The International Space Station has a mass of 4.19 x 105 kg and orbits at a radi

Question

The International Space Station has a mass of 4.19 x 105 kg and orbits at a radius of 6.79 x 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 a 72.5 kg astronaut living inside the station. HINT (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 ) (c) the weight (in N) of an 72.5 kg astronaut living inside the station Need Help? Read ItWatch It

Explanation / Answer

Given that,

m = 4.19*10^5 kg

r = 6.79*10^6 m

mass of earth, M = 6*10^24 kg

(a)

Gravitational force exerted by earth,

F = GMm / r^2

F =  6.67 *10^(-11) * 6*10^24 * 4.19 *10^5 / (6.79*10^6)^2

F = 3.63*10^6 N

(b)

Gravitational PE = GMm / r = F*r

PE = 3.63*10^6 * 6.79*10^6

PE = 2.46*10^13 J

(c)

Gravitational acceleration,

g = GM / r^2

g =  6.67 *10^(-11) * 6*10^24 / (6.79*10^6)^2 = 8.64 m/s^2

Weight of astronaut,

W = mg = 72.5*8.64

W = 626.4 N

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