Question Number 104293 by aurpeyz last updated on 20/Jul/20
$$\mathrm{find}\:\mathrm{the}\:\mathrm{acceleration}\:\mathrm{of}\:\mathrm{gravity}\:\mathrm{at} \\ $$$$\:\mathrm{an}\:\mathrm{alitude}\:\mathrm{of}\:\mathrm{1000k} \\ $$
Answered by OlafThorendsen last updated on 20/Jul/20
$$\frac{{g}\left({z}\right)}{{g}_{\mathrm{0}} }\:=\:\left(\frac{\mathrm{R}}{\mathrm{R}+{z}}\right)^{\mathrm{2}} \\ $$$$=\:\left(\frac{\mathrm{6570}}{\mathrm{6570}+\mathrm{1000}}\right)^{\mathrm{2}} \:=\:\mathrm{0},\mathrm{753} \\ $$$${g}\left({z}\right)\:=\:\mathrm{9},\mathrm{81}×\mathrm{0},\mathrm{753}\:=\:\mathrm{7},\mathrm{39}\:\mathrm{m}/\mathrm{s}^{\mathrm{2}} \\ $$