[Entropy Squared]

If the sun winked out of existence, how long would it take for Earth's orbit to change? Would it be instant or would it take the time (8 minutes?) of light speed to effect the change?

[RightWhale]

If the sun winked out of existence

We could figure this out for sure if we found a double star with both suns orbiting close together and a planet orbiting both at a greater distance. There would be regular motion in the system, but some kind of phase lag in the planet's orbit that could be measured.