To solve this problem we will begin by defining the given variables, since the problem presents repetitive cycles of phrases between the proposed variables.
According to the information presented, it is understood that the satellite altitude is:
[tex]h= 3.20*10^6 m[/tex]
Considering that the radius of the Earth is
r = [tex]6.38*10^6m[/tex]
And the mass of the Earth is
M = [tex]5.97*10^{24}[/tex]
The orbital time period of the satellite is given under the equation
[tex]T = 2\pi \sqrt{\frac{r^3}{GM}}[/tex]
Here,
G = Gravitational Universal constant
M = Mass of Earth
r = Radius
Considering that the radius that appears there is measured from the center of the earth to the height of the satellite, we must add the two positions to find the net distance. Replacing the period would be
[tex]T = 2\pi \sqrt{\frac{r^3}{GM}}[/tex]
[tex]T = 2\pi \sqrt{\frac{(6.38*10^6 + 3.20*10^6)^3}{(6.67*10^{-11})(5.97*10^{24})}}[/tex]
[tex]T= 9336.37s[/tex]
Therefore the orbital period of his GPS satellite is 9336.37s or 2 hours, 35minutes and 36.37seconds
