I wonder if you had the opportunity to do so leisurely.
A suddenly vanishing sun would also mean a spectularly high energy gravity wave hitting the earth.
You might be dead before even realizing that anything is off...
Would that wave be that destructive? I can definitely see it screwing up the orbits of Jupiter's moons, maybe even our own moon, but would it be much worse than a small earthquake?
The Sun's gravity at Earth's distance is only 0.0059m/s². I'm not exactly certain about how the magnetude of a gravity wave relates to the magnetude of the static force, but even if the force fluctuates rapidly at ten times the static force, that's less than a hundredth of a g; enough to be perceivable but you wouldn't even loose your balance.
I thought the same after writing the gravity wave comment. Really not sure what the effects would be and the equations involved are far from intuitive...
Is Randall doing new What-If stuff? I have only seen old articles on his website recently.
There is a really great short story by Larry Niven based on a similar premise:
"Inconstant Moon"
There is also an "Outer Limits" episode based on this. I watched that before knowing the short story and it is one of only 2 or three OL episodes that I still have an active memory of...
There's a pretty cool short story where a guy is looking at the full moon and he realizes that it's gotten way too bright, and that could only happen because the sun has just spontaneously exploded, and he basically just makes peace with the fact that the world is going to be destroyed very shortly.
Assuming its midday, and the moon is on or near the horizon, it would actually still be seen for an additional 1.3 seconds after we see the sun disappear. If its high in the sky however, it would disappear only a few ms after the sun, unless it was in a full or partial eclipse, where it would disappear at the same time to our eyes.