# Deflecting an incoming star, railgun style

A friend of mine, ɹɐqooɟ, lives in a large globular cluster where stellar encounters and collisions are very common. His civilization is a Type 1.8 civilization, having built half of a Dyson Sphere around their star.

Astronomers on his planet (a super-Earth of $$7M_\oplus$$ orbiting a F5V star) have discovered a red dwarf star that will pass less than $$0.8\text{AU}$$ from their planet in $$6733 \pm 50$$ years. This will cause their planet to be ejected out of their solar system, drastically altering the lives of the inhabitants of the planet.

As ɹɐqooɟ's civilization has not yet developed stellar engines, they have decided on launching some massive object (not a black hole, they haven't found a way to create micro-black holes that can be stabilized yet) at $$70\%$$ the speed of light into the red dwarf star, which is $$1.050510$$ light years away. The impact needs to either destroy the star or redirect it enough so that it will completely miss their star system, causing minimal damage.

• If they are launching something massive enough to deviate a star, won't the cure be worse than the disease? It's like firing a naval cannon while holding it in your hands, in term of recoil...
– L.Dutch
Mar 4 at 15:25
• They should know the time of the near pass much closer than that. Accurate to the day, quite frankly, if they are already confident about the distance. The red dwarf will flyby their star at about 90km/s. it will pass through the 1AU distance in 40 days or less. Its gravity is between 0.04 and 0.5 as much as the parent sun. at 0.8 AU it would not deviate the semimajor axis of the planet by more than 5%, WAY less than needed for ejection. They must prepare the tools needed to adjust their planet's orbit by a few hundred m/s, and some gnarly telescopes to observe this unique event. Mar 4 at 15:26
• "some massive object" - this mass has to come from the planetary system, right? What would be an upper bound - Jupiter mass, 10xJupiter, etc? Mar 4 at 18:01
• Do u need your cats waiting for apple to fail from equator, do they need to shoot or other ways to change situation are okay as well Mar 4 at 23:05
• Is handwavium availabe? They could just use their advanced understanding of quantum spacetime and create a large enough wormhole to teleport the incoming star around their solar system... Mar 7 at 14:37

You've got this the wrong way around.

You're trying to deflect an entire star, which engineers refer to as very very heavy.

You're doing this to save a planet, which those engineers might refer to as merely very heavy.

Any technology capable of measurably changing the trajectory of an entire star would be better put towards adjusting your home planet's own orbit, current or future, to ensure that it remains in the neighbourhood that the current occupants like.

If you don't have the technology to change your planet's orbit, you don't have a whelk's chance in a supernova of deflecting a star.

Lets have a slightly less sarcastic look at an existing proposal for moving stars around, though.

A Shkadov Thruster needs similar construction techniques to a Dyson swarm, but basically involves making one giant statite and using it as a solar sail, bound to the star by its own gravity. Upside: your friend might be able to build it, assuming that

• they can get to the problem star in good time
• there's enough mass available at the destination star
• they can get building pretty swiftly

Unfortunately, the thrust of one of these things is rather low, defined by

$$F_A = \frac{L_s}{2c} (1 - \cos{\Psi})$$

where $$L_s$$ is the luminosity of the star and $$\Psi$$ is the mirror rim angle. If we model our star on Barnard's star we have a luminosity of ~1.22x1024W, and if we make the statite a nice hemisphere we have a rim angle of 90° and a thrust of ~2.05x1015N, giving a maximum lateral velocity change of about 1.4mm per second after six thousand years of operation.

You should probably start work at least a million years ago, preferably last galactic year.

I am now wondering if you could speed things up using your own Nicoll-Dyson laser to warm up the target star a little...

If you reconfigured your own dyson elements to make a Shkadov thruster around the much hotter F5V star you'd get 3 orders of magnitude more thrust for only 1 order of magnitude increase in mass... that's a whole 28cm per second velocity after 6000 years! It isn't enough to get you out of the way in time, as you're still only going to have moved less than a quarter of an AU by the time the other star arrives, and it means you can't use your dyson elements to harvest power for other mitigation techniques.

