Gravity: Not Proportional to Inverse Square?

[pantheid]

Hi, a long time ago, back in high school, I remember my teacher was explaining the force of gravity to us. He gave us the equation for the force of gravity, which was proportional to the inverse square of the distance. However, he later said that something about Einstein and other researchers had shown that it was actually proportional to something along the lines of 2.000006 (if memory serves), but I have not been able to find any such material online, and no other professor in college has even mentioned such a thing. Is my memory of the class faulty, is he mistaken, or is this some arcane knowledge that is interesting but unimportant?

 

[yuiop]

The coordinate acceleration due to gravity in Schwarzschild coordinates is:

$\frac{d^2r}{dt^2} = \frac{M}{r^2} \left(1-\frac{2GM}{rc^2}\right)$

The acceleration measured locally at r is:

$\frac{d^2r'}{d\tau^2} = \frac{M}{r^2} \frac{1}{\sqrt{1-\frac{2GM}{rc^2}}}$

I will leave it to you to substitute the mass and radius of the Earth for M and r and see how the Newtonian prediction differs from the GR prediction at the Earth's surface.