The International Space Station has a mass of 4.19 10 5 kg and orbits at a radiu

Question

The International Space Station has a mass of 4.19 105 kg and orbits at a radius of 6.79 106 m from the center of Earth. Find the gravitational force exerted by Earth on the space station, the space station's gravitational potential energy, and the weight of an 86.5 kg astronaut living inside the station.

(a)the gravitational force (in N) exerted by Earth on the space station (Enter the magnitude.)

(b)the space station's gravitational potential energy (in J)

(c)the weight (in N) of an 86.5 kg astronaut living inside the station

Explanation / Answer

M = mass of earth = 5.98 x 1024 kg

m = mass of ISS = 4.19 x 105 kg

r = distance between them = 6.79 x 106 m

Gravitational force is given as

F = GMm/r2

F = (6.67 x 10-11) (5.98 x 1024) (4.19 x 105)/(6.79 x 106)2  

F = 3.6 x 106 N

U = gravitational potential energy = - GMm/r = - (6.67 x 10-11) (5.98 x 1024) (4.19 x 105)/(6.79 x 106)

U = - 2.5 x 1013 J

c)

weight = F = 3.6 x 106

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