As a slightly less implausible solution, PcMan suggested a good way to move a planet is with the use of a gravity tug, which basically involves bringing a large object close to the homeworld in question and using rockets to stop it crashing into the planet (and a clever orbit to stop the rocket plumes impinging on the planet's surface or atmosphere). Their mutual gravitational attraction will cause the planet to change orbit over time.

(PcMan doesn't seem to be writing an answer of their own on this, so I'll tack my take on it down here, but I'll pop it off again if they change their mind)

An acceleration of 1m/s/yr will add up to a good 6km/s over time, which should help push it into a position where its year length and location when the star flies by is, if not necessary safe, might be safer. Moreover, it might give a way to correct a surprise escape trajectory into something more comet like, given the occupants time to sort out a more permanent solution.

To get this acceleration on a planet of mass $$M$$ ~4.18x1025kg, we will need a force $$F$$ of ~1.32x1018N. If the tug is placed at radius $$R$$ 15000km from the planet's barycenter, it needs to mass $$\frac{FR^2}{GM}$$ ~1.07x1017kg. That's in the same ballpark as real-life moon of Saturn, Hyperion. This is a potatoid rock about 360x260x160km in size. Hyperion is a bit bigger than we need by a factor of about 4, so you can slice it up and use the leftovers for reaction mass.

Gravity will pull your tug towards the planet with the same force as it is tugging the planet. You will therefore need an engine capable of exerting similar force to keep your tug in space. Having ownership of a partial dyson sphere will give you all the energy you need (50% of the output of an F5V is going to be of the order of 1.4x1027W, which is quite a lot. Even if only 1% of that was captured, you're still doing well) and you should have no problem powering a suitable mass driver firing ground-up moon to keep your asteroid in place.

The biggest problem you'll have in the future is the fate of your dyson components. They're very valuable, and very hard to replace, as they'll represent a non-trivial proportion of the easily available mass in your planetary system, and the rest of the mass is going to be flung into deep space when your visitor arrives. Moving them into safer locations inevitably entails reducing the power supply available to your tug. You might need to build an absolutely vast fusion plant on it, and grind up a few ice moons to feed it for the final stages of the visitation...

• Just build a gravitational tug, capable of changing your planet's orbit by even as little as 1m/s per year. Adjust its orbit so its average distance from the interloper is exactly the same as their own star's distance to the interloper. In effect, this ensure that the planet's orbit stays exactly as big (same semimajor axis), although its eccentricity may be warped a bit. Use the same little gravitational tug to smooth out any orbital distortion after the event. It should pass with absolutely zero problems for your planet. Mar 4 at 16:50
• @PcMan "just" seems to be doing a lot of heavy lifting, there, though it would appear that the OP's aliens are already capable of shuffling around substantial masses, given the existence of their dyson thing. How big would such a tug need to be? Mar 4 at 16:56
• If you take the asteroid Eros, and "hover" it over the Earth at 8000 km altitude (14300km from center of Earth), that will exactly do the job. Surely if you can build a Dyson sphere, you can accelerate a 7.5km rock at 0.2 g?(indefinitely). Besides, that's the brute force method. You would most likely use a great many multiple encounters with a suitable rock slingshotting close to the planet, then playing pinball with the other planets in the system until it passed close again, and again, and again. That way you get most of your energy input from orbital dynamics and gravity. Mar 4 at 18:36
• @PcMan there are probably some minor issues of reaction mass, but there's lots of rock lying around in space. Probably. Unless it all went to build the units of the Dyson cloud, which is also at some risk, and probably quite a lot more valuable than the planet... Mar 4 at 18:45
• I know 6 trillion tons sounds like a lot , but remember you are in a situation where you need to duck an incoming bullet that weighs quadrillions of times as heavy as that. I'd much rather have to move around a teensy 7e15kg rocklet, than have to directly move a 6e24kg planets, or (yikes!) a 1e30kg star Mar 4 at 18:46

TL;DR don't move the red dwarf - move your planet.

