Show that the gravitational potential at the surface of the Earth is -64 MJ kg-1, given the surface gravitational feild strength is 9.8 N kg-1 and the mean radius of the Earth is 6400 km.
Gravitational potential is the work required to move a mass from a point to infinity.
g varies by 1/r^2 above the surface of Earth.
GP=INT g*(re/r)^2dr=INT gre^2/r^2 dr= -gre^2/r limits
GP= -gre^2(1/re -1/inf)=g*re
GP=-9.8N/kg * 6.4E6=about -64E6 J/kg