Cavenda: Weighing the World 1798
Relativity & Gravity arc, page 44 of 193. Back to The Pixelated Physics Universe
Who they are
Cavenda peers through a telescope at a twitching dumbbell, with the whole Earth balanced on the other end of the beam.
Cavenda is a character of the Relativity & Gravity arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
The physics
A torsion balance hangs a light arm with a small lead ball at each end. Large lead spheres brought close pull on the balls and twist the arm by a tiny angle; from that twist and the swing period you can work out the Earth's mean density. The gravity, twist and period relations below are the standard torsion-balance equations. Henry Cavendish's paper was read to the Royal Society on 21 June 1798, using a torsion balance devised by John Michell. He printed Earth's density as 5.48 times water; his own data give 5.448, and today's value is about 5.51.
$$ \begin{gathered} F = \frac{G M m}{r^{2}}, \qquad \kappa\theta = F L, \qquad T = 2\pi\sqrt{\frac{I}{\kappa}} \\ G = 6.674\,30(15)\times10^{-11}\ \mathrm{m^{3}\,kg^{-1}\,s^{-2}} \quad (\text{CODATA 2022}) \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $F$ | gravitational force between a large and a small ball | N |
| $G$ | gravitational constant | m³·kg⁻¹·s⁻² |
| $M,\ m$ | large and small masses | kg |
| $r$ | centre-to-centre distance | m |
| $\kappa$ | torsion constant of the wire | N·m/rad |
| $\theta$ | twist angle | rad |
| $L$ | lever arm | m |
| $T$ | swing period | s |
| $I$ | moment of inertia of the beam and balls | kg·m² |
Honest caveat: He reported Earth's density, not G. Today's G (CODATA 2022) is 6.67430(15) × 10⁻¹¹ m³ kg⁻¹ s⁻².
Sources
- Cavendish (1798) Experiments to determine the Density of the Earth, Phil. Trans. R. Soc. Lond. 88, 469
- NIST CODATA: Newtonian constant of gravitation
Crossovers
Cavenda meets Kelvinor (Kelvin's Age of the Earth). Cavenda weighed the Earth with a torsion balance and found its mean density. Kelvinor tried to date the Earth from its cooling. Cavenda's number held up; Kelvinor's age was far too short, partly because he did not know about radioactive heating and partly because he ignored convection in the mantle.
Cavenda meets Dark Matter Host (Gravitational Lensing / Invisible Mass). Cavenda measured gravity between lead spheres in a room. Dark Matter Host is seen only through gravity, from galaxies and lensing. Both lean on Newton's constant G, the weakest coupling on the bench.
Wear the lore
- Cavenda – Weighing the World 1798 Physics T-Shirt
- Related infographic poster: Eötvös' Balance – Plate 032 Physics Poster
Concept keywords: Weighing the World 1798, Cavenda, Relativity & Gravity, physics lore, Pixelated Physics