During those six thousand years, adjust the planet's orbit so that, during the encounter - which will last no more than about two months - the planet is on the opposite side of its primary, farthest from the incoming star. Then, prepare and deploy appropriate measures - for example, massive asteroids and moons in slingshot trajectories - so that the newcomer's attraction's effects are neutralized overall.

(That, of course, assuming the stars aren't gonna smash together).

You don't have very many workable options here. Nothing available to a K1.8 civilization will be able to destroy a star, and "redirecting" it requires either kinetic energy or momentum in quantities, again, not directly available.

Accelerating a massive object 70% of the speed of light is not enough to influence a star unless the object is many times a planet's mass -- but, then, you'd have no trouble in relocating your own planet at a much more leisurely pace.

It might be possible to alter preemptively your planet's orbit so that the passing of the star will either not influence it at all, or influence it so as to put it back in its original orbit. This, plus the ability of partially directing the motion of a puny planet for the period of the closest encounter, might be enough.

You could also deploy the "massive object" in such a way as to alter your own star's motion - something of the kind appears in Asimov's Nemesis. But the target star is too close for that - there's no time.

This could be supplemented by the alternative plan of building a lensing statite (or Bowl of Heaven after Benford's idea) around the incoming star. And maybe also your star.

The statite will reflect part of the solar radiation at a single target into the star, causing a controlled flare. This flare will be magnetically focused to impart thrust to the parent star, curving its orbit. Magnetics do not effect work, so you can theoretically focus several hundred thousands tons of matter per second at stellar wind velocities with little trouble once the necessary megacoils have been built. That effectively turns the star into a stellar engine.

The thrust, however, is not enough to work in the available timeframe.

Concentrating the sunlight from your star into a beam would supply a comparatively tiny thrust to your star; at that distance, focusing on the target star is unfeasible, so "pushing it away" is again not an option.

I'm going to do some rounding and assumptions. Also usually for orbital mechanics there is a whole lot of mathing for approaches, but for stars approaching each other on an orbit around a galaxy center the approach is practically a straight line.

Red dwarves have masses of up to 0.6 M☉. Let's assume this one is 0.5 M☉. That's 9.945 × 1029 kg.

1.050510 ly is 66,435.38389 AU. Let's round it up to 66,435.8.

66,435.8 - 0.8 means the star will cover 66,435 AU in 6,733 years. That's ~46,800 m/s, slow enough that we can play with this scenario without involving relativity much. That is, the relativistic mass of the star is practically its rest mass.

At that speed, the momentum of the star relative to you is 4.65426 × 1034 kgm/s.

I could stop here, and let you figure out what kinda mass you need to use to zero that out. But I'll give you an example. ɹɐqooɟ's own planet being launched at 0.7c would have a momentum of 1.22822642 × 1034 mkg/s (considering relativity), which is about a quarter the amount of momentum you need to stop the star. So maybe throw a gas giant instead.

Also don't hit the star with a single solid object much smaller than the star itself. At that speed it might penetrate the star and go out the other side. The star would be deformed for a while but would have got back to shape before it hit you. Instead, pulverize your missile so that the shrapnel covers a lot of area. This way you might be able to stop the star.

