When a flame comes out of a lighter on earth, it points up; which way would it point in a zero g
The short answer - It wouldn't point up, it would just form a burning ball right on the end of the lighter. The 'why' is fairly simple upon reflection, but not particularly intuitive. The burning of gas is it's combination with an oxidant, and the release of energy raises the temperature of the gas (hence 'heat rises'). The warm gas has a lower density than the air around it, and thus flows toward a region of lower density, i.e. - away from the gravitational pull of the Earth. In orbit, the net effects of gravity are balanced by the acceleration around the Earth. Thus, the warmed gases expand equally in all directions, and consume oxygen from the atmosphere equally in all directions. The fire will burn in a ball, outward in a growing sphere. It will usually burn faster than it can supply itself with oxygen, and burn out in a short period of time.
Frank DiBonaventuro, B.S. Air Force Officer, Tinker AFB, OK
'The mathematician's patterns, like the painter's or the poets, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.'