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How large could a solid planet be (in theory) without becoming a star or black hole? Too much in the way of light elements would lead to thermonuclear ignition, but too many heavy elements would eventually cause gravitational collapse.

Similar questions have been asked before, but in this case assume that the planet's composition can be adjusted to any natural material substances in any proportions.

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    $\begingroup$ So you're concerned with size, not mass, correct? $\endgroup$ – HDE 226868 Aug 29 '18 at 17:06
  • $\begingroup$ Great question, spent 2 hours on it, nowhere close to a solution. I have to find super-high pressure density curves for various materials before I can attempt this one. $\endgroup$ – kingledion Aug 29 '18 at 19:30
  • $\begingroup$ My thinking is that it needs to be iron and hydrogen. If its close to the neutron star limit and made of iron, replacing some iron with hydrogen should increase its size. If its made of hydrogen close to thermonuclear ignition replacing some of the hydrogen with something denser that won't burn might help as it would sink to the central core where it would inhibit thermoneuclear reactions in the dense core. Is there anything that will not fuse that is lighter than iron? $\endgroup$ – Slarty Aug 29 '18 at 21:16
  • $\begingroup$ @Slarty if the object is close to "the neutron star limit" (Chandrasekhar limit), it will be turned into "degenerate matter", and it would have nearly identical size regardless of which elements are comprising it. $\endgroup$ – Alexander Aug 30 '18 at 0:17
  • $\begingroup$ Can you use a continuing source of power to keep it from collapsing? If so, the answer might be unlimited. I'd have to think about how to arrange things to make it actually doable (even with unlimited power), but the basic idea is pretty obvious: just provide enough outward force to prevent it from becoming dense enough at any point to collapse atoms, and you won't get a neutron star or black hole. Just keep going bigger and bigger at the same density (which just takes more and more outward force) and it seems like it should work forever. $\endgroup$ – abarnert Aug 30 '18 at 1:59
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An alternative to a carefully engineered supergiant bubble or honeycomb structure is to just throw matter together in the right order to keep it from sustaining fusion in the core.

With that in mind, mass matters more than volume. Thus my answer is: about 1.4 solar masses. Just shy of the threshold of pressure to turn atoms into degenerate matter, and thus becomes a neutron star.

Since iron takes more energy to fuse than it releases, a body with a core made entirely out of iron can't undergo fusion. Start making your planet out of heavy elements until you have a huge ball that's mostly iron. Fission might happen if you throw very heavy elements into your planet in huge chunks, so try to mix things up first. Or stand well back.

After that, just start throwing in whatever is available. Hydrogen is cheap and plentiful in the universe, and since you're going for a huge planet, it's going to be a gas supergiant anyways, rather than a rocky planet; just with an iron core rather than a metallic hydrogen core like our solar systems' gas giants have.

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  • $\begingroup$ I think your on to something there. I used the word "substances" in the question as I was thinking vaguely along these lines. Hyrogen trumps iron in weight terms but Iron trumps hydrogen in thermoneuclear reactivity terms. So a combination of the two mighgt work $\endgroup$ – Slarty Aug 29 '18 at 21:06
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The critical point here is not the mass. It is the mass density and the resulting gravitational force on the atoms your planet is made of. See this post about the requirements for a black hole The same basic idea holds for turning a planet into a star.

In detail: If you make up your planet, the more matter (and thus mass) you add, the stronger the overall gravity of your planet becomes.

The stronger the gravity becomes, the more your matter is compressed, increasing the mass density of your planet (and also pressure and temperature, eventually turning solids to liquid to gas to plasma...) increasing the kinetic force of your atoms.

If the gravitational and kinetic force of the protons exceeds the electrostatic forces which keeps your atoms pushed apart, you start a nuclear fusion reaction and your planet becomes a star. Wikipedia has all the details

Conclusion: As long as you do not exceed a gravitational density threshold your planet can be any size you like. The exact numbers will require a non-trivial amount of calculation for any given case.

