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The ISS orbits just 400 km up, where Earth's gravity is still about 8.7 m/s² — nearly full strength. So why do the astronauts inside float around weightless? Have they escaped gravity, or is something sneakier going on?
The ISS orbits just 400 km up, where Earth's gravity is still about 8.7 m/s² — nearly full strength. So why do the astronauts inside float around weightless? Have they escaped gravity, or is something sneakier going on?
They haven't escaped gravity — they're in permanent free fall, falling toward Earth while moving sideways so fast (~7.7 km/s) that the surface curves away just as fast. This is Newton's apple insight: the Moon is falling too, just fast enough to fall around the Earth instead of into it.
Every pair of masses attracts. The force grows with each mass and falls off with the SQUARE of the distance between their centres. This one law governs the apple, the ISS, the Moon, the planets, and galaxy clusters alike.
The inverse-square law is the heart of it: double the distance and the force drops to a quarter; triple it and to a ninth — but it never quite reaches zero. For any circular orbit gravity is the centripetal force, so . The orbiting mass m₂ cancels, leaving v = √(Gm₁/r) — orbital speed depends only on the central mass and the radius, never on the satellite. At Earth's surface this gives g = GM_E/R_E² ≈ ; at the ISS (r ≈ 6.8×10⁶ m) still ≈ . Astronauts float not because gravity is gone but because the whole station is in free fall — it and everything inside accelerate downward together, leaving no contact force. **Limiting case:** near Earth's surface is nearly constant, so collapses to the familiar with — the everyday law is the close-range limit of the universal one. **Connect it:** an orbit is free fall that keeps missing: the Moon accelerates toward Earth at exactly as predicts at 60 Earth radii — Newton's own check.
Thinking gravity needs contact or switches off in space — it's an inverse-square force between ANY two masses that weakens with distance but never reaches zero.