If the Sun miraculously disappeared, the Earth (and all the other objects in the Solar System) would continue their forward motion in a straight line off into space, instead of following their almost-circular orbits. For the Earth this means it would head off towards the stars at about 30km/s (67,000mph). There may be some subsequent interaction between the planets of the former Solar System, but otherwise we’d continue floating through space probably without ever encountering another object. Even if we did, we’d be long dead, having frozen to death within weeks of the Sun’s disappearance!
