Did Cavendish Calculate G

Calculate the gravitational constant (G) using parameters similar to Cavendish’s historic 1798 experiment

Did Cavendish Calculate G? The Historic Experiment That Measured Earth’s Mass

Henry Cavendish’s 1797-1798 experiment stands as one of the most elegant and groundbreaking measurements in the history of physics. While often described as “weighing the Earth,” Cavendish’s primary achievement was the first accurate measurement of the gravitational constant (G), which appears in Newton’s law of universal gravitation:

F = G × (m₁ × m₂) / r²

The Cavendish Experiment: How It Worked

The apparatus consisted of:

• A torsion balance with a 1.8-meter wooden rod
• Two small lead spheres (0.73 kg each) attached to the rod’s ends
• Two large lead spheres (158 kg each) positioned nearby
• A delicate fiber for suspension and measurement

The gravitational attraction between the large and small spheres caused the rod to twist slightly. By measuring this twist angle (about 0.15 degrees) and knowing the torsion constant of the fiber, Cavendish could calculate the gravitational force and thus determine G.

Historical Context and Significance

1. Newton’s Dilemma: While Newton formulated the law of gravitation in 1687, he couldn’t measure G because gravitational forces between small objects are extremely weak.
2. Cavendish’s Innovation: The torsion balance was sensitive enough to detect forces equivalent to about 1/50,000,000 of the small spheres’ weight.
3. Earth’s Density: Using his G value (6.74 × 10⁻¹¹ N·m²/kg²), Cavendish calculated Earth’s density as 5.48 times that of water – remarkably close to modern values.

Comparison With Modern Values

Measurement	Cavendish (1798)	CODATA 2018	Relative Difference
Gravitational Constant (G)	6.74 × 10⁻¹¹	6.67430 × 10⁻¹¹	+1.0%
Earth’s Density	5.48 g/cm³	5.51 g/cm³	-0.5%
Earth’s Mass	5.98 × 10²⁴ kg	5.972 × 10²⁴ kg	+0.1%

Common Misconceptions About the Experiment

Several myths persist about Cavendish’s work:

• Myth 1: “Cavendish was trying to find Earth’s mass” – Actually, he was measuring G, though his results did enable Earth’s mass calculation.
• Myth 2: “The experiment was done in a vacuum” – While later versions used vacuums to eliminate air currents, Cavendish’s original experiment was conducted in a sealed room with careful temperature control.
• Myth 3: “The apparatus was completely still” – Cavendish actually measured the oscillation period of the balance to account for the fiber’s natural torsion.

Modern Replications and Improvements

Cavendish’s experiment has been replicated with increasing precision:

Year	Researcher	Method	G Value (×10⁻¹¹)	Uncertainty
1798	Cavendish	Torsion balance	6.74	1%
1895	Boys	Improved torsion balance	6.658	0.12%
1942	Heyl	Quartz fiber balance	6.670	0.03%
2018	CODATA	Multiple methods	6.67430	0.00022%

Why Measuring G Remains Challenging

Despite being a fundamental constant, G is notoriously difficult to measure precisely because:

1. Gravitational forces between laboratory-sized masses are extremely weak (about 10⁻⁷ N for Cavendish’s setup)
2. Local gravity gradients from nearby objects can interfere with measurements
3. The experiment requires extraordinary sensitivity to thermal, seismic, and electromagnetic disturbances
4. Systematic errors from apparatus geometry and material properties are difficult to eliminate

Authoritative Sources on Cavendish’s Experiment

For further reading from academic sources:

• NIST Fundamental Physical Constants (U.S. Government) – Official CODATA values for G and other constants
• American Institute of Physics: Cavendish Experiment – Historical documents and analysis
• University of Washington Eöt-Wash Group – Modern precision measurements of G

The Experiment’s Lasting Legacy

Cavendish’s work represents:

• The first precise determination of a fundamental constant in physics
• Experimental confirmation of Newton’s inverse-square law at small scales
• A foundational technique (torsion balance) still used in modern physics
• The beginning of precision gravitation experiments that continue today

The experiment’s elegance lies in its simplicity – using only lead weights, a wooden rod, and a fiber, Cavendish revealed one of nature’s deepest secrets. His measurement of G not only confirmed Newtonian gravity but also paved the way for Einstein’s later work on general relativity, where G plays a central role in describing the curvature of spacetime.