gravity. But is such an idea utterly unrealistic because one could never build such a rocket? Would some kind of nuclear powered rocket work? It seems to me that a nuclear explosion type rocket, assuming you could control it, would give you far more than a 1g acceleration...

The thing to keep in mind is that you have to put E = 1/2 mv² together with E = mc². When v is the same order of magnitude as c, that means the two E's are comparable -- and that means in order to put that kind of kinetic energy into your ship you have to turn an appreciable fraction of your mass into energy. So conventional nuclear reactions -- ordinary nuclear reactors, atom bombs, hydrogen bombs, or always-twenty-years-in-the-future controlled fusion reactors -- are all totally inadequate. Never mind the engineering difficulties; the underlying reactions themselves change less than one percent of the mass into energy. That puts a hard limit on how fast you can go: a few percent of the speed of light. Somewhat faster for fusion than fission, but not game changing. At those speeds dilation is negligible. With a fusion rocket it might be barely possible to get to Alpha Centauri in a human lifetime.

But yes, some kind of nuclear rocket could work. We do know of one nuclear reaction that converts more of the input mass into energy than fusion: matter-antimatter annihilation. So if you want to sustain constant acceleration long enough to get significant time and space dilation, and you want to do it using a rocket, you have no choice: your fuel has to be antimatter.

And you couldn’t sustain life inside such a protected capsule. You’d pull too many g’s. Maybe there’s a middle ground, but all I keep reading about are projects that give us a much slower, but very long, sustained acceleration, e.g. light sails.

The E = 1/2 mv², E = mc² barrier doesn't apply when you don't have to carry all the energy with you as fuel because you're beaming the energy from your home star. Given where we are in the overall ascent of man, that's currently the only feasible approach. We'll have the technology to build a light sail starship hundreds of years before an antimatter starship -- antimatter is just too hard to make and too hard to store for it to be a practical fuel any time soon. It took us two thousand years to get from the first experimental jet engine to one you could power an airplane with.

 

[SLD]

I did mix up my meters with my kilometers! Duh! It would take a couple thousand hours before relativistic effects would be noticeable. Sorry about that!

But one more dumb question. I gather from Bomb#20’s post that even though you cease to accelerate at 1g from the perspective of an earth bound observer, from the perspective of those in the spaceship, they are continually experiencing 1g acceleration? Right? So there’s no need to have a source of artificial gravity.

But wouldn’t they calculate that they are eventually going faster than the speed of light? I realize that they wouldn’t measure the speed of light any different. But they can still do the math and realize at some point that they are going beyond c, from the earth perspective. Is there a real difference between FTL, and space contraction? They wouldn’t experience time dilation, as everything would appear to happen in normal time for them. But if they experienced space contraction, they would still know that the “true” distance is much greater.

Also, what’s then the maximum length of time we could expect to achieve a 1g acceleration? Let’s use some kind of fusion device.

 

[Bomb#20]

But one more dumb question. I gather from Bomb#20’s post that even though you cease to accelerate at 1g from the perspective of an earth bound observer, from the perspective of those in the spaceship, they are continually experiencing 1g acceleration? Right? So there’s no need to have a source of artificial gravity.

But wouldn’t they calculate that they are eventually going faster than the speed of light?

If they're calculating their own speed by checking the star maps they made at home, yes. If they're calculating it by checking if they can catch up with photons, no. Instead they'll observe that their star maps are no longer accurate. They'll measure star positions from their ship and find that the stars aren't as far apart as they used to be. If they cover the distance from home to Alpha Centauri in a subjective year, it will look to them not like they're going at 4c but like Sol and Alpha Centauri are only one light year apart.

Is there a real difference between FTL, and space contraction?

In SF, yes: the difference is whether your friends are still alive when you go home.

They wouldn’t experience time dilation, as everything would appear to happen in normal time for them. But if they experienced space contraction, they would still know that the “true” distance is much greater.

This is relativity. There's no such thing as "true" distance. That's pretty much what the word means.

