Chapter 06, Problem 23 A 6140-kg satellite is in a circular earth orbit that has

Question

Chapter 06, Problem 23 A 6140-kg satellite is in a circular earth orbit that has a radius of 2.43 x 107 m A net externa force must act on the sateliteto make t change to a circular orbit that has a radius of 7.40 x 106 m. What work must the net external force do? Note that the work determined here is not the work Wift done by the satellite's engines to change the orbit. Instead, the work w is w = wlift + wgravitational where w gravitational is the work done by the gravitational force. Units Number the tolerance is +/-2% Click if you would like to Show Work for this question: Open Show Work

Explanation / Answer

When the satellite goes from the first to the second orbit, its kinetic energy changes. The net work that the external force must do to change the orbit can be found from the work-energy theorem:

W = KEf - KEi

W = 1/2 [ mvf^2 - mvi^2]

we know v = sqrt(GMe/r]

put the value of v

W = m/2 * [ GMe/rf - GMe/ri]

W = GmMe/2 [ 1/rf - 1/re]

given rf = 7.4 x 10^6 m

ri = 2.43 x 10^7 m

Me = mass of earth = 5.98 x 10^24 kg

m = 6140 kg  

G = 6.67 x 10^-11

W = 1.15 x 10^11 J

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