Does anyone know the MOST accurate measurement of escape velocity?

Does anyone know the MOST accurate measurement of escape velocity?
On Earth? At the surface of the Earth, or at high altitude?
Wherever. Any precision data on escape velocity would be appreciated. I know escape velocity is kind of a ``loose'' concept (i.e. it's not something that is likely to be tested precisely), but I thought I'd at least ask.
Some guy named zanket in another forum thinks that GR is wrong, and has derived (well, not derived at all, actually) a new equation for escape velocity. It seems he won't be deterred by other precision tests of GR, so I am trying to beat him at his own game.
This is, of course, futile. I have already explained to him that he has violated Lorentz Invariance (crackpots ALWAYS violate Lorentz Invariance), but he has not accepted these arguments.
I am a sucker for punishment, I guess.
Alright, this is just for fun, and not very theorhetical:
Geosynchronous Satellites are known to orbit the Earth at 35,786 km altitude.
Earth's diameter at the Equator (over which geosynchronous satellites orbit) is: 12,756 km so the Earth's radius is 12756/2 = 6328
So, their distance from the Earth's core is 6328 + 35786 = 42114 km
2 * Pi * r = 2* 3.14 * 42114 = 264476 km = The distance around their orbit.
We know that their orbit is circular (has to be or they'd speed up and slow down at different times of day), so they're pretty much going 264476 km per day.
So 264476/24 = 11020 km/hour
So, at a radius of 42114 km , orbital velocity is observed to be 11020 km/h
Not very mathematical, but it's kind of hard to argue very determinedly against direct observation.
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