Answer:
[tex]T=5065.66s[/tex]
Explanation:
The period of a satellite orbiting at a constant speed is given by:
[tex]T=2\pi\frac{r}{v}(1)[/tex]
Here, [tex]2\pi[/tex] is for one revolution, r is the radius of the circular motion and v is the speed of the satellite. Gravity acts on the satellite, which is responsible for the centripetal force.
[tex]g=a_c=\frac{v^2}{r}\\v=\sqrt{gr}(2)[/tex]
Replacing (2) in (1):
[tex]T=2\pi\frac{r}{\sqrt{gr}}\\T=2\pi\frac{6370*10^{3}m}{\sqrt{(6370*10^{3}m)9.8\frac{m}{s^2}}}}\\T=5065.66s[/tex]
