Question

What should be the speed of an artificial satellite moving on a circular orbit around the Earth at a distance of 400 km from the surface of the Earth? Express your answer in km / sec and also miles per hour. This exercise tells you that objects in space are typically moving very fast and gives you an idea of why the impact of a meteorite or comet on Earth can cause extinction level events. Just for fun, watch the movie "Deep impact" as a follow up to this exercise.

Answer 1

7.67001846 km/s or 17157.38529 mph

Step-by-step 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

`(mv^2)/(r)=(GMm)/(r^2)\\\Rightarrow v=\sqrt{(GM)/(r)}\\\Rightarrow v=\sqrt{(6.67* 10^(-11)* 5.972* 10^(24))/(6771000)}\\\Rightarrow v=7670.01846\ m/s=7.67001846\ km/s`

Converting to mph

`7670.01846* (3600)/(1609.34)=17157.38529\ mph`

The velocity of the satellite is 7.67001846 km/s or 17157.38529 mph