Gravity at the Space Station: Zero or Just Free Fall?
During a school space quiz, a student argues that a 70 kg astronaut aboard the International Space Station, about 400 km above Earth's surface, must be weightless because gravity there is zero. Another student says the astronaut is in free fall, not beyond gravity. The teacher gives Earth's radius as 6400 km, surface g as 9.8 m/s², and geostationary orbit height as 35,786 km. The students must compare the astronaut's weight at the ISS with the surface weight and with the weight at geostationary height. They also must explain why a spring balance calibrated in newtons would read nearly zero inside the orbiting station even though gravitational force still acts. The club wants a calculation-backed verdict and a decision on whether the phrase 'zero gravity' is scientifically acceptable.
1. Calculate g at the ISS and at geostationary orbit, and find the 70 kg astronaut's weight at each place. Use the ratio method and compare with the surface weight.
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Use g_h = g(R/(R+h))². At the ISS, R+h = 6400 + 400 = 6800 km, so the ratio is 6400/6800 = 0.941. Squaring gives 0.886, hence g = 9.8 × 0.886 = 8.68 m/s². Weight = 70 × 8.68 = 608 N, compared with 686 N on the surface. At geostationary orbit, R+h = 6400 + 35,786 = 42,186 km, ratio = 6400/42,186 = 0.1517, and its square is 0.0230. Thus g = 9.8 × 0.0230 = 0.225 m/s², and weight = 70 × 0.225 = 15.8 N. So the ISS astronaut still has about 88% of surface gravity, not zero. The inverse-square decrease is real but modest at 400 km.
2. Explain why the astronaut feels weightless and why a spring balance would read nearly zero. Is 'zero gravity' a correct description?
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The astronaut and the station are falling around Earth with nearly the same acceleration, so the floor does not need to push the astronaut. A spring balance measures the normal force or tension, not the gravitational force itself. With no support force, the balance reads zero. This is apparent weightlessness, often called microgravity. 'Zero gravity' is acceptable only as loose shorthand; scientifically it is wrong because Earth's gravitational force still provides the centripetal acceleration. If the station were somehow held stationary at that height, the astronaut would weigh about 608 N.
3. Would the astronaut's mass change between Earth and the ISS? Which quantity changes and why?
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Mass is the amount of matter and remains 70 kg everywhere in ordinary situations; it does not depend on g. Weight changes because weight is the gravitational force, W = mg, and g decreases with height. At the ISS, the astronaut's weight is about 608 N instead of 686 N. In orbit, the measured or apparent weight can be zero because of free fall, but the gravitational force is still present. The distinction matters: a balance that compares masses would still give 70 kg, while a spring scale calibrated in newtons would read nearly zero in the orbiting station.