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Physics Start‑class High‑importance

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	Astronomy Start‑class Mid‑importance
This article is within the scope of WikiProject Astronomy, which collaborates on articles related to Astronomy on Misplaced Pages.AstronomyWikipedia:WikiProject AstronomyTemplate:WikiProject AstronomyAstronomy Start This article has been rated as Start-class on Misplaced Pages's content assessment scale. Mid This article has been rated as Mid-importance on the project's importance scale.

This article was nominated for deletion on 22 March 2009 (UTC). The result of the discussion was no consensus.

Gravitational potential and gravitational potential energy

Gravitational potential is NOT the same as gravitational potential energy. The writer has mixed these two things. Needs fixoring ASAP. —The preceding unsigned comment was added by 130.234.6.46 (talk • contribs) on 06:59, 9 January 2006.

What, specifically, do you believe is incorrect about the article as it presently stands? --Christopher Thomas 07:46, 9 January 2006 (UTC)

The article is just fine, it's just named incorrectly. Gravitational potential energy (U) is equal to the mass of the body multiplied by the gravitational potential (Φ) => U = m * Φ -- the same — Preceding unsigned comment added by 130.234.202.80 (talk • contribs) on 15:39, 31 January 2006 (UTC)

Merge with potential energy

Most of the material on this page is covered at potential energy in the "gravitational potential energy" subsection. I've added "merge" tags to get discussion on what, if any, advantage there is to keeping this material on its own page. --Christopher Thomas 07:59, 9 January 2006 (UTC)

sign (+ or -) of the gravitational potential P

L.S.,

According to me (and others: see other pages of Misplaced Pages; also Vector Methods, D.E. Rutherford) the formula for P schould be: P=+GM/r and not P=-GM/r.

Here follows the reason. For P=+GM/r the accelleration is indeed given by the gradient of P. The components of the gradient of P are:(in ax the x is subscript, so the x-component) ax=-GMx/r3 ay=-GMy/r3 az=-GMz/r3. Suppose y=0 and z=0. Then ax=-GMx/r3. So for positive x, ax is negative (towards the left, so towards the pointmass) For negative x, ax is positive (towards the right, so also towards the pointmass. As it should be, of course: gravitation is an attractive force.

Now, if you should have have: P=-GM/r,then ax= + GMx/r3. For positive x that value is positive, so to the right, away from the point mass. For negative x that value is negative, so to the left,also away from the point mass. That would make gravity a repulsive force.

So, P=+GM/r gives the correct value for the acceleration by a=gradient P. The + or - sign is not trivial and should be correctly chosen in Misplaced Pages. There must me no ambiguity at this point(unless there should be ambiguity in the scientific litterature; in that case the ambiguity should be mentioned in the page).

Besides i remark, as is done by previous contributors, that the potential is not the same as the potential energy of a mass of 1kg (in that case you would not need the concept). The value of the concept is that it gives the acceleration by means of its gradient.

Fransepans (talk) 22:32, 21 September 2009 (UTC)

This is a case of differing sign convention. Per potential, the usual convention is to define a potential ${\displaystyle U({\vec {x}})}$ such that ${\displaystyle F=-\nabla \cdot U({\vec {x}})\cdot Q}$, where Q is the charge upon which the force is acting (in this case, mass). This convention gives the change in potential energy ${\displaystyle \Delta E_{p}}$ over some path ${\displaystyle P}$ as ${\displaystyle \Delta E_{p}(P)=\int _{P}\nabla \cdot U({\vec {x}})\cdot Q\cdot d{\vec {x}}}$. Because a force moves a particle in the direction of decreasing potential energy, a minus sign results in the expression for force. --Christopher Thomas (talk) 23:59, 21 September 2009 (UTC)

L.S., I can agree with the convention (although the literature is not unanimous at this point). I conclude that, according to that convention, in the article a minus sign must be added to the word "gradient": The gravitational field equals MINUS the gradient of the potential. We agree on that. I will edit the page accordingly.

Dimensions are very important

The dimensions such as force, mass, time, and distance are very important from an engineering point of view. Although the pure mathematician may think dimensions are irrelevant, there are engineering oriented people who read the Misplaced Pages. Therefore it is important that we give adequate attention to dimensions in Misplaced Pages articles such as this. RHB100 (talk) 02:23, 27 February 2010 (UTC)

This is a case where too much detail is as bad as too little. The article currently emphasizes the dimensions of the gravitational constant, which is not relevant to understanding the potential, and is written in a potentially confusing manner. Sławomir Biały (talk) 11:11, 27 February 2010 (UTC)

It certainly is not too much emphasis to merely state the dimensions of the gravitational constant. If anything it is too little emphasis since only the dimensions, not the units, are stated and the value is not stated. RHB100 (talk) 21:52, 27 February 2010 (UTC)

It is important that at least the dimensions be stated since it aids the reader in verifying the dimensional compatibility of the equation. One of the first and most important things that one should do upon encountering a new equation is verify the dimensional compatibility. Every well educated engineer with degrees from one or more of the better American universities understands this. As a licensed professional engineer I know the importance of dimensional compatibility. RHB100 (talk) 21:52, 27 February 2010 (UTC)

