For a satellite to orbit around the earth, which of the following must be true 

Time period  $\text{T}=\frac{2\pi }{\sqrt{\text{GM}}}\text{r}\sqrt{\text{r}}$   $\text{ g}=\frac{\text{GM}}{{\text{R}}^{\text{2}}}\Rightarrow {\text{ g}}_{\text{h}}=\frac{\text{GM}}{{\text{r}}^{\text{2}}}=\frac{\text{GM}}{{\left(\text{R}+\text{h}\right)}^{\text{2}}}$

$\text{T}=2\pi \sqrt{\frac{\text{r}}{{\text{g}}_{\text{h}}}}$

$\text{If h}<<\text{R, r}={\text{R, T}}_{\text{min}}=2\pi \sqrt{\frac{\text{R}}{\text{g}}}<2\pi \sqrt{\frac{\text{r}}{{\text{g}}_{\text{h}}}}$

                   ${\text{g}}_{\text{h}}={\text{g}}_{\text{e}}$

If h increases, T increases