Also, what’s then the maximum length of time we could expect to achieve a 1g acceleration? Let’s use some kind of fusion device.

Well, if a thousand hours gets you to v=.12c, 1/2 mv² is about 0.7% of your total mass converted to energy, and that's roughly what fusion reactions can do. So, a thousand hours.

 

[Loren Pechtel]

I did mix up my meters with my kilometers! Duh! It would take a couple thousand hours before relativistic effects would be noticeable. Sorry about that!

But one more dumb question. I gather from Bomb#20’s post that even though you cease to accelerate at 1g from the perspective of an earth bound observer, from the perspective of those in the spaceship, they are continually experiencing 1g acceleration? Right? So there’s no need to have a source of artificial gravity.

But wouldn’t they calculate that they are eventually going faster than the speed of light? I realize that they wouldn’t measure the speed of light any different. But they can still do the math and realize at some point that they are going beyond c, from the earth perspective. Is there a real difference between FTL, and space contraction? They wouldn’t experience time dilation, as everything would appear to happen in normal time for them. But if they experienced space contraction, they would still know that the “true” distance is much greater.

Also, what’s then the maximum length of time we could expect to achieve a 1g acceleration? Let’s use some kind of fusion device.

Nope, they never go FTL. The longer the engine is on the closer to c they get and they'll see the stars zipping past at what a map would say it FTL speeds because of relativistic effects, but neither they nor an outside observer will ever measure them as going FTL.

The only way to measure the relativistic effects are by comparing what they are seeing to what they know--they'll see the stars flying past, but rather than looking like FTL it will look like the stars are much closer together in the direction of their motion. Only a reference to a starmap will show what's going on.

After all, we never notice either the general relativity or special relativity effects that apply here on Earth. They can be calculated but only in the case of the GPS system (and the foreign equivalents) does it matter. (The satellites are moving faster but through flatter spacetime, the error from using Newton instead of Einstein is substantially more than the accuracy of the system.)

 

[steve_bank]

It depends on the nass.

F = M*A
E Work in Joules = Force*Distance

Calculate the total energy in Joules. Then look at propulsion.

 

[lpetrich]

Here are some formulas. I'll use c = 1, as is often done in theoretical work. The rapidity u = 77.4 for 1 g over 75 years. The velocity, momentum, energy, and relativistic gamma factor are:
\( v = \tanh u \\ p/m_0 = \gamma v = \sinh u \\ E/m_0 = \gamma = \cosh u \\ \gamma = \left( 1 - v^2 \right)^{-1/2} \)

For this rapidity, v = 1 - 1.2*10^-67 and γ = 2.1*10³³ -- close to the mass of the Sun in grams.

 

[Keith&Co.]

Oh. Math.
I saw the title and thought....a planet?

 

[steve_bank]

Speed limits are made to be broken. Are there cosmic speed traps with cameras that will take a picture and send you a tickes for exceeding C?

 

[lpetrich]

It isn't a wall that one runs into. it's that it gets harder and harder and harder to get any faster as one gets closer and closer and closer to c. This has been abundantly verified in particle accelerators. The Large Hadron Collider's predecessor in its tunnels, the LEP, got electrons and positrons up to some 104.5 GeV of total energy, about 205,000 times their rest-mass energy. The particles thus traveled at
c * (1 - (1/2)*(1/205,000)² + ... ) = c * (1 - 1.20*10^-11 + ...) = c - 3.6 mm/s

 

[steve_bank]

m = m/sqrt(1-v^2/C^2)

As v --> C m and E appears to go to infinity, a singularity.

I'd have to do more reading. In any inertial frame a second is still a second and a kg is still a kg. I start accelerating at 1g. The engine and energy siurce are in my inertial frame. I see the math, I don't see physically how increasing velocity leads to need more energy to maintain 1g as v increases. There would have to be in effect a retarding force or a form of friction or resistance fundamental to space..

