Level 1: A Pendulum Clock on the Space Station: Does It Run Slow?
Send up a spring clock instead.
A mass on a spring oscillates with a period of 1 s on Earth. The same spring and mass are taken aboard an orbiting space station and set oscillating. The period there is:
A spring's restoring force comes from its stretch, not from gravity. On Earth gravity only shifts the position the mass hangs at; it does not change how stiff the spring is, or how much mass has to be accelerated.
So the spring-and-mass system keeps its 1 s period in orbit, while a pendulum stops. That is why space stations measure an astronaut's mass with a spring device, not with a pendulum.
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