In John C. Wright’s The Golden Age, they light Jupitor making it a sort of mini-star. Is this possible? What would it take?
Brown Dwarfs mass in at 75 to 80 Jupiters. No one’s going to make Jupiter into a mini sun without adding a lot of mass, or messing with the rules that govern nuclear fusion.
About 75 more Jupiters to come along to merge into the barely-minimal mass to become a star. I suppose if one was somehow able to squish Jupiter into a much smaller volume, it might flare up into a short-lived starlike object that glowed feebly for a little while before expanding back to its earlier cooler volume.
No. There’s just not enough mass, despite how huge it is. Do a search–there have been dozens of threads on this topic over the years.
Some people seem to have the idea that since Jupiter is mostly hydrogen that if you dropped a large spark the whole planet would burn. But there’s no oxygen for the hydrogen to combine with…or more precisely, all oxygen present on Jupiter has long ago combined into the most energetically favorable compound possible.
That’s the upper limit for a brown dwarf (and lower limit for a red dwarf, a true “star”). The lower limit for brown dwarfs is about 13 times Jupiter.
Why yes, yes it is. Now if I can only find my head, eveything’ll be OK.
Well, there’s this trick where you use self-replicating universal constructors in the form factor of a rectangular monolith with sides of ratio of the squares of the first three primes to condense the atmosphere…
Stranger
Excellent, we’re half an order of magnitude closer to a solution, and the thread’s only a few hours old. We only need 12 more Jupiters. I suspect a black hole wouldn’t do us any good, because Jupiter would just collapse into it without becoming a star. Uranus and Neptune combined are barely a tenth the mass of jupiter, and the entire asteroid belt less than another 0.1%. The minor planets are, well, minor, plus, we may need them for something else someday.
We’re going to have to go extrasolar for the mass we need. I think we should get the Lensmen to hook us up with some of those loose planets they have fixed up with those inertial nullifiers.
Oh I don’t know about that. A black hole would kick start an accretion disk which would heat the rest of the planet’s atmosphere causing it to expand further away from the hole slowing down the rate of consumption.
I’m not even going to try to guestimate the viability of the plan of course. 
If Shoemaker-Levy 9 couldn’t ignite it, I don’t imagine anything could.
Well, that depends on what the OP is willing to settle for as a “mini-star”. Frankly, brown dwarfs aren’t all that impressive (at least, as stars go).
And Stranger, it wasn’t just primes, and it wasn’t just three of them. A monolith has dimensions in the proportion 1:4:9:16:…
Yes, but you don’t need oxygen to create a star … nuclear fusion isn’t a chemical reaction.
(I feel a little silly pointing out how this failed ignition scenario doesn’t jibe with the OP’s failed ignition scenario…)
I had heard or read somewhere that Jupiter actually produces more energy than it absorbs. I assumed that some sort of fusion was going on. I guess I got that wrong.
There may be some energy produced by gravitational collapse. It doesn’t have a sharp demarkation between the atmosphere and the surface, just a gradient. Gravitational force shrinking the planet can generate energy.
Jupiter also probably has radionuclides at its core that produce heat the same way Earth’s core produces heat. I don’t know if we have a good estimate of how much heavier elements Jupiter has, but it wouldn’t suprise me to find it has more than Earth.
Perhaps, but not enough more to account for the surplus energy from Jupiter. My understanding is that most of that comes from relic heat from its formation, which ultimately comes from gravitational collapse. That is to say, Jupiter collapsed into a planet from the protosolar nebula, and got really hot in the process, and it’s still cooling down from that.
Is Podkayne still around? I seem to recall that she studies gas giants. Perhaps she could give more insight.
As Chronos just noted, if one defines “brown dwarf” as “mass of hydrogen, with admixtures of helium and other elements, too small to ignite by fusion but which radiates at a temperature above what it would if irradiated only by neighboring stars,” then Jupiter is (or is one of) the smallest, coldest black dwarfs known, since its “effective surface temperature” is about 100 degrees above what it should be if the sole source was re-radiation of insolation. Granted that you’re talking the difference between 120 and 220 below zero, this is still interesting.