Cavendish experiment

The Cavendish experiment, performed in 1797–1798 by English scientist Henry Cavendish, was an important test to measure the pull of gravity between small objects in a lab. This was the first time scientists could find how strong gravity is between masses they could hold and study.

Cavendish's diagram of his torsion pendulum, seen from above. The pendulum consists of two small spherical lead weights (h, h) hanging from a 6-foot horizontal wooden beam supported in the center by a fine torsion wire. The beam is protected from air currents inside a wooden box (A, A, A, A). The two large weights (W, W) attached to a separate suspension attract the small weights, causing the beam to rotate slightly. The rotation is read off of vernier scales (S) at either end of the rod. The large weights can be rotated to the other side of the torsion beam (w, w), causing the beam to rotate in the opposite direction.

The idea for the experiment came from another scientist, John Michell, who built a special tool called a torsion balance to do the test. Sadly, Michell passed away before he could finish it. After his death, the tool was given to Francis John Hyde Wollaston and then to Cavendish. Cavendish used the tool, making some changes but staying close to Michell’s plan, and did many tests to get good results.

Cavendish shared what he found in 1798 in a science journal called the Philosophical Transactions of the Royal Society. His work helped scientists learn more about how heavy objects pull each other together and gave important numbers that describe Earth’s weight and how gravity works.

The experiment

Vertical section drawing of Cavendish's torsion balance instrument including the building in which it was housed. The large balls were hung from a frame so they could be rotated by a pulley from outside. Figure 1 of Cavendish's paper

Henry Cavendish created a special tool called a torsion balance to measure the pull of gravity between objects. It had a long wooden rod with small lead balls at each end and big lead balls that could be moved close to the small ones. By watching how much the rod moved when the big balls were near, Cavendish could figure out how strong gravity’s pull was between them.

He found that the Earth is about 5.5 times as heavy as water. His careful measurements showed that Earth likely has a dense, metallic center, which helped scientists understand more about our planet.

Reformulation of Cavendish's result to G

The idea of using a special number to describe gravity, called the gravitational constant, didn’t become common until much later. One of the first mentions of this number was in 1873, 75 years after Cavendish did his experiment.

Cavendish didn’t use this special number. Instead, he talked about how heavy the Earth is. He called his work “weighing the world.” Later scientists changed his results to match today’s way of thinking.

After changing Cavendish’s numbers to today’s measuring system, his guess for how heavy the Earth is gives a value for the gravitational constant that is very close to what scientists use now. Back then, scientists measured weight and mass the same way, so they didn’t need a special number for gravity. Instead, they focused on learning how heavy the Earth was. This was a big mystery back then, and scientists had tried to measure it before, like in the Schiehallion experiment in 1774.

Derivation of G and the Earth's mass

This section explains how scientists today can understand the results from Cavendish's experiment. They use a special balance to measure tiny forces between masses. By watching how the balance moves, they can find a number called the gravitational constant, or G.

Once G is known, scientists can figure out the mass and density of the Earth by looking at how things fall and using simple math.

Symbol	Unit	Definition
θ {\displaystyle \theta }	radians	Deflection of torsion balance beam from its rest position
F	N	Gravitational force between masses M and m
G	m³ kg⁻¹ s⁻²	Gravitational constant
m	kg	Mass of small lead ball
M	kg	Mass of large lead ball
r	m	Distance between centers of large and small balls when balance is deflected
L	m	Length of torsion balance beam between centers of small balls
κ {\displaystyle \kappa }	N m rad⁻¹	Torsion coefficient of suspending wire
I	kg m²	Moment of inertia of torsion balance beam
T	s	Period of oscillation of torsion balance
g	m s⁻²	Acceleration of gravity at the surface of the Earth
M_earth	kg	Mass of the Earth
R_earth	m	Radius of the Earth
ρ {\displaystyle \rho } _earth	kg m⁻³	Density of the Earth

The experiment

Reformulation of Cavendish's result to G

Derivation of G and the Earth's mass

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