Question

Cine se pricepe????VA ROG

Answer 1

Răspuns:

Fie h altitudinea

La suprafata avem:

$G=mg=k\frac{M_pm}{R_p^2} \\ \\ g=k\frac{M_pm}{R_p^2}$

La altitudinea h avem:

$G'=m\frac{g}{2}=k\frac{M_pm}{(R_p+h)^2} \\ \\ g=2k\frac{M_pm}{(R_p+h)^2}$

Egaland ecuatiile obtinem:

$\frac{1}{R_p^2}=\frac{2}{(R_p+h)^2} \\ \\ R_p^2+2R_ph+h^2=2R_p^2 \\ \\ h^2+2R_ph-R_p^2=0 \\ \\ h=\frac{-2R_p\pm\sqrt{4R_p^2+4R_p^2}}{2} \\ \\ =\frac{-2R_p\pm2\sqrt2R_p}{2} \\ \\ (-1\pm\sqrt2)R_p \\ \\ -1-\sqrt2<0$

Dar h nu poate fi negativ

Deci $h=(\sqrt2-1)R_p=(\sqrt2-1)\times 6370\approx 2638.54~km$