Answer:
[tex]r = 5.13 \times 10^6[/tex]
Explanation:
As we know that the centripetal force for the space shuttle is due to gravitational force of earth due to which it will rotate in circular path with constant speed
so here we will have
[tex]\frac{mv^2}{r} = \frac{GMm}{r^2}[/tex]
here we know that
v = 19800 mi/h
[tex]v = 19800 \frac{1602 m}{3600 s}[/tex]
[tex]v = 8811 m/s[/tex]
also we know that
[tex]M = 5.97 \times 10^{24} kg[/tex]
now we will have
[tex]r = \frac{GM}{v^2}[/tex]
[tex]r = \frac{(6.67 \times 10^{-11})(5.97 \times 10^{24})}{(8811)^2}[/tex]
[tex]r = 5.13 \times 10^6[/tex]
