Cosmological problem( Relativistic)

Gravity travels at the speed of light. As the central idea of Relativity, nothing nor even Gravity can travel faster than Light ! So how can the planets change their path before the last light of disappearance of Sun reach to the planets ? Since until the light stops coming from the sun, the sun is still there for us. The light takes 8 min and 12 seconds to reach Earth. So, Earth and all rest planets will react accordingly as the shock wave in the space-time fabric reaches them. Until then they will follow their path around Sun!

this question basically takes into account the fact that gravitational waves travel at the sped of light and hence their effect is observed ,say, the earth after a time delay of 8 minutes and 20 seconds. Now this case would just be the same for other planets in the solar system and hence when the sun would suddenly disappear, it's gravitational field waves waves would still travel at the speed of light and bring out the effect in the planets one by one.