Answer:
7.57 km/s
Explanation:
The gravitational force on the satellite provides the centripetal force that keeps the satellite in circular orbit, so we can write:
[tex]\frac{GMm}{r^2}=m\frac{v^2}{r}[/tex]
where
G is the gravitational constant
[tex]M=5.98\cdot 10^{24}kg[/tex] is the Earth's mass
m is the satellite's mass
r = R+h is the distance of the satellite from the Earth's centre, where:
[tex]R=6371 km=6.37\cdot 10^6 m[/tex] is the Earth's radius,
[tex]h=590 km = 0.59\cdot 10^6 m[/tex] is the altitude of the satellite above Earth
v is the orbital speed of the satellite
Solving the equation for v, we find
[tex]v=\sqrt{\frac{GM}{r}}=\sqrt{\frac{(6.67\cdot 10^{-11} m^3 kg^{-1} s^{-2})(5.98\cdot 10^{24} kg)}{(6.37\cdot 10^6 m+0.59\cdot 10^6 m)}}=7570 m/s=7.57 km/s[/tex]
