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Hypothetical: Hundreds of years into the future. Humanity needs to travel to exoplanets quickly. I'm aiming for hard sci-fi. What kind of propulsion can travel people at 0.1 - 0.9 lightspeed?

Is it possible to build a laser sail so powerful that a spacecraft 3 km by 3km with people and life systems fixed to it can reach above speeds? According to the video in the link below, a one sq. km array of lasers can beam a 16 sq. metre nanocraft up to 0.2 c and would cost 10 billion dollars - which could be affordable today for billionaires like Jeff Bezos (his net worth is 137 billion dollars), the founder of Blue Origins. Admittedly, that's for a tiny craft.

https://www.youtube.com/watch?v=c4z6RZXv5p8 7:18

Context of my novel: There will be rich trillionaires, quadrillionaires or even octillionaires in the future who are willing to pool resources to develop efficient interstellar travel.

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    $\begingroup$ You don’t build better spaceships to hunt exoplanets, you build better telescopes. You will find far more exoplanets far more cheaply. $\endgroup$ – Mike Scott Jan 12 at 6:57
  • $\begingroup$ Welcome to worldbuilding. Please take the tour and visit the help center to make yourself familiar with our standards. Your post, as it stands now, doesn't meet them. You are asking too many questions in one post, which makes it too broad, and they are also quite opinion based. Moreover, since we struggle to reach Earth escape velocity with our present means, what kind of hard science do you expect on fusion rockets and 0.9 c? $\endgroup$ – L.Dutch Jan 12 at 7:19
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    $\begingroup$ @L.Dutch Thanks for pointing out the standards. My apologies with the opinion that 10 billion dollars is pocket change for Jeff Bezos, whose net wealth is 137 billion dollars - it wasn't supposed to be taken literally. I'm unsure what you mean when you say we struggle to reach Earth escape velocity with our present means, given that we've reached that velocity technologically since the Apollo 11 mission to the moon. We also landed probes like the Viking 1 and 2 on Mars in 1976. $\endgroup$ – William Davis Jan 12 at 8:01
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    $\begingroup$ The question makes little sense and shows some lack of basic knowledge by using some concepts slightly wrong. Just my opinion, I'm not a lawyer, so I won't write a book about the law. If you really want to continue with thequestion:. You should absolutely go to the sandbox in the meta. Currently the question seems to me: "a friend said something and I googled for 2 hours, does any of this make any sense for a massive project way over my head?" I'm sure you don't want people to think that, so try the sandbox. $\endgroup$ – Raditz_35 Jan 12 at 8:58
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    $\begingroup$ @William Davis Here you will find quite a few interstellar craft designs that could be built: projectrho.com/public_html/rocket/slowerlight.php $\endgroup$ – Mranderson Jan 12 at 10:52
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Important Edit

el duderino thankfully notified me of a mistake I had in my formulas: $p = \frac{E}{c}$ not what I used before: $p = \frac {E}{c^2}$

This Changes nearly every aspect of my second part (Basic Premise for a self propelling spacecraft) of and is important for every one who has decided to use some aspect for his own world.


Important Edit 2

el duderino has again been able to improve this answer this time with an equation that allows acurate calculations of speed depending on our physically best energy storage method. This includes special relativity and is therefor more accurate than the other equations I used especially when reaching high relativistic speeds.

$v = c \cdot$$\frac {(\frac {mi}{mf})^2 -1}{(\frac {mi}{mf})^2 +1}$ while $mi$ = initial mass, and $mf$ = final mass

And also fixed another calculation error.


Feasibility of solar sails

Solar sails of the proposed size and scale would work in the future. The size of the solar sail only matters efficiency wise.

Photons do not occupy any space so you could condense all the light your lasers emit to a square of $1m$ if you want. Problem here is only that the mirrors we know do not reflect 100% of the light that hits them so you would loose efficiency here when using mirrors from our time. But when considering how inefficient light propulsion is it doesn't really matter.

