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It doesn't have to be a rock, in fact it would probably be depleted uranium or even some crazy material like neutronium.

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    $\begingroup$ No such rock would make the sun go nova: that's the result of specific nuclear reactions, and only happens near the end of a star's life (if it's within a certain mass range). $\endgroup$
    – jamesqf
    Feb 19, 2017 at 18:43
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    $\begingroup$ What exactly do you mean by "near light-speed"? The difference between 99.99c and 99.999c is extremely large. $\endgroup$
    – Mike Scott
    Feb 19, 2017 at 18:44
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    $\begingroup$ Hello and welcome to WorldBuilding.SE! Currently there seems to be some information lacking in your question, which means it's hard to answer it properly. If more people from the community agree with this your question might be put on hold for some time. This allows the community to fix the question together with you so that it fits the site. This is a standard procedure around here. You could start by providing more exact info about the speed and the material. tour and help center provide more info. $\endgroup$
    – Secespitus
    Feb 19, 2017 at 18:51
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    $\begingroup$ Just a little reminder: if your question gets put on hold you can edit it. This just prevents people from answering as edits might invalidate existing answers, which is something we don't like. After some edits your question can be reopened for answers. BTW: Here are some basic infos about the sun not being able to go nova naturally. $\endgroup$
    – Secespitus
    Feb 19, 2017 at 18:55
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    $\begingroup$ Perhaps an edit to Possible foreign body causing the sun to go nova? "Could a foreign body entering the sun cause it to go nova? What speed would it need to go? What size would it have to be, and what material would it need to be made of? If this is not possible, please justify your answer scientifically." $\endgroup$ Feb 19, 2017 at 18:55

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I am not going to give numbers because the issue is way more complex than it appears, but I will add some factors than seem to have been overlooked.

  • First and more important, an object at 0.999999c will not simply travel through space. At that speed, every single atom of matter that it collides with will trigger a nuclear fusion, as it goes so fast that atoms cannot be repelled. A good illustration of that is XKCD relativistic baseball.

  • As the object approaches the sun, the solar winds will be more intense and concentrated; in fact it would be as if you had a nuclear engine in the entire front of the object, pushing it back. A object that is not dense enough will simply be stopped until it goes at a reasonable speed (0.5c?), the issue would be with a bigger one.

  • The relativistic mass of an object at 0.999999c will be 1000 times its rest mass; that will create a 1000 times stronger gravity field that will attract particles toward it (thus slowing it more).

  • If the object still impacts the Sun , its influence in it will be related to its cross-section; an object with an small cross section would simply run through it and cause not much of an issue.

So, I see 4 distinct possibilities, each of which depend of lots of unknown factors:

  • The object slows enough to become another regular celestial object. It happens if it is relation between its mass and its cross-section is low; because the reactions at the side facing the sun slow it.

  • Due to the pressure of the nuclear reaction it its surface, the object breaks in pieces. Collisions between the fragments cause a big explossion that throw the matter of the object in all directions; possible secondary damage due to high velocity debris hitting planets.

  • The object reaches the Sun, but it is small enough that the Sun simply "swallows" it. The energy produced by the desintegration of the object just add a few degrees to the Sun temperature.

  • The object reaches the Sun, and has a cross section (and mass) enough that a significant part of the Sun gas gets fuses with it. In this case, the Sun does not "explode", but its mass is divided between

    • A part of it that fuses with the object and leaves the system.

    • A part of it that is spent in the increased nuclear reaction.

    • A part of it that is ejected as solar wind.

    • A part of it that remains in place (which might be or might be not capable of sustaining hidrogen fusion).

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Note: What is written below this may or may not be valid anymore. See the comments.

According to Wikipedia, the gravitational binding energy of the sun is $6.87\times10^{41}$ Joules, which means that anything impacting the sun would need to possess at least this much kinetic energy in order to cause the sun to explode successfully. Applying the equation$$E_k = \frac{mc^2}{\sqrt{1-(\frac{v}{c})^2}}-mc^2$$from here gives that, assuming that the object is traveling at exactly $99.9999\%$ of light speed, its mass would have to be over $1.08\times10^{22}$ kg to succeed. This is approximately the mass of Pluto. I would imagine you were intending a somewhat smaller object, although this mass might suffice if you're using a neutronium projectile. Increasing the velocity decreases the required mass, although the velocities involved end up being extremely high. For an object weighing (for example) $5$ metric tons, such as a very large space probe, its velocity would have to be $$99.99999999999999999999999999999999999999998\%$$ of the speed of light to blow up the sun. This is possibly impractically high, and the energies of the individual particles approach and in some cases exceed the Planck energy, beyond which physics as we know it breaks down. Eventually, the body would likely form a black hole upon collision with the Sun or even earlier, placing an ultimate lower limit on the size of the impactor that is beyond my knowledge of physics to calculate.

