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    Default Destroying a star

    So I've been reading Cixin Liu's Rememberance of Earth trilogy (The Three Body Problem, The Dark Forest, Death's End) and was wondering about some of the science in it.

    At several instances in the trilogy extremely high veloctity objects are used to destroy stars (and the planetary systems around them). Essentially extremely fast relativistic kinetic kill vehicles, but targetted at the solar system's stars rather than a planet directly. It mentions when one of these objects impacted the star it "tore a hole through the photosphere and the convection zone" that was ~50k km in diameter. In the end it resulted in lower pressure in the core (stuff was being expelled from this "hole") and eventually lead to collapse and stellar explosion.

    I'm wondering if this is actually what would happen? Is it just somewhat technobabble or could it really occur?

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    Default Re: Destroying a star

    My first thought is: very obviously not. Even if you somehow tear a 50,000 km wide hole through the star, the body of said star is entirely gaseous and will rush in to fill the gap extremely quickly. That in itself might cause some sort of shockwave that would cause damage outside the star, but it's not going to stop the star generating energy.
    Last edited by factotum; 2019-11-29 at 11:47 AM.

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    Default Re: Destroying a star

    The first problem would be that in order to tear such a wide hole, the projectile would have to match its size - especially at high velocities. Then there is the problem of penetration depth, which if Newton's calculations are still applicable, is equal to (projectile lenght)*(projectile density)/(target density). Considering that no material can match the density produced by gravity, I think the relativistic bullet would not go very deep.

    That being said, you can still consider a scenario, where you destroy a star by blowing it apart. It might even be possible to do that with a relativistic projectile. The thing is, it would have to deposit enough energy to counter the gravitational binding of all the matter in the star. If you can have that much spare energy, there are way more effective ways of wiping a whole solar system. And if you are waging war on such a scale anyway, you might look into arranging gamma bursts to sterilize big chunks of galaxy in one go.
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    Default Re: Destroying a star

    Quote Originally Posted by factotum View Post
    My first thought is: very obviously not. Even if you somehow tear a 50,000 km wide hole through the star, the body of said star is entirely gaseous and will rush in to fill the gap extremely quickly. That in itself might cause some sort of shockwave that would cause damage outside the star, but it's not going to stop the star generating energy.
    Yeah this is kind of what I was wondering. The description was that material from the core (presumably exposed by the giant "tear") would "erupt" from the hole, which is what lead to the imbanlance in the core leading to the collapse and explosion. The whole filling the hole bit was where I was getting confused by why this would happen.

    Quote Originally Posted by Radar
    The first problem would be that in order to tear such a wide hole, the projectile would have to match its size - especially at high velocities. Then there is the problem of penetration depth, which if Newton's calculations are still applicable, is equal to (projectile lenght)*(projectile density)/(target density). Considering that no material can match the density produced by gravity, I think the relativistic bullet would not go very deep.
    The sun's density is extremely low compared to any bullet you'd shoot at it that could get up to relativistic speeds (until you get near the core anyways). Average density is apparently around 1.4 g/cm^3.
    Last edited by Chen; 2019-11-29 at 09:17 PM.

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    Default Re: Destroying a star

    I'm not a stellar physicist. But my hunches from what I've read:

    The matter at the core of a star is the densest region in both energy and the normal sense. Since you're blowing a lot of that out, the infalling outer regions won't trigger quite the supernova level explosions that the author is envisioning. The star wouldn't be totally destroyed, nor would most of the planets..

    Obviously, anything on the far side of the star will have a really bad time. You have a huge impactor going at relativistic speeds, plus stellar core matter and energy released from the core of the star. In fact, energy from the core of the star all being able to escape would probably scour away stuff on the impactor side as well. Something perpendicular to the hole would probably be able to avoid any immediate radiation problems. How quickly before the infalling matter plugged the hole and made it safe to pass by that region of space, I couldn't say.

    Of course, even assuming they avoided any direct energy spray, two things would happen that would be very unpleasant for anybody living on a planet in that system. The first would be the fact that the post-shot star would have a different energy output. The second is that when the gravitational center of a solar system loses a good chunk of its mass, the orbits of everything around it will shift and possibly destabilize. This wouldn't be immediate - the inhabitants of a sufficiently sci-fi culture would have plenty of time to get to a spaceport - planets will be possibly thrown from the system and even the ones that aren't will be condemned to freeze.

