There are two equations from which a change it the gravitational potential energy U of the system of a mass m and the earth can be calculated. One is U = may (Eq. 7.2). The other is U = - GmEm/ r (Eq. 12.9). As shown in Section 12.3, the first equation is correct only if the gravitational force is a constant over the change it height 11 y. The second is always correct. Actually, the gravitational force is never exactly constant over any change in height, but if the variation is small, we can ignore it. Consider the difference it 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 Eq. (7.2) is it error by 1 %. Express this value of h as a fraction of the earth's radius, and also obtain a numerical value for it.