Gravitational Constant
The gravitational constant G is the proportionality factor in Newton's law of gravity:
Its measured value is G ≈ 6.674 × 10⁻¹¹ N·m²/kg². G is one of the fundamental constants of nature, alongside the speed of light c and Planck's constant h. Unlike those two, G is the least precisely measured of the fundamental constants — and the hardest to improve, because gravity is so weak.
Cavendish's Experiment
Newton's law allows you to predict ratios — the Moon's orbit relative to the apple's fall, Jupiter's period relative to Earth's — without knowing G itself. To measure G, you need to detect the gravitational force between objects whose masses you control. Henry Cavendish did this in 1798.
The apparatus: two small lead balls (each a few grams) mounted on opposite ends of a horizontal rod, suspended by a thin wire. Two larger lead balls (each about 150 kg) were brought close to the small balls, attracting them gravitationally. The slight rotation of the wire-suspended rod was measured optically by watching the deflection of a reflected light beam. The tiny angle, combined with the measured masses and distances, gave G — and allowed Cavendish to immediately calculate the mass of the Earth. (This is what Cavendish called his goal: "weighing the world.")
A Puzzle About G
Feynman notes the strange ratio between the gravitational attraction and the electrical repulsion between two electrons: 1 / 4.17 × 10⁴². This enormous number — more zeros than atoms in the observable universe — is a natural constant embedded in physics. Its origin is completely unknown. Some physicists have speculated it might be related to the age of the universe (measured in natural atomic time units), which would imply G is slowly changing as the universe ages. Calculations show this is very unlikely — if G had been 10% larger even 10⁹ years ago, the Sun would have been enormously brighter and Earth's oceans would have boiled. But the question of why G has the value it does is genuinely open.
Connections
- universal-gravitation — G appears in Newton's law
- four-fundamental-forces — G sets the strength of gravity relative to the other forces
- gravity-has-no-mechanism — we can measure G precisely but cannot explain its value