Problem 3. A satellite of mass 750 kg is in a circular orbit around the Earth at

Question

Problem 3. A satellite of mass 750 kg is in a circular orbit around the Earth at an altitude of 250 km. The air resistance the satellite encounters is small but significant. The resistance makes the satellite drop to a lower orbit (still circular) at an altitude of 100 km. (a) What is the change in the potential energy when the satellite moves from the higher to the lower orbit? (b) What is the change in the kinetic energy when the satellite moves from the higher to the lower orbit? (c) What is the change in the total energy when the satellite moves from the higher to the lower orbit? (d) What is the work done by friction on the satellite while it goes from one orbit to the other? (e) What is the work done by gravity on the satellite while it goes from one orbit to the other?

Explanation / Answer

1]a] Change in potential energy =mg [h2-h1]=750*9.8[250-100]*103 = 1.1*109J

b] when satellite at an altittude of 250 km

Vi=[GM/r+h1]1/2=[6.67*10-11*6*1024/[6.4*106+0.25*106]1/2= 7.76*103 m/s

when satellite at an altittude of 100 km

Vf=[GM/r+h2]1/2=[6.67*10-11*6*1024/[6.4*106+0.1*106]1/2= 7.85*103 m/s

Change in KE= 1/2m[Vf2-Vi2]=1/2*750*[(7.85*103)2-(7.76*103)2 ]= 0.527*109J

c]

Total energy at higher orbit=Pe+Ke

= mgh1+1/2mVi2

   = 750*9.8*250*103+1/2*750*(7.76*103)2=1.84*109+22.6*109=24.4*109J

Total energy at lower orbit =Pe+Ke

= mgh2+1/2mVf2

     = 750*9.8*100*103+1/2*750*(7.85*103)2=0.735*109+23.1*109=23.84*109J

Change in total energy=24.4*109J-23.84*109J=0.56*109J

d] work done by friction = change in total enery=0.56*109J

e] work done by gravity= change in potential energy=1.1*109J

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