There are a set amount of randomly generated asteroids in the game. To remove an asteroid and spawn a new one, you must mine an asteroid completely out. Asteroids vary in size and in the amounts and types of ores.
Currently there are 20 small sized asteroids (up to 1000 size) planetary systems. When you mine one out, another small asteroid will respawn in either the same planetary system or a different one.
Then there are 40 medium sized asteroids that spawn can spawn anywhere in the unknown systems(more than 1 per unkown system is possible). When you mine out one of these, another medium roid will spawn anywhere in the unknown systems.
Finally there are 2 mega asteroids that can spawn anywhere in the unknown systems in size from 80k-110k.