In conclusion, your foreign body will either have to be unimaginably large or unimaginably fast to successfully blow up the sun.

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    $\begingroup$ There is the very important issue that the Sun is not solid. An object going at 99.9999% will just pass through it. It might expel some gas, but not that much. It is not a question of energy, but of an application of it (force), and you simply cannot "break the sun". $\endgroup$
    – SJuan76
    Feb 19, 2017 at 22:42
  • $\begingroup$ @SJuan76 That's a very good point. I may have to rethink some of my answer. $\endgroup$
    – praosylen
    Feb 19, 2017 at 22:57
  • $\begingroup$ the people who are sending this impactor are very technologically advanced, they can make a scrith-like material (tensile strength equivalent to the sitting nuclear force) for example so it could be very massive $\endgroup$
    – user33662
    Feb 19, 2017 at 23:18
  • $\begingroup$ @OP Can they imbue such a small impactor with an extremely powerful magnetic field, powerful enough to stop the impactor inside (what remains of) the sun? If so, then my answer remains valid in its entirety. Otherwise, they'll probably need a generator the size of Pluto to make the field, so it's a moot point. @SJuan76 or anyone that knows, would imbuing the projectile with an extremely strong magnetic field be enough to stop the projectile, or am I missing something? $\endgroup$
    – praosylen
    Feb 19, 2017 at 23:54
  • $\begingroup$ Yes you are. Question is only about the mass, so good answer have to address the fact that this can't be done with the mass alone. Comments may get deleted at any time, without any explanation, so you should answer the question, not comments. Also, are you sure magnetic field would allow for this kind of energy transfer? Wouldn't the missile just fly back and forth, losing only small part of its speed each time? And magnetic field is limited by the speed of light, so for the objects at near light speed it gets really funny to calculate forces. $\endgroup$
    – Mołot
    Feb 20, 2017 at 7:27
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Fact of the matter is, it isn't force or lack thereof that makes a star go nova. It's a depletion of its 'food source'. A star, in the simplest terms, is a ball of gas that is under such immense pressure that the gas is superheated, and the combination of this and quantum mechanics allows for Hydrogen atoms to fuse and become Helium atoms.

The longer a star lives, the heavier the atoms become (this is how the elements on the Periodic Table of Elements are created). Until a time comes when the star runs out of Hydrogen and starts to swell, becoming a Red Giant. If the host star has planets in near enough orbit, these planets are swallowed by the host star.

Eventually, the star collapses unit its own weight and (as Neil deGrasse-Tyson explained it) spills its enriched guts into the surrounding galaxy i.e. it goes nova.

This coalescence of matter, kinetic energy, and all else causes nearby gas clouds to compact and form new stars, and the atoms form the planets that surround it.

For more information, please see this link, or google life of a star, or lifecycle of a star, or something similar.

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  • $\begingroup$ FYI, I am no astrophysicist, so please check sources and see where I am wrong. $\endgroup$
    – Fayth85
    Feb 20, 2017 at 0:36
  • $\begingroup$ The question is about breaking the star into pieces, not about making it go nova. This answer is off-topic by my reading of the question. $\endgroup$
    – SRM
    Feb 20, 2017 at 5:30
  • $\begingroup$ @SRM Not arguing against it being off-topic. But as I figure 'making it explode', unless we're talking about the typical every moment 'explosion' that radiates heat, radiation, light, and so much more... the only other 'explosion' I can think of is it going Nova... which I recall the OP mentioning at first? I dunno if that was edited out, or if I'm just tired. But the previous point still stands ^_^ Either way, this is a weirdly worded question imho. $\endgroup$
    – Fayth85
    Feb 20, 2017 at 20:14

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