Mass in special relativity - Wikipedia

en.wikipedia.org

The word mass has two meanings in special relativity: invariant mass (also called rest mass) is an invariant quantity which is the same for all observers in all reference frames, while the relativistic mass is dependent on the velocity of the observer. According to the concept of mass–energy equivalence, invariant mass is equivalent to rest energy, while relativistic mass is equivalent to relativistic energy (also called total energy).

The term "relativistic mass" tends not to be used in particle and nuclear physics and is often avoided by writers on special relativity, in favor of referring to the body's relativistic energy.[1] In contrast, "invariant mass" is usually preferred over rest energy. The measurable inertia and the warping of spacetime by a body in a given frame of reference is determined by its relativistic mass, not merely its invariant mass. For example, photons have zero rest mass but contribute to the inertia (and weight in a gravitational field) of any system containing them.

 

[Loren Pechtel]

Here are some formulas. I'll use c = 1, as is often done in theoretical work. The rapidity u = 77.4 for 1 g over 75 years. The velocity, momentum, energy, and relativistic gamma factor are:
\( v = \tanh u \\ p/m_0 = \gamma v = \sinh u \\ E/m_0 = \gamma = \cosh u \\ \gamma = \left( 1 - v^2 \right)^{-1/2} \)

For this rapidity, v = 1 - 1.2*10^-67 and γ = 2.1*10³³ -- close to the mass of the Sun in grams.

You didn't give the gamma, only it's formula.

 

[skepticalbip]

The problem with trying to understand relativistic effects is that it is counter-intuitive. The fact that an effect is contrary to expectation only means that a Newtonian effect was wrongly expected.

c is not just the speed of light. c is the maximum speed of causality. For someone traveling between star systems at c, it will take zero time in their reference frame. This is because of time dilation and Laurence contraction, the traveler will see two star systems at the same place. If greater than c were possible then the traveler would get to the destination star system before they left the first star system.

 

[Jimmy Higgins]

The problem with trying to understand relativistic effects is that it is counter-intuitive. The fact that an effect is contrary to expectation only means that a Newtonian effect was wrongly expected.

c is not just the speed of light. c is the maximum speed of causality. For someone traveling between star systems at c, it will take zero time in their reference frame. This is because of time dilation and Laurence contraction, the traveler will see two star systems at the same place. If greater than c were possible then the traveler would get to the destination star system before they left the first star system.

This is why they don't go to the bathroom in Star Trek. Because they are travelling so fast, they've gone before they went. And this is important because taking a relativistic dump could take a long time.

 

[Elixir]

c is not just the speed of light. c is the maximum speed of causality.

... outside of entangled/paired quantum particles, of course.

 

[skepticalbip]

c is not just the speed of light. c is the maximum speed of causality.

... outside of entangled/paired quantum particles, of course.

You've slipped into QM and away from Relativity. There are several points of incompatibility between the two theories. According to QM, there are uncaused events so avoid any "laws" of causality.

 

[steve_bank]

The problem with trying to understand relativistic effects is that it is counter-intuitive. The fact that an effect is contrary to expectation only means that a Newtonian effect was wrongly expected.

c is not just the speed of light. c is the maximum speed of causality. For someone traveling between star systems at c, it will take zero time in their reference frame. This is because of time dilation and Laurence contraction, the traveler will see two star systems at the same place. If greater than c were possible then the traveler would get to the destination star system before they left the first star system.

I'll compare it to breaking te sound barrier. Credible people thought it was impossible. YThey sloly increased spped on succevie tests. Problems surfaced not predicted by theory and were solved.

Fibaly the speed of sound was passed in stable flight.

We can't know what happens in a spacecraft until we actualyl try it which is not likely possible.

Will something surpass relativity as relativity surpassed Newtonian?


To an obsever in one frame mass appears to chnage in another frame. Wirthin each frame a kg and second appears the same., C will always stay the same.

So, in my frame as I accelerate does it it take increasingly more energy to maintain 1g?

I don't know enough theory to put my finger on it, but something does not seem to add up.