    Finally, though; you'd need a planet sized impactor in order to pull that off, and the energy to get said impactor up to relativistic speeds. That's a significant gravitational attractor all on its own. If you want to disrupt a whole solar system, you don't need to shoot a massive bullet through their sun. Just driving through should seriously mess up a lot of orbits.

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    Default Re: Destroying a star

    'Destroying' a star is going to basically mean dispersing enough of its mass that fusion halts, so we're talking something of order 1/10th to near 100% of its mass depending on the size of the star. Stuff like poking a hole and letting the core escape doesn't make sense - it's like saying that if you dug a pit down to the core-mantle boundary, the Earth's core would suddenly squirt out into orbit. Stuff would come up, but as soon as you've filled the pit partway with core stuff you'd be in static equilibrium again. Momentum could push you past that, and you might be able to shape the pit to focus that into a jet that sends a bit of material up at escape velocity, but not the bulk of it.

    So how much energy needs to be delivered to make this happen? If you could transfer things perfectly, its something on the order of GM^2/R (with a constant out in front that depends on the density profile). So we could ask for example how long you'd need to run a Dyson sphere around a star in order to gain the energy to disperse it?

    Sol's gravitational potential is ~4x10^41 joules. Sol's radiant output is ~4x10^26 watts. So you would need to harvest the total energy output of Sol for 10^15 seconds (about 30 million years) to be able to destroy it. Plus or minus a factor of 10 or so.

    Or, you could do it with 10^24 kg of antimatter, which is about 1/10th the mass of the Earth.
    Last edited by NichG; 2019-11-30 at 12:02 AM.

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    Default Re: Destroying a star

    Quote Originally Posted by Chen View Post
    The sun's density is extremely low compared to any bullet you'd shoot at it that could get up to relativistic speeds (until you get near the core anyways). Average density is apparently around 1.4 g/cm^3.
    I had an impression that the core needed to be pierced to have the described effect. Going through the less dense parts would not have any structural effects I think. I might have been mistaken though.

    Funny enough, even with this low density and bullets made out of tungsten you would only pierce the sun rougly for 15 times the length of the bullet. So an Earth-sized bullet would stop way before reaching the core, since the radius of the Sun is 100 times that of Earth. Granted, uneven density will lead to deeper penetration, but at the same time less impactful.
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    Default Re: Destroying a star

    Quote Originally Posted by Chen View Post
    So I've been reading Cixin Liu's Rememberance of Earth trilogy (The Three Body Problem, The Dark Forest, Death's End) and was wondering about some of the science in it.

    At several instances in the trilogy extremely high veloctity objects are used to destroy stars (and the planetary systems around them). Essentially extremely fast relativistic kinetic kill vehicles, but targetted at the solar system's stars rather than a planet directly. It mentions when one of these objects impacted the star it "tore a hole through the photosphere and the convection zone" that was ~50k km in diameter. In the end it resulted in lower pressure in the core (stuff was being expelled from this "hole") and eventually lead to collapse and stellar explosion.

    I'm wondering if this is actually what would happen? Is it just somewhat technobabble or could it really occur?
    It seems to be mostly BS to me. I'm not big on stellar physics, but I do know that stars aren't solid, are incredibly big, and have such high levels of gravity that they literally bend time.

    The big thing is the solid bit. You'd basically cause a massive 'splash' if you chucked something into the sun. In order to decrease the sun's mass, you'd need to hit with enough force to cause matter to escape the Sun's gravity. And for enough matter to escape to actually destabilize the star. But just punching a hole in the star? It would reform behind the hole, and likely do so fast as to not have any major effects besides a burst of radiation.
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    Default Re: Destroying a star

    Maybe this is overly simplistic, but a star is basically a cloud of very hot gas that stopped collapsing under its own gravity because of the heat generated by fusion in the core. The only "practical" way to blow one up is to increase the rate of fusion dramatically, so that gravity is no longer sufficient to hold the gas together, i.e. a supernova.

    I don't see how shooting a thing into the sun at very high speeds accomplishes this at all.
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    Default Re: Destroying a star

    Quote Originally Posted by warty goblin View Post
    Maybe this is overly simplistic, but a star is basically a cloud of very hot gas that stopped collapsing under its own gravity because of the heat generated by fusion in the core. The only "practical" way to blow one up is to increase the rate of fusion dramatically, so that gravity is no longer sufficient to hold the gas together, i.e. a supernova.

