Question

At what height above the surface of the earth , does the weight of an object decrease to 0.8 of the original

Answer 1

$$g=\dfrac{GM}{R^2},\\\space\\ g_n=0.8g=\dfrac{0.8GM}{R^2}=\dfrac{GM}{R^2_n},\\\space\\ R_n=\dfrac{R}{\sqrt{0.8}}=7127\text{ km},$$

which corresponds to a height above the Earth's surface of

$$H=R_n-R=752\text{ km}.$$