Talk:Newton's law of universal gravitation

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[edit] meaning of the formula

At the time of writing, the introduction is in an inconsistent state, with the formula being

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

and the commentary saying that it is considered a repulsive force for consistency with Coulomb's Law. Clearly you can both give the "F" value a negative sign and say you consider the force repulsive, or you can give it a positive sign and say you consider it attractive.

This really matters only when you consider the vector form of the law. In this case, once you have defined which force and which vector distance you mean by F12 and r21, the sign is not conventional: it must agree with the attractive nature of the force.

At the time of writing the article defines:

F12 is the force on object 2 due to object 1
\mathbf{\hat{r}}_{21} \equiv \frac{\mathbf{r}_2 - \mathbf{r}_1}{\vert\mathbf{r}_2 - \mathbf{r}_1\vert} is the unit vector from object 1 to 2.

Then the correct formula would be:

\mathbf{F}_{12} = -G {m_1 m_2 \over r_{21}^2} \, \mathbf{\hat{r}}_{21}

That is, the force due to object 1 on object 2 acts in the opposite direction to the position of object 2 with respect to object 1.

Stefano 21:52, 11 May 2006 (UTC)

[edit] Law or theory?

I've usually heard this described as a law, and indeed that is the title of the article. However the first line of the article says that it is a theory. This should be either changed, or explained in the article. Harley peters 01:35, 27 October 2006 (UTC)

[edit] Guys, "Newton's law of universal gravitation" is invalid for almost a century!

Wikipedia shouldn't propose a "law" that is outdated for almost a century. When one types "Gravitational force" one may expect to see a contemporary, Einsteinian equation for this force, which BTW, I placed a few years ago in Wikipedia but then it has been deleted when someone started to rearrange gravitation pages according to his/her poor understanding of gravitation.

How Wikipedia is going to help in understanding the contemporary physics if such a simple thing as ordinary gravitational force is called a "force of attraction" while we know for almost a century that nothing is attracted here to anything else. Just imagine how would Einstein feel if he knew that almost a century after he discovered where the gavitational force comes from, some guys in Wikipedia think that it comes from Newtonian "spooky action at distance" (from "attraction" according to Newtonian physics).

So please eiter restore my old post with Einsteinian equation for gravitational force or, if you don't like it for some reason, put your own version of it. But let it be Einsteinian and not Newtonian physics, which is nice for historical and many practical reasons but unfortuntely not true. I also hope that at certain point you don't return to geocentric planetary system as being good enough for the readers of Wikipedia and easier for you to make sense of. Jim 20:53, 5 November 2006 (UTC)

[edit] The old "feather and hammer in a vacuum" chestnut...

Can somebody who knows the deal explain that to me?

I understand that two small objects different in mass, but attracted to the same massive object, will accelerate at the same rate, because the increased inertia counteracts the increased force (f=ma). However, shouldn't the massive object have a greater amount of acceleration in the case of the larger (small) object? It has the same mass in both cases, but in the second there is greater force. Therefore wouldn't the relative acceleration as seen by an observer on the massive object be greater for larger objects? This has been bugging me for years agnabbit! --Sophistifunk 04:53, 22 November 2006 (UTC)

You are of course right. If you take for small objects the Earth and the Moon and for the massive object the Sun then the acceleration of the Sun towards the common center of mass with the Earth will be greater than acceleration of the Sun towards the common center of mass with the Moon.
The force acting between the Sun and the Earth is Fse = Gmsme / r2 so the acceleration of the Sun towards their common center is ase = Fse / ms = Gme / r2. The force acting between the Sun and the Moon is Fsm = Gmsmm / r2 so the acceleration of the Sun towards their common center is asm = Fsm / ms = Gmm / r2 and so since me > mm so is ase > asm. Jim 17:26, 22 November 2006 (UTC)
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