    I don't see how shooting a thing into the sun at very high speeds accomplishes this at all.
    Supernovas are the opposite no? Too little fusion/degeneracy pressure which results in a collapse of the core under its own gravity leading to a shockwave that expels the outer layers of the star.

    The idea in the novel seemed to be to cause enough matter to be expelled from the star and its core for the core to collapse (due to reduced fusion due to lack of material) and cause a supernova.

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    Default Re: Destroying a star

    I haven't read these books.

    Quote Originally Posted by Radar View Post
    I had an impression that the core needed to be pierced to have the described effect. Going through the less dense parts would not have any structural effects I think. I might have been mistaken though.

    Funny enough, even with this low density and bullets made out of tungsten you would only pierce the sun rougly for 15 times the length of the bullet. So an Earth-sized bullet would stop way before reaching the core, since the radius of the Sun is 100 times that of Earth. Granted, uneven density will lead to deeper penetration, but at the same time less impactful.
    That 15 times the length of the bullet business is plain wrong. Relativistic speeds means near enough to the speed of light that you have to take relativity into account in the maths, which is probably about 0.25 c, but at higher proportions of c (over 0.999999), the time dilation on the bullet means that it has time to exit the other side of the star before it evaporates. It's not the bullet that does most of the damage, it's the shock wave that pulls matter out after it.

    Quote Originally Posted by Chen View Post
    Supernovas are the opposite no? Too little fusion/degeneracy pressure which results in a collapse of the core under its own gravity leading to a shockwave that expels the outer layers of the star.

    The idea in the novel seemed to be to cause enough matter to be expelled from the star and its core for the core to collapse (due to reduced fusion due to lack of material) and cause a supernova.
    Accelerating the bullets to the sort of speed where they'd do that much damage to a star would be a non-trivial exercise, plausibly impossible in the real universe.
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    Quote Originally Posted by halfeye View Post
    That 15 times the length of the bullet business is plain wrong. Relativistic speeds means near enough to the speed of light that you have to take relativity into account in the maths, which is probably about 0.25 c, but at higher proportions of c (over 0.999999), the time dilation on the bullet means that it has time to exit the other side of the star before it evaporates. It's not the bullet that does most of the damage, it's the shock wave that pulls matter out after it.
    It is not about evaporation of the bullet - it is about losing momentum to the body in which you dug the bullet in. Especially at high speeds there is no time to move the matter aside - you are just pushing it in front of you - this was the core assumption of Newton for this estimation. Between the material struck being plasma and the bullet having significant relativistic speeds things might change from those simple calculations, but there still should be some correspondence here.

    Do not get me wrong there - energy will still be deposited into the star with all the destructive potential, so more then a flare will appear on the far side of impact. It is just that there will be no noticable piercing effect.
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    Default Re: Destroying a star

    Quote Originally Posted by Chen View Post
    Supernovas are the opposite no? Too little fusion/degeneracy pressure which results in a collapse of the core under its own gravity leading to a shockwave that expels the outer layers of the star.

    The idea in the novel seemed to be to cause enough matter to be expelled from the star and its core for the core to collapse (due to reduced fusion due to lack of material) and cause a supernova.
    A star remains in equilibrium when the heat generated in the core pushes the atoms apart to a degree that is equal to the weight of the star pushing the atoms together. When the star runs out of fuel, the amount of heat generated goes down and gravity wins, crushing the core so hard that protons and electrons fuse together into neutrons. When protons and neutrons fuse together they very suddenly take up considerably less space, causing cavities to form into which material from the higher levels rushes in. Because of the massive gravity of huge stars rush towards the core extremely quickly. As atoms from the upper layers all rush toward the core they are bumping into each other. And even before they reach the core, the upper layers bounce off the lower layers. The lower layers get kicked towards the core and the upper layers get kicked out into space.

    To stop fusion in the core generating heat, you either have to reduce pressure or temperature. Even if you remove massive amounts of material from the core, the remaining core will just shrink down a tiny bit into a slightly smaller sphere and pressure from the material above will squeeze it to a point where the generated fusion heat will be equal to the gravitational pressure.

