What kind of path would the planets follow if suddenly their attraction to the sun no longer existed?
If the sun were plucked from the sky, then nothing would happen until the message the sun had gone had been communicated to the planets at light speed. So for the first eight minutes, nothing at all would happen to the orbit of the earth. Then when the sun was gone and the topology of space had changed accordingly, the gravitation of other bodies would become the dominant force and the planets may either drift aimlessly or start to pull for instance towards Jupiter.
