The international space stations (ISS) orbits the earth once every 92.0 min. Ass

Question

The international space stations (ISS) orbits the earth once every 92.0 min. Assuming that the ISS has a circular orbit: A) find the radius of the ISS orbit. How high above the surface of the earth is the ISS? B) find the tangential velocity of the ISS C) what is the centripetal acceleration of the ISS as it orbits earth? The international space stations (ISS) orbits the earth once every 92.0 min. Assuming that the ISS has a circular orbit: A) find the radius of the ISS orbit. How high above the surface of the earth is the ISS? B) find the tangential velocity of the ISS C) what is the centripetal acceleration of the ISS as it orbits earth? A) find the radius of the ISS orbit. How high above the surface of the earth is the ISS? B) find the tangential velocity of the ISS C) what is the centripetal acceleration of the ISS as it orbits earth?

Explanation / Answer

A)

T = time period = 92 min = 92 x 60 = 5520 sec

r = radius of orbit = ?

M = mass of earth = 5.98 x 1024 kg

using lepler's third law

T2 = 42 r3 /(GM)

(5520)2 = 4 (3.14)2 r3 /((6.67 x 10-11) (5.98 x 1024))

r = 6.75 x 106 m

R = radius of earth = 6.37 x 106 m

h = height above the surface of earth

h = r - R = (6.75 x 106) - (6.37 x 106) =

h = 3.8 x 105 m

B)

orbital velocity is given as

v = sqrt(GM/r)

v = sqrt((6.67 x 10-11) (5.98 x 1024)/(6.75 x 106))

v = 7.7 x 103 m/s

c)

centripetal acceleration is given as

a = v2/r

a = (7.7 x 103)2/(6.75 x 106)

a = 8.8 m/s2

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