    It would be much much easier to completely vaporize every planet in the system than trying to get a star to explode.
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    Default Re: Destroying a star

    Quote Originally Posted by Yora View Post
    To stop fusion in the core generating heat, you either have to reduce pressure or temperature. Even if you remove massive amounts of material from the core, the remaining core will just shrink down a tiny bit into a slightly smaller sphere and pressure from the material above will squeeze it to a point where the generated fusion heat will be equal to the gravitational pressure.
    Unless, of course, the star is so small that it's only barely got enough mass to trigger fusion in the first place, but such a star would be a very small red dwarf and thus extremely unlikely to host habitable planets.

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    Default Re: Destroying a star

    Quote Originally Posted by Yora View Post
    A star remains in equilibrium when the heat generated in the core pushes the atoms apart to a degree that is equal to the weight of the star pushing the atoms together. When the star runs out of fuel, the amount of heat generated goes down and gravity wins, crushing the core so hard that protons and electrons fuse together into neutrons. When protons and neutrons fuse together they very suddenly take up considerably less space, causing cavities to form into which material from the higher levels rushes in. Because of the massive gravity of huge stars rush towards the core extremely quickly. As atoms from the upper layers all rush toward the core they are bumping into each other. And even before they reach the core, the upper layers bounce off the lower layers. The lower layers get kicked towards the core and the upper layers get kicked out into space.
    I think it's even more complex than that, as the core falls inward, it builds up more pressure and temperature, so it does fuse heavier elements, all at once, so what was a stable hydrogen or helium fusion becomes a runaway chain reaction carbon or oxygen fusion, and that's where the energy of the supernova comes from.
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    Quote Originally Posted by halfeye View Post
    I think it's even more complex than that, as the core falls inward, it builds up more pressure and temperature, so it does fuse heavier elements, all at once, so what was a stable hydrogen or helium fusion becomes a runaway chain reaction carbon or oxygen fusion, and that's where the energy of the supernova comes from.
    Starting up fusion of higher elements depends on how massive the star was. The supernova is essentially a shockwave from burned out (at current fusion level) star collapsing due to lack of heat source. Since the core becomes even more tight, the falling upper layers hit it really hard and just as Yora said there is an explosion. So momentarily the pressure and temperature gets crazy high and all the elements heavier then the iron are actually produced only in those extreme conditions. Still, the energy released in a supernova is only from gravitational potential energy. Synthesis of heavier elements actually takes significant energy, so it is not a runaway reaction. Additionally, supernova's are spreading all those elements around the cosmos and only thanks to them we are here. It is kind of poetic that we are truly made from star matter.
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    Default Re: Destroying a star

    I think understing supernovas become more clear when you think of one with a core that collapses into a black hole instead of a neutron star. Nothing can impact and bounce off a black hole. If it hits the black hole it goes in and stays in.* The extreme compression of infalling material that causes the explosion must be happening before it reaches the stellar remnant. And it has to be there that the fusion of "superheavy" elements happens. "heavy" elements like oxygen, neon, and silicon are already created in large stars before the core collapses.

    *There is an interesting hypothesis that the first stars in the early universe could get so big that the collapsing core formed a black hole with an event horizon that was large enough that the bounceback region would be inside of it and the supernova be fully trapped inside the black hole. You'd have these super-hyper-giants that undergo a massive shrinking and brightening, and then suddenly just wink out of existence.
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    Pfft, its so simple even a pre warp society could do it! All you have to do is launch a lunar body sized mass of water sealed in a container that wont melt till it penetrates deep into the star. When it melts, the water will undergo steam expansion taking up roughly 1700x the volume, causing an absolutely unreal steam explosion that blows the star apart in an amazing orgy of violence! Ok, you can all bow down before my sheer unadulterated brilliance. I bet you cant tell that I have absolutely zero education in matters of, well, whatever this stuff would be covered under. Because my logic is flawless. /serious nod ok, now to wait for the millions of things that make this the dumbest idea since chocolate pants
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    Default Re: Destroying a star

    This thread has reminded me of Larry Niven's "A World Out of Time". In that, a hostile power bloc based outside the Solar System uses a giant fusion motor to stop the tenth planet (Persephone, in this case, a gas giant out beyond Pluto somewhere) in its tracks. The planet then falls into the Sun, and somehow triggers its (early) transformation into a red giant. I was never too sure how the physics of that actually worked, or what would happen in reality if you chucked a Jupiter-sized mass of mostly hydrogen into the Sun.

