008 (part 1 of 3) 10.0 points A spacecraft of 71 kg mass is a circular orbit abo
ID: 1794850 • Letter: 0
Question
008 (part 1 of 3) 10.0 points A spacecraft of 71 kg mass is a circular orbit about the earth at a height of 2.4 RE. the radius of the earth is 6.33 × 100 m. about the earth? The acceleration of gravity is 9.81 m/s2 and What is the period of the spacecraft's orbit Answer in units of h. 009 (part 2 of 3) 5.0 points What is the spacecraft's kinetic energy? Answer in units of GJ. 010 (part 3 of 3) 8.0 points Express the angular momentum of the space- craft about the center of the earth in terms of its kinetic energy and find its numerical value. Answer in units of J s.Explanation / Answer
008.
Use Kepler’s third law,
T2 = [42/GM]*r3
r= (2.4 RE +RE) = 3.4RE = 3.4*6330*10^3 m
Plugging values,
T2 = [42/(6.67*10^-11*5.97*10^24)]*(3.4*6330*10^3)3
T=25084 s
T= 6.97 hr
009.
v=2r/T
v=(2*3.14*3.4*6330*10^3)/25084
v=5388.22m/s
KE=1/2mv^2=1/2*71*5388.22^2 = 1.03*10^9 J =1.03 GJ
010.
Angular momentum = L= mvr
L=mvr = ½*(2m)*v*(vT/2) = 2T*(1/2mv^2)/2
L= 2T*KE/2
Plugging values,
L= (2*25084)*(1.03*10^9)/(2*3.14) = 8.23*10^12 J.s
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