Talk:Newton's law of universal gravitation

G is the probabilistic effect of overall attraction

F = G \frac{m_1 m_2}{r^2}\ , where:

F is the force between the masses,
G is the gravitational constant (6.673×10−11 N·(m/kg)2),
m1 is the first mass,
m2 is the second mass, and
r is the distance between the centers of the masses.
Diagram of two masses attracting one another

— Preceding unsigned comment added by 2.84.213.243 (talk • contribs) 15:50, 18 December 2014 (UTC)

This formula is already explained in the article; I don't think the theory is "probabilistic". -- Beland (talk) 08:44, 18 May 2024 (UTC)

On the surface of a sphere of uniform density

As new section was added today by @Grufo but it has no references. All content needs to be verifiable, seeWP:BURDEN. Johnjbarton (talk) 00:53, 20 July 2024 (UTC)

All content needs to be verifiable: It is high school math, easily verifiable by a large audience. Here you go.

A volume is equal to a mass divided by a density:

$V={\frac {m}{\rho }}$

If the body is a sphere, its volume is also equal to:

$V={\frac {4}{3}}\pi r^{3}$

Therefore, in a sphere of uniform density the following equation holds true:

${\frac {m}{\rho }}={\frac {4}{3}}\pi r^{3}$

And so:

$m={\frac {4}{3}}\pi \rho r^{3}$

If we take a gravitational acceleration on the surface of a sphere

$A=G{\frac {m}{r^{2}}}$

and replace $m$ with ${\frac {4}{3}}\pi \rho r^{3}$, we obtain

$A={\frac {4}{3}}\pi G\rho r$

Similarly, if we take Newton's law of universal gravitation for two identical masses

$F=G{\frac {m^{2}}{d^{2}}}$

and assume that $d=2r$ (in fact the centers of mass of two spheres in contact are separated by a distance equal to $2r$), we obtain

$F=G{\frac {m^{2}}{4r^{2}}}$

Finally, after replacing $m$ with ${\frac {4}{3}}\pi \rho r^{3}$, we obtain

$F={\frac {4}{9}}\pi ^{2}G\rho ^{2}r^{4}$

--Grufo (talk) 01:37, 20 July 2024 (UTC)

Your addition needs a reference. Johnjbarton (talk) 02:36, 20 July 2024 (UTC)

Once again, it is trivial math. The exact same solution can be found at Surface gravity#Relationship of surface gravity to mass and radius: do you see references there? I don't – and I don't see why special rules should be applied to this page when it comes to trivial calculations. --Grufo (talk) 03:02, 20 July 2024 (UTC)

Your addition needs a reference to — at least — demonstrate notability. Trivially of math is not a sufficient reason: 1 1=2 is trivial too. - DVdm (talk) 10:14, 20 July 2024 (UTC)

1 1=2 is trivial too: …Which is why if you wrote 1 1=2 and someone asked you to find a source for it you would consider them an idiot – and rightly so. --Grufo (talk) 13:14, 20 July 2024 (UTC)

Verifiability is not the main issue here, but the arbitrariness of the example. The shell theorem presented in the previous paragraph already tells us that the distribution of the mass doesn't really matter, so why present something like this? If this was a textbook, it would make a possible exercise, but then WP is not a textbook. Jähmefyysikko (talk) 14:25, 20 July 2024 (UTC)

@Grufo Wikipedia is a community built encyclopedia. That means we need to work together to develop it. One of the self-developed rules for cooperation is the requirement for verifiable sources. (Another is civility).

I deleted your section because 1) it was not referenced, 2) is was "trivial" as you yourself posted here, 3) it was as far as I can tell simply two examples, like problems on a physics test, not separate information, 4) not integrated with the article.

If you disagree you can build WP:CONSENSUS to include the content. But I encourage you to move on to more constructive additions. Johnjbarton (talk) 14:28, 20 July 2024 (UTC)

I appreciate the general tone of this discussion. However I see a shift on the object, and some arguments are in contradiction with each other. If the math is too trivial to be referenced, it means that that alone constitutes verifiability (i.e. anyone can do the math). If the point becomes “How do we decide what is worth talking about in an article?”, well, we don't normally reference that – we don't even have the tools for it (how do you reference a general focus?). For that, we normally rely on editors' common sense. And while I agree that I can happen to be the only one that finds it noticeable that when applied to two spheres in contact a “weak” force like gravity can build up a considerable force quite fast, and two balls with a radius of a couple of metres are already able to pile up 1 newton of force – and therefore the article should not mention it because there is no consensus – what I believe is a waste of time is talking about one thing (“references”) when the point is another (“I don't like the addition” – which would be a perfectly valid point). The paragraph was so small that I think we have spent already too much energy talking about it. However I do have a minor request for the next times: do not ask editors to add “references” when the point is not “references” – as correctly mentioned, to restore that paragraph I would need to build consensus in a talk page, not add footnotes to an article. --Grufo (talk) 22:41, 20 July 2024 (UTC)

Thanks, but to clarify, my points are not contradictory but reinforcing. If you supplied a reference I would read it, learn why it is notable, and then work to properly integrate it with the article. Johnjbarton (talk) 22:53, 20 July 2024 (UTC)

(edit conflict) Regarding "If the math is too trivial to be referenced, it means that that alone constitutes verifiability (i.e. anyone can do the math)": Yes, if anyone can do the math, there should be no reason to find a source, but if no-one has ever done the math in a relevant publication, and if no-one subsequently mentioned that publication in the relevant literature, then —by design— in Wikipedia, and generally in any encyclopedia, the thing will not be mentioned. - DVdm (talk) 23:01, 20 July 2024 (UTC)

If no-one subsequently mentioned that publication in the relevant literature: Of course you can find trivial calculations in literature – for example, from a fast look on Google, here, p. 2 (and also at Surface gravity § Relationship of surface gravity to mass and radius, for what it is worth) you can find the first equation, and here the second equation (the second link does not mention the source of the exercise, but it is a perfectly sound textbook exercise). However, as “trivial” as it is, you can't expect entire dedicated chapters. Newton's equations are manipulated in all kinds of interesting ways. --Grufo (talk) 01:04, 21 July 2024 (UTC)