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There is, for sure, effect of gravity on fire. We know for a fact that fires on Earth are "pointy" while those in zero-gravity are "round". This is because fire is simply glowing gas. Gas is matter and matter has weight. For a body to have weight, gravity must influence it in some way. 

Fires on earth are anchored by gravity, but the combustion gases are hot and light, so they rise. As the flame goes up, more air is sucked into the base of the fire, feeding more oxygen to the fire and making it burn more strongly.

Nirdesh Pokharel