• @PcMan thanks for calling attention to that, I'll fix :) Mar 4 at 16:15
• So ɹɐqooɟ's civilization has to build a Earth-sized cannon and fire a Neptune-mass frag bomb at the star. Is there any alternative to building a space cannon and launching billions of tiny, untrackable objects? Because the number of inaccurate chunks will be over 50%, as the large amount of shrapnel fired very far away will miss more than it hits, unless you build a cannon with smaller diameter (i.e. a railgun). Now, how are you supposed to pack a Neptune inside a 10 meter gun? I suppose you could do it in multiple shots, but that would take a while, as well as more propellant. Mar 4 at 16:28
• @fasterthanlight cannons are for little people. Anyone with a dyson cloud should be using Nicoll-Dyson beams to push stuff around. There's certainly enough potential power in the partial cloud to accelerate a big mass to silly speeds over the required ~kyr, but I don't know how effectively it would disrupt the target star... Mar 4 at 18:16
• @StarfishPrime in terms of impulse delivery for the energy money, mass is a better carrier than photons Mar 4 at 23:09
• Whatever gun you fire it from needs at least the same mass, and even then it will be thrust in the opposite direction just as hard, halving the actual velocity. Mar 4 at 23:35

The question implies that the civilization has just discovered the red dwarf star and is frantically asking for suggestions from far more primitive civilizations.

It also states that the approaching red dwarf star is 1.050510 light years away.

So I have to ask why did it take them so long to discover the position and velocity of the red dwarf star?

This table:

https://en.wikipedia.org/wiki/List_of_nearest_stars_and_brown_dwarfs#Distant_future_and_past_encounters[1]

And this graph:

https://en.wikipedia.org/wiki/List_of_nearest_stars_and_brown_dwarfs#/media/File:Near-stars-past-future-en.svg[2]

Depict past and future close encounters of various stars with our solar system. Note that many of those calculated encounters are many times 6,733 years in the past or future. So why hasn't the much more advanced alien civiliation discovered the approaching star tens of thousands of years ago?

It seems to me that a civilzation that advanced will have no trouble with their planet being ejected from their solar system into outer space.

Many members of their species should live in enclosed space colonies on various hostile worlds or in artifical space habitats. It is quite possible that their communities on their home planet also have their own self contained ecosystems, to avoid interacting with and damaging what is left of their planet's natural ecosystems. If they already live in enclosed space colony like structures on their homeworld, it won't affect them much if their homeworld takes a different orbit.

And to preserve the natural habitat and organisms of their homeworld they can build a giant satellite with fusion powered lights to shine at the surface of their planet to similate the natural light and heat of their star.

And if their space travel technology is advanced enough to consider diverting an incoming star, they should be able to move their entire population off their homeworld to other places in their solar system or in nearby solar systems long before the red dwarf star passes in 6,7333 years. And if their planet is hurled out of the solar system it should remain close enough for easy space travel (using their incredibly advanced technology) to other planets and space habitats in their system for many thousands of years. So people who want to move between the ejected planet and any colonies remaining in the star system will have a lot of time to do so.

And what about their one half Dyson sphere? If it will not be disrupted by the passing star, it will be a good place for any dispaced persons to move to, since i assume that moving much of the population there was the original plan.

If ɹɐqooɟ lives in a dense cluster, this is a problem that will need to be solved periodically. That means there must be a better solution.

Fortunately, if ɹɐqooɟ's civilization has built half a Dyson Sphere, they have built a stellar engine. They just need to deform the hemisphere enough to form an oblate ellipsoid (so most of the reflected energy misses their own star) and jack up the albedo of the interior surface as far as possible (ideally, they'd make it specular rather than diffuse, but making it bright first is more important). Let the hemi-ellipsoid act as a solar sail to support its own weight, and it'll tow the star and at least the inner planets of their system along with it -- allowing them to alter the orbit of their sun to run outside the dense part of their cluster where close stellar encounters are once in a billion years or so, instead of several times in a million.

And yes, this will also work with a Dyson Swarm -- just deploy a solar sail from each particle of the swarm and use those sails to keep all of the particles on one side of the star. It's slower than a solid reflector, but doesn't require dismantling the entire system to get the mass to build with.

