about 8 minutes

8 minutes for the last sunlight to have reached us, but the gravitational pull which keeps the Earth orbiting the sun would vanish instantly. We'd feel an enormous lurch as the Earth stopped following a curved path and continued on in a straight line.

1) "If the sun disappeared, for eight-and-a-half minutes we’d have no idea that the sun had gone. We’d still see it – lingering, like a ghost – in the sky above Earth’s day side. As soon as the last of the sun’s light reached us – eight-and-a-half minutes after the sun itself disappeared – the sun would blink out and night would fall over the entire Earth. Not until that instant would Earth sail off in a straight line into space. Einstein’s special theory of relativity tells us that no signal in the universe – not even the tug of gravity – can travel faster than the speed of light – about 300,000 kilometers, or 186,000 miles, per second. Though free from the sun’s gravity, we’d be traveling at the same speed as before – about 18 miles, or 30 kilometers per second. So Earth would be traveling at the same speed as always into eternal night. " Source and further information: http://www.earthsky.org/faq/sun-light-motion-change 2) "since orbiting or free-falling toward a graviational source is just an inertial movement from the perspective of GR, we wouldn't even feel the effects after those 8 minutes. the folks on the near side of the earth would miss the sunlight, but the folks on the far side wouldn't know any difference (except from communications) until the sun fails to rise when it's expected to." "The correct answer to "what happens if the sun dissappears" according to General relativity is "the sun can't disappear". This situation is quite analogous to the question of "what happens according to Maxwell's equations if a charge disappears". The conservation of charge is _built into_ Maxwell's equations, and they do not have a sensible solution where charge disappears. Similarly, the conservation of energy and momentum is _built into_ the theory of General Relativity (in the form of certain differential conservation laws - while these laws don't generalize to the usual intergal form that's another topic.). These differential conservation laws would be violated if the sun suddenly disappeared, so General Relativity does not make any prediction as to what would happen in that event. Instead, it says that that event cannot happen." Source and further information: http://www.physicsforums.com/showthread.php?t=139158&page=2 3) "If the Sun disappeared, the temperature would drop to close to absolute zero (-460 degrees F) and we would burn up all the Earth's reserves of coal, oil, and natural gas in about three days just to keep ourselves warm." Source and further information: http://library.thinkquest.org/15215/Friend/temperature.html 4) Further information: http://www.esreality.com/?a=post&id=1247449 http://www2.abc.net.au/science/k2/stn-archive1/posts/topic14246.shtm http://iidb.infidels.org/vbb/showthread.php?t=151491