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    Quote Originally Posted by factotum View Post
    This thread has reminded me of Larry Niven's "A World Out of Time". In that, a hostile power bloc based outside the Solar System uses a giant fusion motor to stop the tenth planet (Persephone, in this case, a gas giant out beyond Pluto somewhere) in its tracks. The planet then falls into the Sun, and somehow triggers its (early) transformation into a red giant. I was never too sure how the physics of that actually worked, or what would happen in reality if you chucked a Jupiter-sized mass of mostly hydrogen into the Sun.
    It will surely not trigger the red giant stage, which happens specifically when the star runs out of hydrogen and starts using helium instead. Considering that Sun is 1000 more massive then Jupiter, there would be no significant changes in the reaction tempo.

    There would be a lot of things going on in the solar system though. All the orbits could be heavily distorted, which is already bad news and then the collision will surely send a serious ammount of energetic particles into space. If an inhsbitet planet hit this particle stream, it would be very bad news for anyone living there. Exact level of destruction is difficult to estimate.
    Last edited by Radar; 2019-12-01 at 04:18 AM.
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    Also, wouldnt it take a very VERY long time for this tenth planet to even REACH the sun? If its just being allowed to basically coast in under gravitational pull, and starting from outside pluto, thats a lot of ground it has to cover. In addition, wouldnt it be more likely to slam into various other planets instead on its way? God only knows what kind of snowball effect that would have on the entire solar system long before it reaches the sun (assuming it even would)
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    I've been saying for years that science fiction is dead. There's only space fantasy now.
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    Quote Originally Posted by Traab View Post
    Also, wouldnt it take a very VERY long time for this tenth planet to even REACH the sun? If its just being allowed to basically coast in under gravitational pull, and starting from outside pluto, thats a lot of ground it has to cover. In addition, wouldnt it be more likely to slam into various other planets instead on its way? God only knows what kind of snowball effect that would have on the entire solar system long before it reaches the sun (assuming it even would)
    The solar system is a very good approximation of entirely empty. The chances of an object falling in from the edge of the system colliding with another planet are extremely low. The gravity of the big planets (e.g. Jupiter) do tend to draw objects toward them, but remember, this event was an engineered one--the people who set it up could calculate the planet's course and make sure it didn't come close to any other planets.

    As for how long this would take, it's never made clear in the book exactly how far Persephone is from the Sun. If we assume for the sake of argument it's twice as far as Pluto, and we treat the "falling in" scenario as being an elliptical orbit with major axis of that distance, we can use Kepler's laws to calculate the orbital period of such a body; it works out as 716 years for a complete orbit. Obviously it will only take a quarter of that time for the fall into the sun, or 179 years. So, yes, that's rather longer than the fall took in the novel, as I recall!

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    Quote Originally Posted by Traab View Post
    Also, wouldnt it take a very VERY long time for this tenth planet to even REACH the sun?
    It would take a while yes, but not so long as you seem to be thinking, i'd estimate somewhere between one and five years (I didn't try to do any maths on that). Ninja'd and made to look a bit silly <edit> but now I'm in doubt again. </edit>

    <edit>

    Quote Originally Posted by factotum View Post
    The solar system is a very good approximation of entirely empty. The chances of an object falling in from the edge of the system colliding with another planet are extremely low. The gravity of the big planets (e.g. Jupiter) do tend to draw objects toward them, but remember, this event was an engineered one--the people who set it up could calculate the planet's course and make sure it didn't come close to any other planets.
    I agree with most of the above.

    As for how long this would take, it's never made clear in the book exactly how far Persephone is from the Sun. If we assume for the sake of argument it's twice as far as Pluto, and we treat the "falling in" scenario as being an elliptical orbit with major axis of that distance, we can use Kepler's laws to calculate the orbital period of such a body; it works out as 716 years for a complete orbit. Obviously it will only take a quarter of that time for the fall into the sun, or 179 years. So, yes, that's rather longer than the fall took in the novel, as I recall!
    I'm having trouble seeing this as correct. It assumes that all ellipitcal orbits with the same major axis take the same time. I have trouble seeing that as likely, the speed along a circular orbit is constant, and relatively slow, the speed of a body freely falling toward another compared to which it was initially at rest constantly rises, I don't remember how to do the maths, and I can't be bothered, but it seems unlikely that the minor axis of an orbit is totally negligible.