The real problem your solar sails have is that they are a one way ticket to another place in the universe. Because in order to get back you would again need a huge laser array to propel you the other way again. And under certain circumstances slowing down might also be a problem. (When your not heading to another star)

Another problem is that with increasing distance less and less light hits your solar sail and with that disables your sail from further increasing it's speed.

Which is why a spacecraft capable of fully maneuvering it self would be the best bet.

Basic Premise for a self propelling Spacecraft

When you want a space craft that any one of your insanely rich characters would use for him self you would want a spacecraft that can also come back some day. I will here present how propulsion works with photons but the same is true for any of the other elemental particles. As posted here photons have impulse even though they have no mass. Instead of calculating momentum like this:

  • $p = m \cdot v$ (p = momentum, m = mass of object, v = speed of object)

you do this for a photon/every other elemental particle:

  • $p = \frac {E} {c} = \frac{h \cdot f} {c}$ (E = Energy, h = planc constant, f = frequency, c = speed of light)

Example

Problem is the amount of momentum you get from this is VERY small.

Normally

Chocolate has 2200$kj$ chemical energy for our body per 100$g$ if the chemical enrgy would be used to propel it self forward you would get this: $E = 0.5 \cdot m \cdot v^2$ if we change this Formula around to get speed it looks like this: $v^2 = \frac {E}{0.5 \cdot m}$ now with numbers: $v^2 = \frac {2200000j}{0.5 \cdot 0.1kg} = 44000000$ now we take the square root and we arrive at 6633.25 $\frac {m}{s^2}$ or 23 879.7 km/h

Acceleration with light

When we do the same thing but use the energy to power a flashlight with 100% efficiency and the same weight of 100$g$ we arrive at: $p = \frac {2200000j}{299792485 m/s} = 0.0073$ and because $p = m \cdot v$ we can say $v = \frac {p}{m}$ and with numbers $v = \frac {0.0073}{0.1kg} = 0.073 m/s$ this is less than a million instead of 2.7 billions times worse than the "normal propulsion" technique which is far from what we achieve on earth but no where near as far as what we achieve with light propulsion. (in a best case scenario in practice it would look even worse but not nearly as bad as in my old answer)

As you can probably guess the biggest problem of your self propelling space craft will be how to store all of the fuel/energy needed for propulsion without increasing the weight of the space craft more than the added fuel can push.

Energy storage

Disclaimer

This cannot be considered hard science any more because things suggested below are highly unlikely to actually be implementable in real life.

"Solution"

I already ran the numbers for the most plausible fuel/energy storage options. And they are all far from achieving anything. So this is the last possibility I came up with:

Pure Mass Energy (this is to my knowledge the most weight efficient storage system allowed by physics):

The problem with the solution

To free the energy stored in pure mass you need anti matter and anti matter likes to react with everything labeled "matter" which in most cases means everything. And thereby makes it unable to be stored with current technology and likely even with future technology. And when you cant store your fuel you cant take it with you which includes taking it on a space ship for an interstellar journey.

Actual Solution

Mass in physics is as far as I know pure energy and is calculated by this formula: $E = m \cdot c^2$ which for one Din A6 card means $E = 0.001kg \cdot 299792458^2m/s = 8.99 \cdot 10^{13}j$. Which puts the speed at 299.87 m/s for a metric ton of space craft which is still pretty slow but with a space craft that weighs 2 tons and possesses fuel with more than 8 tons you would reach 0.923c according to the formula I mentioned in the edit 2. Without this formula you would always reach light speed:

$E=mc^2$. So, $p = E/c \implies p = mc^2/c = mc$. Finally, $v = p/m \implies v = mc /m = c$

Conclusion

So with the best energy storage system it is actually feasible and usable as a back wards ticket.

Which in turn gets us back to the solar sails which now don't look to bad because they can be used for the way away from earth while the fuel on board can be used for the way back home.

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  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$ – L.Dutch Jan 14 at 19:57

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