Answer:
8488 miles
Explanation:
The orbital period around an earth is given as:
[tex]T=2\pi \sqrt{\frac{r^3}{Gm} }[/tex]
Where G = constant = 6.67 x 10ˉ¹¹ N m² kgˉ², m = mass of object, T = period taken to round the earth, r = distance from the center of the earth to the orbiting object = radius of earth + orbital altitude.
Given that T = 7.84 hours = 28224 seconds, m = 5.972 x 10²⁴ kg, radius of earth = 3,958.8 miles = 6371071 m
[tex]T=2\pi \sqrt{\frac{r^3}{Gm} }\\\\squaring:\\\\T^2=4\pi^2 (\frac{r^3}{Gm} )\\\\r^3=\frac{GmT^2}{4\pi^2} \\\\r=\sqrt[3]{\frac{GmT^2}{4\pi^2} } \\\\r=\sqrt[3]{\frac{6.67*10^{-11}*5.972*10^{24}*(28224)^2}{4\pi^2} } \\\\r=20031232.62\ meters[/tex]
r = radius of earth + distance from the ISS to the surface of the earth
distance from the ISS to the surface of the earth = r - radius of earth
distance from the ISS to the surface of the earth = 20031232.62 meters - 6371071 meters = 13660161.62 meters
distance from the ISS to the surface of the earth = 13660161.62 meters = 8488 miles
