…as it did in Arthur C. Clarke’s 2010: Odyssey Two and the movie based upon the book, how long would it be able to burn? Considerably shorter than a “real” star, I presume.
Someone who knows the actual numbers will hopefully chime in, but I believe that smaller stars burn through their fuel at a much slower rate than larger stars, and so last much longer, despite the bigger stars having more fuel to start with.
According to this page about stallar evolution Wiki (in the section on “Low-mass stars”): “Recent astrophysical models suggest that red dwarfs of 0.1 solar masses may stay on the main sequence for almost six trillion years, and take several hundred billion more to slowly collapse into a white dwarf.”
That’s the gist of it: The lighter the star, the longer it lives.
It’s mainly because it needs a high pressure in the core to burn fast, and that high pressure can only arise if the mass is great.
That’s the very short version anyway. (The cliff notes to the cliff notes).
-Tikster
Paging Angua.
At its current mass, Jupiter can’t undergo fusion (which is what I assume you mean by burning) at all. Fusion is a statistical process, requiring that you get all the atoms sufficiently close together and at a high enough energy/temperature that you get the nuclei to fuse. Without sufficient mass to maintain pressure/temperature to the level to create conditions for fusion, there’s no way that Jupiter could maintain fusion at all, even if you started a reaction somehow. So, in order to cause Jupiter to burn it would require generating, via an external source, some pressure or conditions to cause thermonuclear fusion–say, an artificial gravity source–and you would have to maintain these conditions; in short, it would be an energy-negative reaction. (The only way that stars continue to fuse is by lumping together enough potential energy, in the form of mass, to create the conditions suitable for fusion. Since gravity is conservative, you don’t have to keep adding energy to sustain it, and in fact as particles fuse their nuclei become more dense, but require higher energies; see the C-N-O cycle.)
There is an alternative; you could make the conditions more favorable for fusion via some catalyst that causes the atoms to become denser, i.e. the atomic orbitals are smaller (have a higher probability of being close to the nucleus) and the nuclear interactions (the so-called “strong force”) has a much more significant influence, able to pull nuclei together despite the repulsive electrostatic forces of the valence electron shells or the nuclear protons. This would require an exotic charged particle like a muon or a tau lepton which would take the place of an electron, “condensing” the valence shell of a light element and making a fusion event substantially more likely, after which the muon or tau would be free to move on and catalyze another reaction. The problem, however, is that such particles are unstable and only exist for a very short period of time (picoseconds on average), are sometimes destroyed in the reaction, and are unable, under current understanding of the Standard Model, to maintain an energy-positive output. However, Monolith builders may have figured out some way to produce exotic particles more efficiently or whatever scientific handwaving you like, and make the reaction sustainable.
To what extent it could progress depends on the rate of the reaction, how much energy you can get versus what it costs you to produce these charged particles, and what the actual composition of Jupiter’s mass is; we suspect the core is metallic hydrogen surrounding an outer shell of superdense carbon/nitrogen compounds, wrapped around a small rocky/nickel-iron inner core, but that’s almost completely unverifiable speculation. Despite all the pretty pictures we have of Jupiter, what it is made of, how it formed, and what goes on below the upper layers is a complete mystery.
Stranger
Heck, it’s easy. You just transport a zillion of those obelisk thingies into the Juperterian atmosphere, they transport in a godzillion cubic feet of hydrogen, then they suck some already-ignited plasma from the sun to kick-start the reaction. No fancy particles needed. 
Then it’s a plain “main sequence” star, and being a small one, it burns forever (as far as we’re concerned).
Well, yeah. Duh.
I’d be more interested in how it would effect the earth.
Would it just appear as a bright star? (assuming we’ve keeping Jupiter’s mass constant and catalysing the fusion reactions)
Or would it appreciably light up our rocky planet?
What about somehow managing to smash Jupiter and Saturn together? Would that hit the critical mass required to begin fusion?
Nope. You need about 80-100 Jupiter masses to get to a brown dwarf stage. Since Jupiter holds most of the non-stellar mass in our solar system, you could thrown everything into it without even getting close.
Depending on its own output, it would be scarcely brighter than it is now (where it appears as a very bright star), or considerably brighter still. However, it is also three times as far away as the Sun at closest approach, and of course wouldn’t be seen at all for a significant fraction of the year. It’s effect on Earth would be minimal, probably not bright enough to even cast shadows.
No.. Actually, my recollection is somewhat more like 80 Jovian masses to achieve minimal pressures for fusion, but whatever. The Sun–a pretty smallish star in the scheme of things–is about 1000 times more massive than Jupiter. I would guess that lacking sufficient gravity to hold the atmosphere against radiation pressure, it would blow out much of the upper atmosphere pretty quickly, too, eliminating a lot of potential fuel.
Stranger
I wondered this too. If Jupiter were somehow turned into a star or replaced with the smallest feasible star possible, what would that mean for life on the planets? Would we get fried or warmed up too mcuh to exist here? Or would Mars become nice and hospitable?
Mars wouldn’t be all that hospitable - for a fraction of a Martian year it would be near enough to “Lucifer” to get an appreciable warm-up, but for most of the year it would be too far away for the second sun to make much of a difference. Much less of a difference to us as it’s never much closer than fifty-odd million miles - call it half the Earth-Sun distance - for a month or so once a year, and would be putting out way less heat and light. It’d be a fairly spectacular night-time object though. Similarly the other giants wouldn’t be much affected by Jupiter’s upgrade as they’re quite spaced out.
Heck, Jupiter’s ego is already huge! I don’t even want to think about how it’ll change his personality if the tabloid magazines start calling him a star…
This is the first time I’ve heard the number “godzillion”. Is this the population of Japan?
The problem is that even if you could heat Jupiter enough so it was as hot as the sun, it would simply blow apart- it doesn’t have enough mass to hold itself together against that much internal energy. IIRC, in the book/movie the monoliths formed an artificial core of ultradense matter that Jupiter collapsed into, so it’s mass was compressed into a very small volume, small enough that it could be sun-hot and still hold together by it’s own gravity. Sort of like a very small artificial white dwarf. The result was a star just the right luminosity for Europa to have liquid water at it’s surface.
So you’d have to calculate Europa’s distance and the needed temperature to get the needed luminosity. Then since the new Jupiter would be more like a white dwarf than a mainstream star, you would have to solve the physics for how massive the central core would need to be (assuming neutronium density) to hold in the remaining mass against the required energy output. and have the right balance of surface area/ temperature to keep Europa comfy. Oh, and hopefully the resulting star gives off it’s energy mainly as visible light rather than x-rays.
Complicated.
I remember Clarke saying that the new star was bright enough that some nocturnal animal species got confused, and some even became endangered because their internal clocks had been so messed up. And of course in the movie, the new star is bright enough to be seen in the daytime in Washington, Moscow, Hawaii, etc.
Say we take Proxima Centauri as a bench mark. It’s too massive and bright for a Jupiter star but it’ll give us an idea at least.
At 4 AU it should be have roughly a magnitude of -12, which would be comparable to a full moon. A Jupiter star would be dimmer.
That seems bright to me, but we are dealing with a star, no matter how small it may be.
As opposed to the portuguese-speaking population of S. America, which is measured in brazillians.
It must be a monstruously large number.