A satellite is moving in a low nearly circular orbit around the earth. Its radius is roughly equal to that…

$V\mathit{=}\sqrt{\frac{\mathit{G}\mathit{M}}{{\mathit{R}}_{\mathit{e}}}}$

From angular momentum conversation

$-\frac{GMm}{R_e}+\frac{1}{2}m{\left(\sqrt{\frac{3}{2}}V\right)}^2=-\frac{GMm}{R_{\max }}+\frac{1}{2}m{V}_{\min }^2$

From angular momentum conversation

$\sqrt{\frac{3}{2}}{\mathrm{VR}}_{\mathrm{e}}={\mathrm{V}}_{\min }{\mathrm{R}}_{\max }$

Eliminating  ${\mathrm{V}}_{\text{min }}$ from equation (i) and (ii) we get

$R_{\max }=3{\mathrm{R}}_{\mathrm{e}}$