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 89.1 kg astronaut living inside the station. HINT

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

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

(c) the weight (in N) of an 89.1 kg astronaut living inside the station N

Answer 1

we will use the universal law of gravitation :

m1 and m2 are the masses of the two bodies and r is the distance between their center.

in the above case

M: the mass of the earth =

G: universal Gravitation constant =

m: the mass of space station

r: is the distance of the space station from the center of the earth, which is the radius of the orbit.

putting the values in the above equation we get.

_____________________________

b)

assuming the potential at infinite distance to be zero , the potential at a distance r for a body of mass M is given by

.

The potential V is nothing but the gravitational potential energy of a body of unit mass in the field of mass M.

for a body of mass m in this potential field, the potential energy is

in the problem, given

M: the mass of the earth =

G: universal Gravitation constant =

m: the mass of space station

r: is the distance of the space station from the center of the earth, which is the radius of the orbit.

putting these values we get

________________________________

c)

the weight of the astronaut would be , the force applied by the earth on the astronaut

here m: is mass of the astronaut.

[note: we may be tempted to think that the weight of astronaut would be "ZERO" in the space, as astronaut fell "weightlessness". but they feel weightlessness as the normal force on them from the ground is "zero", and this W is cancelled out by the centrifugal force due to their rotation around the earth, Necessarily they are in a free fall. if a body is in free fall, it would feel zero weight, it does not mean that its weight is zero.].