The International Space Station is orbiting at an altitude of about 370 km above the
earth's surface. The mass of the earth is 5.976 × 10
24
kg and the radius of the earth is
6.378 × 10
6 m.
(a) Assuming a circular orbit, what is the period of the International Space Station's
orbit?
(b) Assuming a circular orbit, what is the speed of the International Space Station in its
orbit
1
Expert's answer
2012-01-20T07:22:15-0500
(a)& Assuming a circular orbit, what is the period of the International Space Station's orbit?
The gravitation force is equal to the centripetal force:
GMm/r² = mV²/r, or GM/r = V².
T = 2pi*r / V V² = [ 2pi r / T ]² GM/r = [ 2pi r / T ]² 6.67*10^(-11) * 5.98*10^24 / [ (6.378*10^6 + 370*10³ ) ]³ = [ 2pi / T]² T = 5514s
(b)& Assuming a circular orbit, what is the speed of the International Space Station in its orbit
V = sqrt [ 6.67*10^(-11) * 5.98*10^24 / [ [ (6.378*10^6 + 370*10³ )] V = 7690 m/s.
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