I think you'd end up hitting stuff if you tried to orbit at sea level.
However, if we assume you're talking about a hypothetical perfectly smooth "pool ball" planet.. well, I have no idea. I actually spent 10 minutes trying to find this on the web, but couldn't find a thing. I thoguht of trying to calculate it myself, but I don't know jack about physics. (Though I can discuss theoretical physics, I'm useless with the actual math of physics.)
Though I did find the following interesting fact: You'd have to travel at about 3% of lightspeed to make the signals on a cell phone have a doppler effect great enough to render the cell phones inoperable. (assuming you're on a 900mhz phone.)
That seems like something that'd amuse you, though I am unsure why I think that.