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If gravitation is negligible for small masses, then how was Cavendish's experiment a success since the balls used were very small compared to the sizes of celestial objects?

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    $\begingroup$ Even today, we only know the gravitational constant G to ~4 significant digits. You may enjoy Bending Spacetime in the Basement, by AutoDesk founder, John Walker. $\endgroup$
    – PM 2Ring
    Commented May 26 at 11:48
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    $\begingroup$ The gravitation of small masses is negligible in the presence of a much larger mass (as in the case of a satellite orbiting the earth, for example). In the Cavendish experiment, there are no celestial bodies involved. $\endgroup$
    – paulina
    Commented May 26 at 11:51
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    $\begingroup$ It depends on how negligible negligable is. $\endgroup$
    – Lee Mosher
    Commented May 26 at 23:31
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    $\begingroup$ Just read the original paper. $\endgroup$
    – my2cts
    Commented May 27 at 5:20
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    $\begingroup$ @paulina the Cavendish experiment was pretty down-to-Earth, meaning in the vicinity of Earth. Does it count as a celestial body? $\endgroup$ Commented May 27 at 10:10

4 Answers 4

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  1. Of course Cavendish had to put those small masses much closer together than celestial objects (usually) are. But that was not enough...
  2. The masses to detect the force had to be suspended by a long thin wire to allow for almost unimpeded movement and make them very sensitive. But that also was not enough...
  3. He then had to move the other pair of masses back and forth periodically to get the detector masses into resonant motion. Only then was the effect big enough to see.

Note that Cavendish did not use a light beam deflected by a mirror to detect the movement, which is often part of modern versions of his experiment. If you have a steady beam of light this can make the experiment even more sensitive. But at the time of the original experiment, with candle light or light from a moving Sun, this would not have been very practical.

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    $\begingroup$ I've not read Cavendish's paper, but all reports of it I've seen say that he measured the equilibrium displacement of the 'inner' (moving sphere) assembly, using a vernier and telescopes, contradicting your (3). [The dynamic part of the experiment was measuring the period of natural oscillations of the inner assembly in order to determine the torsional constant of the suspension.] $\endgroup$ Commented May 26 at 15:32
  • $\begingroup$ I would gladly have added it as point 4). But most reports that I see mention it as present in the modern version but do not actually make that claim that Cavendish used it. This answer by Hedley Rokos extends the reasoning even further: quora.com/… "Had Cavendish had the light source available, he would still not have had the detectors and recording system, ..." $\endgroup$ Commented May 26 at 15:49
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    $\begingroup$ I'm not a physicist (so I'm not sure about this), but is another point that the closest celestial body (ie, earth) was exerting a force on the balls perpendicular to the force that Cavendish was? This let Cavendish turn earth's gravity into a part of the equilibrium state (in some sense, part of the calibration) instead of part of the noise he had to measure. $\endgroup$
    – yshavit
    Commented May 28 at 22:18
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    $\begingroup$ Still not enough: "To prevent air currents and temperature changes from interfering with the measurements, Cavendish placed the entire apparatus in a mahogany box about 1.98 meters wide, 1.27 meters tall, and 14 cm thick, all in a closed shed on his estate." Also, "[Millikan may have performed 'cosmetic surgery' on the data, but David Goodstein concluded that Millikan excluded no drops from this group of complete measurements. Reasons for a failure to generate a complete observation include annotations regarding the apparatus setup, oil drop production, and atmospheric effects]". aka control $\endgroup$
    – Mazura
    Commented May 29 at 9:35
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    $\begingroup$ @Mazura But what Millikan did shouldn't have any effect on the original Cavendish experiment, by causality. $\endgroup$ Commented May 29 at 9:39
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Gravitational forces are indeed negligible for small masses in everyday life. We just don't carry around with us detectors that are sensitive enough to register those forces, which are far far too small for us to feel with our own senses.

What Cavendish was the first to do was to invent a detector that was indeed sufficiently sensitive to measure those incredibly tiny forces.

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  • $\begingroup$ After years of implicitly assuming that gravitational forces between tabletop objects were just too small to ever be observed directly, it was astonishing for me to see, in real time, the tiny but inexorable attraction between a depleted uranium source mass and a test mass at the end of a torsion pendulum. $\endgroup$
    – Buzz
    Commented May 29 at 0:00
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    $\begingroup$ @buzz, yes it is cool, isn't it? $\endgroup$ Commented May 29 at 0:01
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    $\begingroup$ The apparatus (and knowing when it's being affected by things you're not trying to measure) is everything, +1. Which is why he put it in a box, in a shed, and viewed it with a telescope. And why Millikan discarded some data. en.wikipedia.org/wiki/Oil_drop_experiment $\endgroup$
    – Mazura
    Commented May 29 at 9:43
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To make a more general point, "negligible" is not the same thing as "non-existent". What allows anything to be negligible is the context. There is nothing that is universally negligible, otherwise we would never know about it anyway (I suppose I should say we can't know about anything that is universally negligible). The context can be determined on physical grounds, but also on grounds of what the goal of your analysis is; essentially how good is "good enough".

For the Cavendish experiment, of course the effects that were being measured were not negligible, otherwise nothing would have been observed. However, if you are worried that you will get in a car crash due to the gravitational attraction between your car and the cars around you, then there is no need to worry since those forces are indeed negligible in the context of normal driving.

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Torsion balances are exquisitely sensitive, so Cavendish was able to measure a force between two small objects that would be considered negligible in any ordinary context.

“Negligible” is always in context, and it does not mean zero nor does it necessarily mean impossible to measure.

As far as I know, there is no consensus as of now that there is some amount of gravity that is theoretically impossible to measure, but open to correction on that point.

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  • $\begingroup$ A limit on the Cavendish experiment would be the Casimir effect. $\endgroup$
    – user71659
    Commented May 29 at 17:44

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