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So, I envision a world that has forgotten it's en route to another galaxy -- it's been in transit for only a million years, hasn't even properly left its "home" behind (still stars in the sky, at least behind), but while a million years isn't very long as sublight intergalactic travel goes, it's a very long time for a civilization, even fairly long for a species.

The mode of travel is by Shkadov thruster -- take your star and at least the inner part of your solar system with you, accelerating continuously but at micro-G levels. So, a civilization (Kardashiev level 1? 2?) builds the enormous light-pressure-levitated reflector that makes the star itself into a photon thruster, and over the lifetime of a star, the star can travel (close) intergalactic distances.

Doing this with long-lived stars like G, K, and M class is very slow, but these stars, if reasonably young at the start of the journey, have the potential to live long enough to complete the journey, perhaps even with a turnover maneuver (swap the reflector to the other side of the star, to reverse thrust) to arrive in the destination galaxy at a velocity that will capture, instead of just blasting through on a one-way trip to the next galaxy cluster.

A light pressure levitated parabolic reflector, however, will not be passively stable -- instead, it will (like a ringworld or rigid Dyson sphere) require regular or continuous adjustment to stay in position, so the system doesn't veer off course or the reflector tilt enough to just fall into the star (that would be a bad year -- or century -- for all involved).

I'm no astrophysicist, nor even the ordinary earthbound variety -- I took physics in high school and college, but the non-calculus flavor. It's been forty years since I evaluated an integral, and nothing I've read about Shkadov thrusters suggests this -- but there have been laser pulse propelled technology demonstrators that were passively stable on the pressure wave from air expanded by the focused pulse.

So, is it possible to design a Shkadov thruster's reflector with a shape that would make it passively stable, allowing the "passengers" to continue obliviously on their journey (obviously without a turnover to decelerate)

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    $\begingroup$ Just a thought: If your intention is just to make your civilization oblivious of the thruster (they still would see a weird big object in space) you could also make it fully automated, actively stable. Whoever can build a Shkadov thruster should be able to put a robotic / machine intelligence aboard that can take care of itself, maybe even for an indefinite amount of time. $\endgroup$
    – ascripter
    Jul 1, 2020 at 15:45
  • $\begingroup$ They'll surely be able to see distorted stars or sun in the reflective surface of the dish, "north" circumpolar at night (in fact, that might be the whole northern hemsiphere sky -- ISTR that the reflector is bigger than Earth's orbit for a Sol-like star). They'll have forgotten why that is. $\endgroup$
    – Zeiss Ikon
    Jul 1, 2020 at 15:56

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If by "passive" you mean not needing to expend mass in the form of reaction thrusters, then yes.

A Shkadov thruster creates an equilibrium between the outward force of solar winds and the inward force of gravity. As the star goes through its cycles the levitative distance will expand and contract, but as long as the sun never flares up enough to push the reflector off into the orbit of a planet or lets it fall down enough to contact with the star itself, altitude variance won't be an issue. It will just mean that at some points in your journey you will be accelerating at faster speeds than others.

To maintain alignment, your relector just needs rudders and solar cells. Imagine holes in the reflector with rotatable reflectors in the gaps. As the main dish drifts off course, power collected from the solar cells can be used to rotate the rudders. These rudders will exert angular momentum on the reflector allowing it to correct its course. Your mega structure would then just need a basic AI to keep track of where it is going and to align the rudders accordingly.

Now the tricky part is making a system that will not break down over the period of time in question.

For this we can look to the concept of Von Neumann Probes. There is no way to make a Shkadov thruster (with or without rudders) that will all on it's own not break over the course of millions of years, but you can create an autonomous system for maintaining the Shkadov thruster using self replicating maintenance drones.

It is like this: Most organisms don't survive more than a few decades, but a species of organisms can survive for hundreds of millions of years. Unlike organisms, Von Neumann maintenance drones can checksum themselves (preferably using a majority rules, long-key hash check) with each replication ensuring that they never evolve; so, the drones made on year 1 are identical to the ones still made on year 10,000,000.

Using a combination of recycling and the resources of the uninhabitable planets, moons, and asteroids in the system, your drones will be able to continuously collect everything they need to keep the engine running without ever having to visit the inhabitable worlds or ask anyone for instructions on how to do thier job.

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    $\begingroup$ I was actually thinking in terms of mechanisms, even Kardashev 2 types, being unlikely to last literally billions of years, and designing the reflector such that, barring intervention, it'll maintain heading at least until the star enters the red giant phase. $\endgroup$
    – Zeiss Ikon
    Jul 1, 2020 at 15:59
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    $\begingroup$ @ZeissIkon You could use self replicating drones to maintain it. See updates to answer. $\endgroup$
    – Nosajimiki
    Jul 1, 2020 at 16:49
  • $\begingroup$ Okay, I was thinking about how even a von Neumann system couldn't avoid evolution -- but error correction (preferably more robust than a checksum or even MD5, but that's the general idea) can cut the error rate enough to be reasonably confident of same function after a million generations or more -- even with multiple petabytes of code involved. $\endgroup$
    – Zeiss Ikon
    Jul 1, 2020 at 17:02
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    $\begingroup$ @ZeissIkon If each drone replicates on average once every 10 years, while maintaining a population of 1 trillion drones, and each new copy is tested against a majority rules system of other drones, then with a 4kilobit hash check, your odds of a mutation going unnoticed before the cold death of the universe are about 1 in 1e1213... so no, you don't have to worry about evolution. $\endgroup$
    – Nosajimiki
    Jul 1, 2020 at 19:41
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Spin the star.

It takes more energy to change the direction of a spinning object in the axis perpendicular to its rotation. This is spin stabilization or gyroscopic stabilization, and it is why it is easier to stay upright on a moving bicycle - the spinning wheels act to gyroscopically stabilize the bike. Spin stabilization is used for spacecraft and satellites. Also rifled bullets, which are a great example of passive stability. No-one steers a bullet in flight. Maybe body English but that is it.

To spin your star, you will divert some of your thrust to exert a tangential force. Probably a number of these around the star would make sense to make sure they are not asymmetrical. Your spinning star will resist course changes. A good thing about this - your star is probably already spinning to some degree. Use that!

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    $\begingroup$ That doesn't do anything address the inherent instability of a light-pressure levitated reflector array. $\endgroup$ Jul 1, 2020 at 16:20
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    $\begingroup$ As far as I know, all stars are expected to spin from their formation, but since there's no coupling between star and reflector other than gravity and radiation, that won't stabilize the reflector. Perhaps you intended to write that I should "spin the reflector" like a hubcap on a wheel? $\endgroup$
    – Zeiss Ikon
    Jul 1, 2020 at 16:59

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