## Essential University Physics: Volume 1 (3rd Edition)

We know equation 8.5: $U=GMm(\frac{1}{r_1}-\frac{1}{r_2})$ We must show that $U=mg\Delta r$, so we find: $GMm(\frac{1}{r_1}-\frac{1}{r_2})=mg\Delta r$ $GM(\frac{1}{r_1}-\frac{1}{r_2})=g\Delta r$ We know from the book the $\Delta r = r_1-r_2$, so we find: $GM(\frac{1}{r_1}-\frac{1}{r_2})=g( r_1-r_2)$ $g( r_1-r_2)=g( r_1-r_2)$