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musickatia [10]
3 years ago
15

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.
Physics
1 answer:
Drupady [299]3 years ago
5 0

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

\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

Converting to mph

7670.01846\times \frac{3600}{1609.34}=17157.38529\ mph

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

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