Thursday, October 25, 2018

Measuring the Universal Gravitation Constant

Vertical section of Cavendish balance

In 1798, the English physicist and chemist Henry Cavendish was the first to measure Newton's universal gravitational constant (G) using a spectacularly ingenious method, which has been scarcely improved later. The method was devised by John Michell, who died without being able to carry it out, so Cavendish performed the experiment. In fact, his objective was not to measure the constant, but the mass of the Earth, but the value of the constant could be inferred from the result.
Cavendish’s instrument was a torsion balance from which two identical balls of lead hung. Next to these balls, one on one side and one on the other, hung two much larger lead spheres, 175 kg each, which attracted the first two, producing a slight twist of the balance, which Cavendish could observe by means of a small telescope located outside the enclosure, to avoid observer interference. He thus detected a displacement of about 4 mm, which he measured with a precision of ¼ mm. This allowed him to calculate that the density of the Earth is 5.448 times greater than that of water, from which it is possible to deduce the mass of the Earth and the value of G:
This is the official value, which is known with quite a low accuracy (1 in 10,000), compared with other universal constants.
Cavendish’s experiment is still being used to measure the universal gravitational constant. Two recent experiments performed in China by a team directed by Luo Jun, using steel balls and vacuum chambers to prevent interference, has got the following results:
G=6.674184×10-11 ±11.64 ppm
G=6.674484×10-11 ±11.61 ppm
where ppm means parts per million. The uncertainty of the results of these two experiments is the lowest obtained so far when measuring G.
The value of G accepted previously, based on experiments carried out during the last 40 years, is the following:
G=6.67408×10-11 ±47 ppm
The two values obtained in the new experiments are, therefore, slightly above the generally accepted value, but have a much smaller uncertainty (about 4 times lower). The minimum uncertainty previously obtained among all the measurements taken (there have been many) was 13.7 ppm, slightly worse than that of the new experiments. In comparison, the uncertainty of the Cavendish experiment was 1%.
To understand the meaning of these numbers, we must remember three different statistical concepts which are used in measurements:
         Accuracy: distance between the measured value and the real value.
         Precision: ability of an instrument to give the same results in different measurements.
    Uncertainty: Applied to an instrument, we speak of calibration uncertainty. Applied to a specific measurement, it measures the dispersion of the values ​​obtained when performing several times the same experiment.
Accuracy and precision of a measurement
Note that measurements can be very precise but little accurate, and vice versa. This explains why the different measurements made of this constant, including the last two made by the Chinese team, do not match each other, in the sense that, if we convert them into intervals, they don’t overlap. So, the two previous measurements, converted to uncertainty intervals, would be:
(6.674106, 6.674262) y (6.674407, 6.674561)
It can be seen that both intervals are above the commonly admitted value, although one of them (the smallest) is totally included in the most probable interval considered above, while the other is outside and above that interval.
An article in Science News shows an explanatory graph that makes it possible to compare the results (accuracy and uncertainty) of the two new experiments with those previously made. It can be seen that the dispersion of the results is quite large, and that the intervals rarely overlap.
All this means that we must keep performing experiments.

The same post in Spanish
Thematic thread on Standard Cosmology: Preceding Next
Manuel Alfonseca

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