5. -11 points MI14 6.8.062. My Notes You will need to use the Momentum Principle

Question

5. -11 points MI14 6.8.062. My Notes You will need to use the Momentum Principle to do the first part of this problem, and the Energy Principle to do the second part. A satellite of mass 4500 kg orbits the Earth in a circular orbit of radius of 7.5 x 106 m (this is above the Earth's atmosphere).The mass of the Earth is 6.0 × 1024 kg What is the speed of the satellite? m/s What is the minimum amount of energy required to move the satellite from this orbit to a location very far away from the Earth? Additional Materials section 6.8

Explanation / Answer

(a)

According to momentum principle,

GMm / r^2 - mv^2 / r = 0

mv^2 / r = GMm / r^2

v = sqrt (GM / r)

v = sqrt [(6.67*10(-11)*6*1024) / (7.5*106)]

v = 7304.8 m/s

(b)

From energy conservation principle,

Energy to move the satellite,

E = GMm / r - (1/2)mv^2

E = (6.67*10-11*6*1024*4500 / 7.5*106) - ((1/2)*4500*(7304.8)^2)

E = 1.2*10^11 J

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