Measurement of the Gravitational Constant (G)

The value of the universal gravitational constant G is determined experimentally, not derived theoretically, by directly measuring the (extremely small) gravitational force of attraction between two known masses separated by a known distance. Because gravity is so weak compared to the other forces acting in a lab (friction, air currents, electrostatic effects), this measurement requires an extraordinarily sensitive instrument: the Cavendish balance (also called a torsion balance).

The apparatus (Fig. 5.5) consists of a light, rigid rod suspended horizontally at its midpoint by a very thin, long vertical metallic fibre. Two small lead spheres of equal mass m are mounted at the two ends of this rod, and a small mirror is fixed to the suspension fibre so that a reflected beam of light can be used to precisely read off any twist of the fibre. Two much larger lead spheres, each of mass M, are then brought close to the two small spheres, one on each side, positioned so that each large sphere attracts its nearby small sphere with the same magnitude of force F but in a rotational sense that reinforces the other -- producing a net TORQUE on the rod (not a net force, since the two forces are equal and opposite but offset). This torque twists the suspension fibre until the fibre's own elastic restoring torque exactly balances the gravitational torque, at which point the rod comes to rest at some measured angle of twist. …