[RadioAstronomer]

the Sun simply disappeared, would the Earth shoot off tangentally immediately, or would there be an 8.3 minute delay?

It would take 8.3 minutes. Here is a good link:

http://itss.raytheon.com/cafe/qadir/q629.html

[Southack]

"It would take 8.3 minutes."

If so, then the orbit of the Earth's plane must be centered around where the Sun was located 8.3 minutes ago (78,186 miles from its present location).

Yet is that what we observe??