    </edit>

    In addition, wouldnt it be more likely to slam into various other planets instead on its way?
    This thing is supposed to be Jupiter mass or more? only Jupiter could significantly affect it's course. Actually hitting something is very unlikely, the diameter of the Earth is about 8,000 miles, Jupiter's diameter is 80,000, the Earth's orbit is is 2 * pi * 93,000,000 long, the chances of an impact are thousands to one against.
    Last edited by halfeye; 2019-12-01 at 01:48 PM.
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    Default Re: Destroying a star

    I admit I was thinking about the sheer time involved (even if "only" 179 years) and thinking that at some point its going to get close enough to another planet to be side swiped by it as it orbits. But I was thinking about total travel time and not how small a portion of that would be within the solar orbit of each planet. As was said, there is a lot of empty space between worlds orbits. Hmm, I wonder how its passing would effect the kuiper belt and asteroid belt? Would it only remove a negligible amount through direct contact and catching more in its wake? Would the disturbance of its passing throw everything there out of whack? Would it turn the impact of the gas giant with the sun into a game of bullet hell as it drags god only knows how many comets and asteroids along for the ride?
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    Default Re: Destroying a star

    Quote Originally Posted by Yora View Post
    I've been saying for years that science fiction is dead. There's only space fantasy now.
    Cixin Liu's trilogy is very much science fiction, it's engaged in a fairly deep level of speculation about how alien societies would relate to one another. It's just not very hard science fiction, with even Three Body Problem rather dependent on a fairly fundamental misunderstanding of how the Centauri system is actually structured. He handwaves a lot, most of it isn't all that important, but the inability of highly advanced civilizations to actually wield the extremely powerful long-range destructive weapons he claims is actually a hugely important critical point with regard to the series. Specifically the 'dark forest' philosophy of interspecies relationships totally collapses if the 'hunters,' upon locating other individuals, are unable to actually strike at them.
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    Default Re: Destroying a star

    Quote Originally Posted by halfeye View Post
    I'm having trouble seeing this as correct. It assumes that all ellipitcal orbits with the same major axis take the same time.
    That's exactly what Kepler's Third Law is. The period of a body's orbit is related to the semimajor axis of the orbit (e.g. half the major axis of the ellipse) no matter how elliptical said orbit is.

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    Default Re: Destroying a star

    Quote Originally Posted by Traab View Post
    Pfft, its so simple even a pre warp society could do it! All you have to do is launch a lunar body sized mass of water sealed in a container that wont melt till it penetrates deep into the star. When it melts, the water will undergo steam expansion taking up roughly 1700x the volume, causing an absolutely unreal steam explosion that blows the star apart in an amazing orgy of violence! Ok, you can all bow down before my sheer unadulterated brilliance. I bet you cant tell that I have absolutely zero education in matters of, well, whatever this stuff would be covered under. Because my logic is flawless. /serious nod ok, now to wait for the millions of things that make this the dumbest idea since chocolate pants
    You fool. You insolent coward. The only way to kill a star simply and quickly is to maneuver a Cosmic Candle Snuffer into place, and the star's fires will run out of oxygen.


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    Default Re: Destroying a star

    Quote Originally Posted by factotum View Post
    That's exactly what Kepler's Third Law is. The period of a body's orbit is related to the semimajor axis of the orbit (e.g. half the major axis of the ellipse) no matter how elliptical said orbit is.
    Wikipedia gives me:

    The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.
    That doesn't clearly say to me what you are saying it says. For one, planetary orbits are close to circular. We are talking about a straight line "orbit". Distant orbits are very energetic, despite being slow, and the acceleration is more or less even to the extent that the orbit is more or less circular. The acceleration on the infalling object is increasing exponentially as it nears the star.

    I'm not saying I know you are wrong, it just doesn't feel right, and I don't know you are right.
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    Default Re: Destroying a star

    This Reddit site predicts 65 days for the Earth to fall into the sun if our orbital velocity magically went to zero, which is about 1/6th of our orbital period, not one quarter. They calculate it two different ways and both times arrive at the same answer.

    Here's a link to wikipedia's Free-fall page.
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