However, if you are writing fiction and not a documentary, consider an artificial planet-like structure that is mostly hollow for extremely large sizes. This way you will prevent to much matter from concentrating on one point. The limit there is your stellar neighbourhood, with nearby stars starting to mess with the integrity of your construct through gravity.

The largest known planet so far seems to be about 1.7 times the size of Jupiter (Source), which is utterly large.

Of course if you need a solid or liquid surface, or human beings being able to live on it without aid, your planed has to be much smaller.

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  • $\begingroup$ Of course, a Jupiter+ sized hollow sphere will collapse. $\endgroup$ – Schwern Aug 29 '18 at 18:14
  • $\begingroup$ Actually no. Why should it? If in doubt, you do have the option of introducing a bit of support structure (careful about mass concentrations though). Of course you need the right (probably exotic) materials. You can build incredibly large in space as long as you are not hindered by the gravity of your construct or nearby objects. What limits our current space constructions is the transport capacity of our rockets. $\endgroup$ – fer-rum Aug 30 '18 at 12:12
  • $\begingroup$ The construct itself has mass and thus gravity. The completed hollow sphere will still feel the force of its own gravity on its own surface and have to hold itself up against that. It's only inside a perfect sphere where gravity cancels out. See the Shell theorem. Any portion of a Jupiter-sized sphere is, effectively, a flat sheet and that doesn't hold up well against the perpendicular pull of its own gravity. A thicker surface is stronger, but has more gravity, requiring a thicker surface with more gravity... The question calls for natural materials, no unobtanium, and those cannot hold. $\endgroup$ – Schwern Aug 30 '18 at 19:52
  • $\begingroup$ OTOH the force of gravity may be very slight. A 1km thick shell the same density as the Earth of 1.7 Jupiter radius is 9.81×10^23 kg. The surface would feel an acceleration of just 0.005 m/s^2. Might be possible, someone would have to calculate what sort of load that sphere could handle. $\endgroup$ – Schwern Aug 30 '18 at 20:08
  • $\begingroup$ I never said it would be a trivial problem :) However the core concept is to distribute the matter across the largest possible space. Since the force of gravity grows quadratically as distance shrinks, the wider the construct is distributed across space, the less the impact of its own gravity. If you can deal with it you can also leave holes in the surface to reduce matter density further. Just beware if you want the whole thing to rotate - then you get a truckload of additional "engineering challenges". $\endgroup$ – fer-rum Aug 31 '18 at 10:27
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There are many massive bodies of the universe that don't do thermonuclear burning. The problem may be that they are all classified as stars.

A naturally formed planet contains hydrogen (and deuterium) and can not avoid burning it at least a little if its mass exceeds 12 Jupiter masses. If there is no deuterium, though (naturally, it burns out) this object will look like planet and not a star - so we can technically call it a planet. If the mass of the object goes higher - to 65-80 Jupiter masses, it starts burning Lithium, and, ultimately, Hydrogen-1 - which means this object a "real" star.

But what if the object does not have any "combustible" elements? Naturally, this occurs when larger stars burn out - their core becomes iron, which can not fuse any more to produce energy. These objects are called "white dwarfs" (if their mass still under Chandrasekhar limit, which is about 1.4 Solar masses). They are still hot, though, and it takes trillions and quadrillions of years for them to cool down and become "Black dwarfs". Can we call "black dwarf" a planet?

Still, the mass can go higher. An object heavier than 1.4 Solar masses, but lighter than about 3 Solar masses (Tolman–Oppenheimer–Volkoff limit) will become a Neutron star. Natural neutron stars are even hotter than white dwarfs, and longer time would be needed to cool them down. Can we call a cool Neutron star a planet?

Unfortunately, it does not look like we can go any higher than 3 solar masses. This object would collapse into a black hole, which likely would not fit into any definition of a planet.

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