• A plain old Shkadov thruster seems like it probably isn't powerful enough to act over ~10kyr timescales, even with an F5 star. I've found some suggestion that a combination of a partial dyson shell and starlifting could create a single polar jet that would get things moving a bit more briskly, but I don't know that even that is enough to get things done in time... Mar 4 at 21:21
• @StarfishPrime starlifting may be 2.5 orders of magnitude more efficient, at least in dwarf case with 5000km/s jets Mar 4 at 23:29
• @StarfishPrime You have ~6000 years to deflect a star's existing path by an AU or so -- enough that it doesn't knock your planet out of orbit, doesn't need to be an intergalactic trajectory. Acceleration of nanogees is plenty. A Shkadov should do the job, and it doesn't even have to be a perfect one (parabolic with 90%+ reflectivity and perfectly specular). Mar 5 at 12:10
• @ZeissIkon i ran some numbers and came out with a displacementof the order of a quarter of an AU. I appreciate I might be out on that one, but probably not by an entire order of magnitude. I'm also not certain that a single AU movement by the parent star will be enough to avoid ejection, but I'm also not prepared to run a gravity simulation to find out ;-) Mar 5 at 12:42
• (though I do not that even if the starlifting thruster is just a single order of magnitude more powerful than a Shkadov thruster, not even as much as the 2-3 that @MolbOrg suggested, it could be enough to help) Mar 5 at 12:48

I'm putting this in another answer, because it's very much different from my other one.

FRAME CHALLENGE:

In a dense cluster, planets that can develop life must be exceedingly rare -- perhaps nonexistent -- because, as I noted in my other answer, close encounters between stars must be relatively common. Current theory has most stars originating in gas clouds that amount to clusters similar to the Pleiades, and later being ejected from the resulting multi-star system. Globular clusters are far denser than these, and the only thing that could keep them from ejecting all their stars over time is if they formed in an organized state -- which would make them more like the disk of a galaxy than the globular shape we observe (meaning any globular cluster is continuously in process of ejecting its population).

The close encounters that eject stars from clusters need not be close enough to eject planets from their stellar orbits -- but some fraction of them will be, and the denser the cluster, the larger that fraction. The end result is that the habitable lifetime of a planet in a dense cluster will be much shorter than the lifetime of a star, and many of the planets in the cluster will be rogue -- wandering the cluster, waiting to be ejected even from the cluster's gravitational binding by another encounter (which will happen millions of years after the surface is frozen over).

Therefore, a Kardshev 1.8 civilization cannot be native to the cluster, never mind the planet they're on; they had to have colonized in cosmologically and geologically recent time (say, within the past million years), from much further away, and done so without the kind of careful forward checking that ought to be applied to such an endeavor.

That doesn't change the answers on what they need to do, but it might very much change the background of the fictional situation.

Propel the star using fusion rockets made of starstuff.

Your railgun projectiles are made of uranium and plutonium. They are designed to undergo fission when compressed in the outer layers of the target star. These fission reactions will produce heat exceeding that produced by the star as well as a shockwave through the starstuff, compressing the material and accelerating ongoing fusion within it. This accelerated fusion will release orders of magnitude more energy than the fission bomb itself. Many of these bombs arrive and detonate simultaneously and synergistically.

This reaction does not occur in the center of the star but off to one side. The result - an blast of energetic hot plasma from one relatively small area of star. It is a fusion rocket. The rocket you produce will push the rest of the star in the opposite direction.

• Doesn't this require Jupiter-masses of uranium to be found, somewhere? Mar 5 at 9:23
• @StarfishPrime If the K1.8 civilization doesn't have transmutation, how would they have built half a Dyson sphere? Mar 5 at 12:05
• @StarfishPrime - the idea is not to punch the star with a Jupiter cueball but to leverage the penchant of fissile and... fusile? matter to turn into energy. Then you can make the energy to move the star there, largely using the star itself. If it is purely kinetic energy you have to put all that energy into the cueball on your side and you will have big energy bills. Re Jupiter size I thought there was some upper limit on how big a fission mass can be because it blows itself apart but that is out of scope. A bunch of small ones is fine. Mar 5 at 13:09
• @ZeissIkon depends on how dense the shell is. You could make something pretty diaphanous with large but low density sails/solar collectors/optical phased arrays, for example; making an actual thick crunchy shell isn't necessary. Mar 5 at 14:23
• @Willk even delivered in little itty bits, it is still jupiter-masses of fissile uranium and that sort of stuff is awkward to come by, right? Plutonium even more so. Mar 5 at 14:28

Why bother trying to save a sinking ship, when you (should) already have lifeboats?

