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# Answer to Question #6048 in Mechanics | Relativity for Erica Evoli

Question #6048
The International Space Station is orbiting at an altitude of about 370 km above the earth&#039;s surface. The mass of the earth is 5.976 &times; 10 24 kg and the radius of the earth is 6.378 &times; 10 6 m. (a) Assuming a circular orbit, what is the period of the International Space Station&#039;s orbit? (b) Assuming a circular orbit, what is the speed of the International Space Station in its orbit
1
2012-01-20T07:22:15-0500
(a)& Assuming a circular orbit, what is the period of the International Space Station&#039;s
orbit?

The gravitation force is equal to the centripetal force:

GMm/r&sup2; = mV&sup2;/r, or GM/r = V&sup2;.

T = 2pi*r / V
V&sup2; = [ 2pi r / T ]&sup2;
GM/r = [ 2pi r / T ]&sup2;
6.67*10^(-11) * 5.98*10^24 / [ (6.378*10^6 + 370*10&sup3; ) ]&sup3; = [ 2pi / T]&sup2;
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*10&sup3; )]
V = 7690 m/s.

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