Building a bridge to the stars

Question

Could I, purely in quantity of material only, build a solid bridge to a star?

Ignore anything like strength, relative motions of systems, that is all taken care of, using lalalaicanthearyouium - this is not remotely based in any actual science.

All I want to know is whether there is enough material for a decently powerful race to build a solid bridge spanning actual light years from things they have lying around nearby, i.e. a solar system, a couple of stars - but not a whole cluster or galaxy.

The bridge should be along the lines of the classic film trope - "it looks like metal, but it's not any material we've seen before, Bob!" - that sort of solid.

Although using iron held together with lalalaicanthearyouium would also be fine if there is enough iron lying around. "My God, Bob, it's just iron ... but how can that be?!?"

Answer 1

That is a surprisingly reasonable project!

Let's dismantle the Earth, and use it as building material to Alpha Centauri. The Earth is $5.974 \times 10^{24}~\text{kg}$, and Alpha Centauri is roughly $4.13 \times 10^{16}~\text{m}$ away, so that is almost 150,000 tons of building material per metre. That is enough for any bridge. Even if you stretch it all the way to the galactic centre, you still have about 20 tons of materials per meter.

Given a cost of about £14,000 per metre for a motorway, a bridge to the star will cost you 600 billion billion ($6×10^{20}$) £. (assuming the same cost...)

Happy building!

Answer 2

Yeah, ok, you've got your billion-billion tons of lalalaicanthearyouium, but:

How long would it take?

I don't have very good data on this, but let's assume that the 1973 expansion to the Chesapeake Bay Bridge is a reasonable model (powers of ten are more important here, you'll see that even if I'm off by a full factor of 10 it won't really change much). The bridge is 4.3 miles long and took 4 years to construct.

6920 meters in 1461 days, or about 4.75 meters per day (really 4.73, but 4.75 is a nice round number). And that's assuming that a bridge is constructed from one bank, across the river, to the other and not bottom-up: remember, we're building with lalalaicanthearyouium which is both weightless and has an infinite tensile strength (not to mention plentiful, cheap, and as easy to work with as steel, if not more so).

The nearest star, the sun, is 149,604,618,000 meters away. A little math and... 86.2 million years later you've got a bridge to the sun!

Job well done.

You're going to need some serious industry to shorten that duration. You'd need thousands of sites building bridge segments and flying them into space in a near-continuous stream and that'd still only take you down to a tens of thousands of years. The good news is that because lalalaicanthearyouium is weightless, you simply need to drive down the constructed portion of the bridge, to the end, maneuver the new section into place, bolt it down, then drive back down the other side (traffic flowing as a loop up and over the rising vertical spire of the bridge).

TL;DR, I'm pretty sure you won't be taking a night train to Rigel any time soon.

Edit:

So I thought about this a bit more, and at the x1000 speed mentioned via multiple construction sites and combining the results, we get the following numbers:

• It still takes 86,200-ish years to complete
• Construction progresses at 4750 meters per day, or just under 200 meters per hour.
• This is also 0.2 km/h or about 4% walking speed.
• This means that if we scale up another 25 fold, our construction speed equates to a comfortable walking speed.
• Under the idea that The Anathema (see comments below) proposes of building from the bottom, someone could walk along the structure once it is half-finished and reach the far end at the same time it reaches the destination (walking the first half with the second half constructed behind them). The trip would take 1,724 years.
  • Better pack a lunch.
• This still only gets us to the Sun. Reaching Alpha Centauri (nearest extra-solar star) increases the distance and build time 276,173.784 times.
• If we want to increase our build speed by the same amount, then our construction speed reaches 0.127% the speed of light...assuming that the speed of sound within lalalaicanthearyouium is at least this value.
  • Bad news, this is greater than the speed of sound in steel by two powers of 10 (0.00127c ~= 1119 Mach, Steel: 17.78 Mach) and even greater than that of diamond (34.98 Mach) and beryllium (37.58).
  • Which would require our lalalaicanthearyouium to not only be weightless, but unimaginably dense/rigid [citation needed: cannot find a relationship between a material's properties and its speed of sound].
    • Which lead me to just learn that a neutron star can't exceed 3.2 solar masses in size or its density results in a material-speed-of-sound that exceeds c. Turns out that that's pretty darn accurate.
    • Oh hey, science paper from 1988 that did some math and made a nice chart. The top half of that chart is the velocity of the longitudinal wave. 10⁹ cm/s^-1 is just about 5% the speed of light.

Answer 3

It's not completely ridiculous

For simplicity's sake, I assumed you're making a bridge that's one lightyear long, has a cross-section of one square metre and plugged that into Wolfram Alpha. We're looking at roughly 9.461 quadrillion m³ ($ 9.461 * 10^{15} $ m³) of material which corresponds to a solid sphere with a radius of 131.2 km.

If we consider that the Death Star II had a diameter of 160km, I'd say what you're setting out to accomplish is not entirely without precedent.

You could for instance grab 15 Eunomia, turn it entirely into lalalaicanthearyouium and have enought material to build yourself a whole lightyear of interstellar bridge.

Won't it collapse under its own gravity?

