|MadSci Network: Astronomy|
Good question. Obviously you've heard or read that if Jupiter was much bigger it could have been a star, and of course Jupiter contains all the right material as it's mostly Hydrogen.
It is true that if Jupiter had been bigger it could have become hot enough to ignite a "thermonuclear" fusion chain reaction, i.e., burn like a star.
However, it is not quite big enough and although astronomers may say it only needs to be a bit bigger, it actually has to be about 8 times more massive (which isn't much to an astronomer but might sound a lot to you). Having said that, as mass is proportional to volume, 8 times more mass is only about twice the diameter (it will be a bit different for a planet as the density will not be uniform).
See The Jovian System for some interesting stuff on Jupiter.To start up a thermonuclear fusion reaction both the temperature and the pressure must be very high. Four hydrogen nuclei (protons) have to fuse to form a Helium nucleus. High speed (temperature) lets them collide hard enough to stick, and high pressure crowds them all together to increase the chance of a collision.
Back to Jupiter, it's hot inside because over the eons it collapsed from a gas cloud and as the cloud collapsed under gravity the pressure increased and caused it to heat up just like if you put your finger over the end of a bicycle pump and compress the gas it heats up, and you can feel it!
As for the Sun, it will keep going for a few more billion years. It's not an old star about halfway through life and there is no mechanism for it to trigger any star-like activity on Jupiter.
Even when the Sun dies out to black dwarf, its remains will still be the most massive object in the Solar system, and any planets which remain will still orbit around the Sun.
At the moment (December 2003) Jupiter rises in the east at about midnight and by dawn is high in the southwest. It appears as a bright yellowish star in the constellation of Leo and will become a prominent feature in the evening sky in January and February 2004.
Try the links in the MadSci Library for more information on Astronomy.