Question

Calculate the acceleration due to gravity at a depth 384 km from the surface of the earth

Answer 1

The acceleration due to gravity is given by

$$g=G\frac{M}{R^2}=G\frac{M}{(R_{\rm Earth}-h)^2}$$

$$M=\rho V=\frac{4}{3}\pi\rho (R_{\rm Earth}-h)^3$$

$$g=\frac{4}{3}\pi\rho G (R_{\rm Earth}-h)\\$$

$$=\frac{4}{3}*3.14*5510*6.67*10^{-11}*(6378-384)*10^3\\=9.2\:\rm m/s^2$$