Let's see. Imagine a bunch infinite amount of 1 metre wide lalalaicanthearyouium spheres lined up next to each other. We start by calculating the gravitational force the second sphere exerts on the first using Newton's law of gravity:

\begin{align} F_1 & = G\frac{m_1m_2}{r^2} \\ & = G\frac{m^2}{1^2} \\ \end{align}

For the third sphere's force on the first one we get:

$$ F_1 = Gm^2 $$

What we're getting here is an infinite sum, so let's write that out and see what it gets us.

\begin{align} F_t & = \sum_{r=1}^\infty G\frac{m^2}{r^2} \\ & = Gm^2\sum_{r=1}^\infty \frac{1}{r^2} \\ & = Gm^2\frac{\pi^2 }{6} \end{align}

This is great news, The gravitational pull of an infinite series of spheres lined up next to each other on the first sphere is equal to $\frac{\pi^2 }{6} \approx 1.645$ times the gravitational pull between the first two. Of course, a bridge is not actually a series of spheres, but this should not be a problem since this approximation work better when the two objects are further apart. at a few kilometres, there will hardly be a difference.

You can improve on this calculation by making the distance between the segments (except for the first one) variable, and scaling the mass with the distance between, so they still accurately represent slices of the bridge. And then take the limit of the distance going to 0:

$$ F_t = \lim_\limits{d \to 0} Gdm^2 \sum_r^\infty \frac{1}{(\frac{1}{2}+rd)^2} $$

Calculating this limit is left as an exercise to the reader.

Answer 4

Other people looked carefully at the amount of materials required and found that it would not be unreasonable to make a "bridge to the stars."

However, there's more to this than just building the bridge. You also need some sort of vehicle to traverse the bridge.

Yes

Bridge Crawlers

In most ways the devices used to move stuff along the bridge to the stars would act like elevators (just like for a space elevator).

I assume that this would be the case for your bridge to the stars.

Eliminates Propellant Needs

The most important benefit of using elevator cars to crawl on your bridge to the stars is that it removes the need to bring along propellants - since the bridge becomes your propellant. You will still need to bring the other stuff you require to survive in space (life support, power, etc.).

Might eliminate the need to generate power

Depending upon how you make your bridge, you may be able to transmit electrical power through the lalalaicanthearyouium structure of the bridge. Lalalaicanthearyouium had better be a superconductor though or transmission losses will kill you, lol.

Conclusion

Basically, not only are the material requirements reasonable, building one would actually make the travel easier.

We just need to pretend stellar motion doesn't occur :)

Answer 5

Say your bridge has 1 square metre cross section and a density of 1 metric ton per cubic metre. Then one lightyear of bridge would be approx $10^{16}$ tons. The Earth is about $10^{22}$ tons. If Earth was to contain a percent unobtainium and if it was dismantled to get material, it should work.

Answer 6

What would prevent your superstructure from rolling up to a giant hank of lalalaicanthearyouium (handwavium) under its own mass?

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I mean it has to be flexible to link two solar systems (which are of course in motion related to each other). I mean if it has the mass of 100kg/m, then it weights 4.0680272*10¹⁸ kg which is all gravitated to its center of mass. I would assume if it is strong enough to not brake apart, it would roll up in a spiral then entangle itself.

Answer 7

Several answers have addressed the numbers--you can build it.

What nobody seems to have touched is what good is it? Bridges have an implicit assumption of gravity being normal to the bridge surface. What gravity you will encounter is parallel to the bridge, not normal to it. You have a strip of lalalaicanthearyouium to the stars that can only be climbed, not walked upon.

If you're going to do something I would think it would have to be a ladder, not a bridge.

(I'm ignoring the problem of a lack of fixed endpoints. In reality that's going to make it useless anyway.)

Answer 8

Really, this is just an upscaled space elevator.

Most others have already pointed out that it may be possible from a materials point of view, but I don't think anyone's pointed out what other issues you might have.

Let's look at an Earth-Moon bridge for a more local example:

One problem we have is that the Moon orbits at a different velocity to the Earth's surface - so anchoring it at this end could be a problem. The Moon itself is tidally locked, with the same face always pointing at Earth, but there is still a small wobble during its orbit, so anchoring might be easier there. Oh, and the Moon is receding (slowly) and the Earth's rate of spin is slowing, too (one is a consquence of the other).

Then, we have this giant ribbon of material undergoing gravitational attraction towards the Earth, gravitational attraction towards the Moon, and so it will be under massive tension. Not too mention, the Sun and other planets will have some gravitational influence.

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Let's get back to the Sun-star bridge:

As as been mentioned - all stars are in relative motion to each other - but locally, this isn't all that fast.

One problem is that to prevent the bridge from just collapsing into the Sun, its will need to be in orbit around the Sun. I'm pretty sure the maths on this is going to get very complicated for an elongated body (compared to the relative small spherical bodies we're familiar with).

This in itself will setup tension along the bridge (some of the bridge is being pulled toward the Sun, some of the bridge is accelerating away from the Sun as it orbits).

Then, eventually, as the bridge is extruded out towards the other star, we're going to have to account for additional tension of the bridge being pulled in towards that star.

And then there's the gravitational effects of all the other local stars.

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I think what all this adds up to is a mathematical nightmare of orbital mechanics...