If the sun disappeared what would happen to the path the planets follow?
I would imagine that the planets would just go a drift in space or try to find another orbit like Jupiter sense it's the biggest planet in our solar system.
Regarding the Earth's motion (and the motion of every other planet), there suddenly wouldn't be any centripetal force to curve the Earth's path. So the Earth would sail off in a straight line, in the direction it was moving at the instant when the sun's gravity disappeared. Although everything would become very dark, you wouldn't feel anything different. Even now, as we follow the curved orbit around the sun, the direction of the Earth's motion only changes by about one degree per day, so we don't feel it.