I have some confusion about the potential energy created by a gravitational field.
http://ocw.mit.edu/courses/physics/8-01t-physics-i-fall-2004/assignments/ic_sol_w07d3_1.pdf
This link says that the energy of an object falling through the centre of the earth is $\frac{1}{2}mgR_e$. So shouldn't the energy required to lift an object to a height $h$ above the surface be $$ mMG(\frac{1}{2R_e}+\frac{1}{h})~~?$$ This is not consistent with the commonly used $$\frac{mMG}{h+R_e}.$$ Why does the potential energy decrease as you go higher?!