[revelation]

As [1] suggests, the best possible time for that distance would still be 82 ms.

[1]: http://www.wolframalpha.com/input/?i=as+the+crow+flies+from+...

[abecedarius]

54 ms for neutrinos taking the chord through the Earth (using 0.22 from your result). (That's only 4ms faster than light through vacuum along the great circle. Disappointing.)

http://www.wolframalpha.com/input/?i=2+*+sin+%280.5+*+0.22+*...

[sliverstorm]

What, are we not allowed to be depressed that 10 years later we are still tied down by physics?