ɹɐqooɟ's civilization is a post-type-I Kardashev, which guarantees they have the ability to colonize other worlds, and indeed should already have done so as part of a rational strategy for minimizing the risk to their species as a whole from a catastrophic interstellar event like the one you're describing (averting "eggs in one basket"). Instead of trying to save their homeworld, they should instead focus entirely on vastly expanding their colonization project, with a view to relocating the entirety of their homeworld's population (including indigenous flora and fauna) to other, safer worlds. 6.7 millennia gives an excellent head-start on this, as well as terraforming efforts for their new worlds.

This may or may not be feasible, depending on how dependant they've become on the energy harvested from their Dyson sphere/swarm, but that will almost certainly be destroyed and/or displaced anyway by the rogue star, so they'll need to make a plan to deal with that loss either way.

I'm assuming of course that ɹɐqooɟ and his people have access to effectively faster-than-light transit. If not, colony/generation ships are probably going to be a safer bet (think Mass Effect's Quarians).

The star will arrive in 6700 years. In that time it needs to be moved perpendicularly by an unknown amount, comparable in size to 0.8 AU. So we need to change its velocity by about 1.1E-4 AU/year. When we take a moment to use factor label notation and check our units like we always should, that works out to:

(0.8 AU / 6700 y)(1 y / 3.15E+7 s)(150E+9 m / 1 AU) = 0.59 m/s

Our impactor has a speed of 70% c = (0.7 * 3.0E+8 m/s) = 2.1E+8 m/s.

Now momentum = relativistic mass * velocity, so we can say we need a mass 3.6E-8 smaller than that of the star. Assuming a red dwarf at, say, 100 Jupiter masses, that means (3.6E-8 kg impactor / kg star)(100 * 1.9E27 kg star) = 6.8E+21 kg. Oh but wait, we need to consider 1/gamma = (1-(0.7)2)0.5 = 71% ... the actual rest mass of the object is 4.9E+21 kg. You need something smaller than Iapetus, larger than Haumea.

• U calculated change of velocity wrong, with 5000m/s change, when it arrives at target system it will miss the target by 6733 a.u. they need 0.7m/s change due collision multiple by safety margin a.u.'s they need Mar 4 at 23:35
• It's absolutely possible I missed something that large in this slapdash calculation, but I didn't see it. Mar 5 at 2:24
• it in 0.00011 a.u./year = 1a.u./year seconds, so u unrolled fraction of au to a whole au thus having miscalculation of the result. Mar 5 at 3:36
• Oh no ... you're right, I never actually multiplied by that first factor I wrote. It's a lesson that no matter how fast you're typing for what forum, the fastest way is always to put it in factor label format. Mar 5 at 6:25
• yeah, units are important, greatest mistakes are because of them - NASA approves, lol. idk I could edit it but u may add it as well - the comparison with moon, as an object most people are familiar with, as u did that with fractions of gs giants before. So as another improvement may be a statement that it is mass needed to deflect the trajectory by that 0.8 and if we need a greater safety margin like 3x of that then we need to multiply the mass. idk, if u find it fun, would be interesting to estimate do they have enough energy for all that, even if a placement isn't exactly good - optional Mar 5 at 8:00

To deflect a star they would have to launch an object, comparable with the star in mass. 70% of the speed of light cannot change the required order of magnitude of mass.

So, it would be much, much easier to change the orbit of their planet the way they would want with such energy.

