Why does an astronaut appear to be weightless in a satellite orbiting the Earth?

Question

BlackTom AI · Accepted Answer

Objects in orbit are in continuous free fall toward Earth while moving sideways fast enough that their path curves around the planet rather than hitting it.

1) Relevant concepts
- Gravity provides a downward (centripetal) acceleration a = GM/r^2 toward Earth's center.
- "Weight" felt by a person is the contact (normal) force from a surface; apparent weight is zero if there is no contact force.
- In orbit both the spacecraft and the astronaut accelerate at the same rate under gravity, so there is no contact force between them.

2) Step‑by‑step reasoning
- The spacecraft and astronaut experience the same gravitational acceleration a = GM/r^2, so they fall together.
- Because they fall together, the astronaut does not press on the floor of the spacecraft; the normal force is zero.
- With zero normal force, the astronaut feels weightless even though gravity is still acting.

3) Calculations (intermediate steps)
- Use a = g (Re/r)^2 to compare gravity at altitude. For the ISS ≈ 400 km above Earth:
  Re = 6.371×10^6 m, r = Re + 400×10^3 m = 6.771×10^6 m.
  (Re/r)^2 = (6.371/6.771)^2 ≈ 0.941^2 ≈ 0.885.
  a ≈ 9.81 m/s^2 × 0.885 ≈ 8.69 m/s^2.
- Gravity at orbital altitude is therefore still strong (≈8.7 m/s^2), so the astronaut is not free of Earth's gravity — instead both astronaut and station accelerate together.

4) Why the correct answer is correct
- Option c states the astronaut is in a constant state of free fall. That matches the physical situation: orbit is sustained free fall with the required centripetal acceleration provided by gravity, producing no contact force and thus apparent weightlessness.

5) Why the other choices are incorrect
- a: Incorrect — the astronaut is accelerating (centripetal acceleration toward Earth).
- b: Incorrect — mass does not vanish in space; mass is intrinsic and remains.
- d: Incorrect — the Moon does not provide a compensating opposite force equal to Earth's; gravitational forces from other bodies are negligible for the local weightless effect and do not cancel Earth’s pull.
- e: Incorrect — Earth’s gravity at orbital altitudes is still substantial (see calculation), so the astronaut is affected by gravity.

6) Conclusion
Therefore the correct answer is c. The astronaut is in a constant state of free fall. This explanation confirms the provided answer.

Why does an astronaut appear to be weightless in a satellite orbiting the Earth?Single choice

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