Answer:
7.67001846 km/s or 17157.38529 mph
Explanation:
G = Gravitational constant = 6.67 × 10⁻¹¹ m³/kgs²
M = Mass of the Earth = 5.972 × 10²⁴ kg
m = Mass of satellite
v = Velocity of satellite
The distance between the Earth's center and the satellite is
r = 6371000+400000 = 6771000 m
As the centripetal force balances the force of gravity we have
[tex]\frac{mv^2}{r}=\frac{GMm}{r^2}\\\Rightarrow v=\sqrt{\frac{GM}{r}}\\\Rightarrow v=\sqrt{\frac{6.67\times 10^{-11}\times 5.972\times 10^{24}}{6771000}}\\\Rightarrow v=7670.01846\ m/s=7.67001846\ km/s[/tex]
Converting to mph
[tex]7670.01846\times \frac{3600}{1609.34}=17157.38529\ mph[/tex]
The velocity of the satellite is 7.67001846 km/s or 17157.38529 mph