The civilization can poison the star with matter that squelches fusion.

They wouldn’t fire a single projectile, they’d fire a steady stream of refined metals — iron, titanium, just about anything from the lower half of the periodic table that is plentiful in their solar system will do.

The first projectile will impact the red dwarf thousands of years before it nears their solar system and with a steady firing rate, and in a few hundred years of such abuse the star will become unbalanced in terms of fusion and gravity and go nova — a safe distance from the civilization in question.

• Note that our own sun is made from the same material that Earth is made of, which means lots of heavy metals. It is ~.16% iron already. This suggests that ~500 Earth-masses of Iron is not enough to stop fusion in a G-class star. I'm not really sure that it is possible to get enough heavy metals to poison a star, even if you were able to fire them into the core of something so hot and dense... Mar 4 at 21:28
• What will be the remnant? If the remnant (like a white dwarf) retains most/some/a lot of the mass of the star, then this method is useless. Mar 4 at 22:09
• Dwarfs are less fusion driven, we can look at brown dwarfs see how long it takes to cool down and get to come critical sttage, if any, it will take a looong time Mar 4 at 23:41
• This seems a bit like trying to get a raccoon out of your house with a flame thrower ... fortunately, one that doesn't work. Iron is the most stable nucleus there is - aside from being cold, I don't picture it doing much to interfere with nuclear reactions. In a red dwarf it would be well distributed by convection, and unlike in a supergiant there is still plenty of hydrogen fuel left at the core to continue the fusion reaction. Mar 5 at 2:32
• This paper gives some models: academic.oup.com/mnras/article/335/4/1147/963097 It concludes that each unit increase of [Fe/H] increases the absolute magnitude by -0.8. In more intuitive units, each tenfold increase of metal content doubles the power output of the star, approximately halving its life time. The sun has 1% metal content by mass. Increasing that to 10% would half its remaining life from 5 to 2 billion years. Not useful. Mar 5 at 11:21

In terms of distance, 1 light year is about 65,000 AUs. The mass of the star is about 60% of our current star.

If you wanted to move its path slightly, you would probably want to smash something very large into it, since the momentum of the system (far away from the superplanet) will be the same regardless.

At 70% of the speed of light, there's about a 40% boost to momentum when compared to the classical calculations $$\gamma=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$$.

The star is moving at about 46 km/s. According to this article, a star moving at 106 km per hour could pass at jupiter's radius without much trouble, or about 5 AUs.

You need to change its momentum by 1/13,000 of its current momentum (5/65,000), which corresponds to about 0.6 solar masses * 46 km/s, or 160 km/hour.

The momentum of an object colliding with the star, let's say perpendicular to its path, would have a momentum of about 3 * 10,000 km/s * M, where M is the mass of that object (in AU).

You need that momentum to equal about 1/13,000 times the momentum of the star, or

1/13,000 * 0.6 * 46 = 0.002123 AU * km/s


Now, since we currently have 30,000 km/s, we can solve:

30,000 km/s * M_0 = 0.002123 AU * km/s

M_0 = 7.08e-8 AU = 1.4e23 kg


That's about an object twice the mass of the moon.

The least amount of energy required to accelerate an object to 70% of the speed of light is 5 * 10^39 joules.

The sun generates 3.846 * 10^26 W. Per year, this is 1.212 * 10^34 joules, and over 6500 years, this would be 7.88 * 10^37 joules.

I'll assume the dyson swarm can capture roughly the same output of energy as our sun, with the F5V star being brighter and likely a bit bigger.

You are short the required energy to do this about 60 times, assuming perfect energy conversion.

## Possible, more realistic assisting factor

Depending on what neighboring celestial bodies there are, it may be possible to deflect its path more. All you need to do is push is slightly closer to something that has a lot of mass. If, for example, the trajectory it was on relied on it being deflected by a black hole, then moving it slightly closer to that black hole could dramatically change its path, requiring far less energy than would otherwise be needed.