There are two equations from which a change in the gravitational potential energy U of the system of mass m and the earth can be calculated. One is u = mgy the other is U = -(Gm_e * m)/r_e (where m_e and r_e are the mass & radius of the earth respectivly). As shown the first equation is correct only if the gravitational force is a constant over the change in height Δy. THe second is always correct. Consider the difference in U between a mass at the earth's surface and a distance h above it using both equations, and find the value of h for which u = mgy is in error by less than 1%. Express this value of h as a fraction of the earth's radius, and also obtain a numerical value for it.
I thought something like this:
| GM_e * mh |
| -------------- - mgh | < .01
| r_e(r_e + h) |
I'm not sure if thats correct however.