The space shuttle enters the atmosphere traveling at a speed of roughly 8 km/s a

Question

The space shuttle enters the atmosphere traveling at a speed of roughly 8 km/s at an altitude of about 100 km, but by the time it lands its speed has decreased to about 100 m/s. Note that the gravitational potential energy of the earth-shuttle system also decreases during this process. However, the shuttle's temperature upon landing is not much larger than it was in space. (a) If the shuttle has a mass of 2 times 10^6 kg, how much total energy has to be converted to some other form? (b) Where must this energy go?

Explanation / Answer

a)

initial KE of the shuttle = 0.5*(2*10^6)*(8000)^2 = 6.4*10^13 J

initial gravitational PE of the shuttle = -GMm/r

= -6.67*10^-11*(5.97*10^24)*(2*10^6)/(6400000 + 100000)

= -1.225*10^14 J

final KE = 0.5*(2*10^6)*100^2 = 1*10^10 J

final PE = -6.67*10^-11*(5.97*10^24)*(2*10^6)/(6400000 ) =-1.244*10^14 J

So, change in energy of the system :

= ( 6.4*10^13 - 1.225*10^14 ) - (1*10^10 - 1.244*10^14)

= 6.59*10^13 J <------answer

b)

This energy must be lost to the atmosphere (in terms of sound enrgy + heat energy )

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