Write the equation and value of the orbital periodic time of a satellite revolving very close to the surface of the Earth.

The orbital period $T$ of a satellite revolving at a distance $r$ from the center of the Earth is given by $T = 2\pi \sqrt{\frac{r^3}{GM}}$.
For a satellite revolving very close to the Earth's surface,$r \approx R_e$ (the radius of the Earth).
Substituting $GM = gR_e^2$,we get $T = 2\pi \sqrt{\frac{R_e^3}{gR_e^2}} = 2\pi \sqrt{\frac{R_e}{g}}$.
Using $R_e \approx 6.4 \times 10^6 \ m$ and $g \approx 9.8 \ m/s^2$,we calculate:
$T = 2 \times 3.14 \times \sqrt{\frac{6.4 \times 10^6}{9.8}} \approx 6.28 \times 808 \approx 5074 \ s$.
Converting to minutes,$T \approx 84.6 \ \text{minutes}$.