The Cavendish Experiment To Measure the Gravitational Constant, G

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Cavendish Experiment: Torsion Fiber. Image by Kossi Physics

The Cavendish experiment uses two small but equal masses at the ends of a light horizontal bar that is suspended on a wire and free to rotate in a horizontal plane. The wire acts as a torsion pendulum, which can rotate in a horizontal arc.

Cavendish carefully measured the position of these two masses when no horizontal gravitational forces acted on them. Then, Cavendish placed two larger masses close to the suspended masses.

The gravitational force the larger masses exert on the smaller masses cause the torsional pendulum to rotate a very small amount.

Measuring the rotation in the torsion pendulum allows the experimenter to calculate the force exerted between the smaller and larger masses.

Knowing the accurate masses and distances as well as the gravitational force allows calculating the value of G, the gravitational constant.

The gravitational force exerted between the larger masses and the smaller suspended masses is very small. Hence the angle that the torsion pendulum rotates is also very small and correspondingly difficult to measure.

To measure this small rotation, Cavendish used a small mirror mounted on the rotating wire. The reflection of a light source shining on this mirror, at a sufficient distance from the wire, moved far enough that Cavendish was able to measure the angle through which the torsion wire rotated.

As an analogy think of rotating a long straight pipe around one end. For even a very small rotational angle the opposite end of the pipe moves a larger distance.

Cavendish Did Not Actually Calculate G

Most physics books state that Cavendish performed the Cavendish experiment and measured the value of G, or the gravitational constant. However historical evidence suggests that Cavendish used the experiment to measure Earth’s density and did not actually calculate G – not until much later were Cavendish’s results used to calculate the value of G.

The Value of the Gravitational Constant

Diagram of the original Cavendish experiment. Image Credit: Henry Cavendish 1798.

Once physicists knew the value of G, they could measure accelerations of orbiting and falling objects to calculate the gravitational forces exerted by Earth and other astronomical objects. Physicists and astronomers can now use the gravitational forces to calculate the masses of Earth and other astronomical objects.

 

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