I like that the movement is the primary obstacle, as that is a bit different. Although the fact you can't move diagonally seems a step too far maybe (Not sure if that is an intentional design decision?)
It would benefit from a lot more feedback across the board, I think feedback would be useful when you fire, when a bullet hits, when you move/accelerate, when you crash into an asteroid, when you get close the part of the sun that kills you, when you get close to an enemy and when you are destroyed. There are load of options for feedback like that, so some kind of new animation, an explosion sprite, some particle effects, the sprite flashing, a slight change in movement, a brief slo-mo or some good old-fashioned screenshake.