Răspuns:
Fie h altitudinea
La suprafata avem:
[tex]G=mg=k\frac{M_pm}{R_p^2} \\ \\ g=k\frac{M_pm}{R_p^2}[/tex]
La altitudinea h avem:
[tex]G'=m\frac{g}{2}=k\frac{M_pm}{(R_p+h)^2} \\ \\ g=2k\frac{M_pm}{(R_p+h)^2}[/tex]
Egaland ecuatiile obtinem:
[tex]\frac{1}{R_p^2}=\frac{2}{(R_p+h)^2} \\ \\ R_p^2+2R_ph+h^2=2R_p^2 \\ \\ h^2+2R_ph-R_p^2=0 \\ \\ h=\frac{-2R_p\pm\sqrt{4R_p^2+4R_p^2}}{2} \\ \\ =\frac{-2R_p\pm2\sqrt2R_p}{2} \\ \\ (-1\pm\sqrt2)R_p \\ \\ -1-\sqrt2<0[/tex]
Dar h nu poate fi negativ
Deci [tex]h=(\sqrt2-1)R_p=(\sqrt2-1)\times 6370\approx 2638.54~km[/tex]
