Newton's G sets the absolute strength of gravity, but it had only ever been confirmed in the sky (orbits, the Moon's fall) — can you measure it on a tabletop, between two lab masses, and so weigh the Earth itself?
▶ Launch the interactive simulationHang a light beam carrying two small lead balls (mass m, half-arm L) from a thin torsion fibre. Bring two large lead balls (mass M) up beside the small ones at centre distance b, on opposite sides, so their pull twists the beam as a couple. Two observables pin down G without ever measuring the fibre's stiffness κ directly: the OSCILLATION PERIOD gives κ = 4π²I/T² (I = 2mL²), and the EQUILIBRIUM DEFLECTION balances the couple, κθ_eq = 2GMmL/b². Read the deflection by optical lever (a light beam off a mirror throws a spot a distance s = 2Dθ onto a far scale). Forward-model the real damped swing θ(t) = θ_eq[1 − e^(−t/τ)cos 2πt/T] with seeded reading noise; measure T from the peak spacing and θ_eq from the late-time mean.
the gravitational constant G = 6.674×10⁻¹¹ N·m²/kg² — recovered as G = 4π²b²Lθ_eq/(MT²) from only the apparatus geometry and the two measured numbers, NEVER from G or κ. The small mass m cancels entirely — it is never needed. With G in hand the lab inverts the surface field g = GM_⊕/R_⊕² to weigh the Earth: M_⊕ ≈ 6×10²⁴ kg and a mean density ~5.5× water — far denser than any surface rock, so the planet must hide a heavy core, exactly the conclusion Henry Cavendish drew in 1798 (building on John Michell's apparatus). The first time a fundamental constant of nature was extracted on a bench rather than from the heavens.