If the sun suddenly disappears, how long will it take the planets to be deviated from their orbits? ?

Roughly instantaneous due to the sun being unquestionably by far the largest object in our Solar System, thus having the most gravity. If the Sun suddenly disappears, so does the Sun's enormous gravity. Therefore all the planets would be flung out into deep space at an extremely fast speed, in fact 1000's of miles per second. Each would also have a frozen core and a frozen surface. And the Earth will no longer be unique in the fact that it harbours life.

I really hope that I have helped.

I think in that event we would disappear the same way the sun did. You mean if it fell into a worm hole? Maybe some of the outer planets would fly off into space eventually to join in some other systems (God help the inhabitants there while they are settling down).

Mercury and Venus would be goners too, and likely Mars. It all depends on how fast gravity disappears during the event.

Perhaps, if the event is slow, we would spiral slowly into the inevitable worm hole opening. If we are VERY LUCKY we might emerge in a new place orbiting our Sun once more. Chances for the correct distance appearing remote.

Or maybe it would suck up everything including the Oort cloud. Garbage disposal scenario. Total recycling. Meeting the ultimate event horizon. Long thin exclamation points and then nothingness.

The distortion of spacetime appears to travel at the "speed of light in a vacuum"

Thus, the fabric of spacetime would become "flat", for Earth, roughly 8 m and 20 s after the disappearance of the Sun's mass.

What is not clear is whether the transition from curved to flat would be smooth, or whether it would be accompanied by gravitational waves that could stress (and even shear) the material in orbit. In the latter case, depending on how suddenly the mass disappears, it is possible that there would be no planet left to be "deviated".

It takes time. That was a central question to Newton's theory of gravity that wasn't answered until Einstein came along.

Gravitational waves (or the influence of gravity between two objects) is transmitted at the speed of light. Therefore, if the sun were to disappear, our orbit would deteriorate as soon as we were able to see it disappear, and not a moment before.

gravity moves at the speed of light so for earth it would stay on course for about 8 minutes after the sun disappeared then we would continue straight in whatever direction we are facing and also the world would go black. other planets would be affected either earlier or later depending of course if they are closer or further away from the sun. i.e. mercury would be affected first, neptune last.

It would take different lengths of time for each planet. The Earth, for instance, would leave its orbit about eight minutes afterwards. For the outer planets, it would take up to a few hours.

The ONLY thing that keep the planets in their orbit is the gravity of the sun.

If the sun SUDDENLY disappeared (like, "POOF!") all the planets would go off on straight-line trajectories (tangents).

depends on how far they are away from the sun

The earth will contiue in its orbit for 8.6 minutes

changes in gravity move at the same speed as light - it takes 8.6 minutes for light from the sun to get to the earth.

About eight and a half minutes, because gravity propagates at the speed of light.

instantaneous. Just imagine you are swinging an object on the end of a string and the string snaps.