Evaporate? You mean cease to exist? That's a mere thought experiment that cannot happen in the real world. Matter doesn't just disappear, its gravitational influence will always exist. The sun will "evaporate" over a period of hundreds of billions of years. As the sun expands, its density will reduce, and as such it will warp spacetime to less of an extent... it will decrease in gravity. But this will be the least of our problems on Earth, we'll be long gone before the decreased gravity results in our planet drifting away from the sun.

Trying to imagine the gravitational consequences of the sun suddenly disappearing is a waste of time. You'd be better off trying to figure out how to rig the lottery... at least that might be possible.