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Consider all of sudden the sun vanishes. What would happen to planetary motion. Will it continue to move in elliptical path or move in a tangential to the orbit immediately after sun vanishes or move in elliptical orbit for some time after the vanishing of sun or any other cases?

If so, please explain...

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marked as duplicate by Waffle's Crazy Peanut, Qmechanic Apr 11 '13 at 17:11

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I think this was answered under "The speed of gravity?". –  Retarded Potential Apr 11 '13 at 16:26
    
What is the speed of gravity –  Hash Apr 11 '13 at 16:28
    
This seems to call for an evaluation of fictional physics. The sun can not simple cease to exist. Perhaps one should consider the case where the sun is replaced by a uniformly expanding spherical shell of matter and observe the situation when that shell passes the Earth's radius, but even then you have to make special arrangements to not have equally big trouble from the shell itself. –  dmckee Apr 11 '13 at 17:12
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In fact, this was a major problem to both Einstein & Newton. According to Newtonian, Gravity is instantaneous. In such a case, the planets would immediately escape into outer space. But, this event strongly neglects SR because, the event would be so fast that Earth will be out of orbit before we all would see the last light from the vanished-away sun. This problem was resolved with GR.

In GR, these gravitational waves travel at the speed of light and hence, the solution to this question - We'd definitely see the last visible light from the sun and then, the Earth breaks its orbital path, moves on its own along a straight line until it interacts with any other massive body..!

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In addition to what Crazy buddy says, at the end of that seven minutes, we should also expect a torrent of gravitational waves from the sudden change in the gravitational field.

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