What do you mean by turned off? If it just stopped shining then things would just stay the same but would be a lot darker. As for if the Sun just disappeared then the Earth would carry on in its trajectory until the light reached it then it will go off at a tangent some ~8 minutes later. I think gravity waves travel at light speed as well. The good Doctor would be a better person to ask though.
God, grant me the serenity to accept the things I cannot change,
Courage to change the things I can,
And wisdom to know the difference.
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