I find it distracting from the much more meaningful point that the potential has units of energy per unit mass. Also, when saying "which has dimensions", the referent is unclear: the reader is expecting dimensions of the potential (the subject of this article), but is instead given the dimensions of the gravitational constant. This sort of information belongs in a footnote, if in the article at all. Surely professionalism also demands the ability to follow footnotes (if not wikilinks to the gravitational constant article). Sławomir Biały (talk) 23:53, 27 February 2010 (UTC)

Update. I have started a dedicated section on Units and dimension. Please populate this with information that would be useful to "professionals". Sławomir Biały (talk) 00:17, 28 February 2010 (UTC)

It needs to be in the main section not relegated to a footnote. The reader needs to see the dimensions or units of all the factors on the right side of the equation and verify that they are compatible with the left side of the equation.

Sławomir Biały, don't you know, dx^3 is not a differential element of mass. Any competent mathematician should know this. Where did you study math?

Here ρ(x) is the distribution function, and d^3x is the volume element. Sławomir Biały (talk) 02:20, 28 February 2010 (UTC)

I believe this notation, using ρ for the mass density, is a fairly standard one. I will wait a few days for others to comment, and then restore the original version of the formula. Also, back to the original topic of the thread, I don't think the value of the gravitational constant G needs to be right next to the formula for V. It seems to be that the better place for that is in the new section that I have created for a fuller discussion of the units and dimensions. Sławomir Biały (talk) 03:15, 28 February 2010 (UTC)

I'd suggest that giving the exact value of G right beside the formula for V is distracting (the wikilink is sufficient). I also don't think the dimensions of G are necessary either. I do think it's a good idea to give the dimensions of the potential right after giving the formula. Regarding the notation switch from ρ(x)dx to dm, I'm ambivalent: in some sense dm is more conceptual, on the other hand, the notation ρ(x)dx is more friendly to the less experienced reader. So who is the target audience?

I'd also suggest that in the newly added expansion of the denominator the article should not assume that the reader is aware of the convention that if v is a vector quantity then v is its magnitude. Either something should be said about this, or the notation should be changed.

I also think the first thing someone should think about when seeing an equation for a physical quantity is what it says about the dependence of the quantity on others. I would place verifying the dimensional consistency of a >200 year old equation low on my list.

As a last comment, I find it generally better in a content dispute to revert the article back to the previously held "consensus" version of the article and to use the discussion page to build a new consensus (this would appear to be this). RobHar (talk) 03:57, 28 February 2010 (UTC)

Comments:

• I don't see any problem with giving the numerical value of G, including units, in the 'Mathematical form' section. It's true that the article is supposed to be about potential and not about the gravitational constant, but I don't think that giving the value is crossing the bounds of WP:TOPIC. Don't don't agree entirely with RHB100's reasons for including it, but since this is essentially a physics article it seems appropriate to include the values of constants used. However, the placement on the same line as the formula is awkward. Perhaps it can be incorporated into the text by rewording the paragraph.

I took a stab at a rewording that may work as a compromise. Not claiming it's perfect but hopefully it's a step towards addressing everyone's concerns. It's a small point but the previous wording had M being used both as a position in space and as a mass value; there's not much harm in confusing the two for a point mass but it shows the previous wording wasn't perfect either.--RDBury (talk) 05:09, 28 February 2010 (UTC)

• I've always seen the volume element written as dV, but this would be problematic in this article because V is also used for the potential. The dm form is correct but in practice it would just be factored as ρdV anyway. If there is a way to work around the coincidence of V being used to mean two different things then I think that would be the best way of writing it, otherwise I don't really have a preference.

It appears that Φ is also commonly used for the potential, so using it instead of V would allow using V for volume as is customary. So I vote to replace all the Vs with Φs and use dV as the volume element.--RDBury (talk) 05:39, 28 February 2010 (UTC)

• The 'Units and dimension' and section that was added, seems inappropriate per WP:TOPIC whether or not the value of G is included in the other section. This is an exercise in dimensional analysis anyway so I don't think it adds value.

--RDBury (talk) 04:45, 28 February 2010 (UTC)

The use of the differential element of mass, dm, is more common than what some people realize. Dynamics professor, Dr. Peter W. Likins, taught at UCLA before going on to become Dean of Engineering at Columbia, and President of Lehigh and Arizona. In his dynamics text, "Elements of Engineering Mechanics", Likins used dm wherever appropriate such as in defining angular momentum. In the dynamics text, "Methods of Analytic Dynamics" by Leonard Meirovitch, dm is used wherever appropriate. I think that in dynamics texts used in engineering schools, the use of dm is fairly standard. RHB100 (talk) 23:32, 28 February 2010 (UTC)

I, for one, am not contending that dm is uncommon. In fact, it is very common in sufficiently advanced physics texts as well (by which I mean textbooks that would be used in sophomore physics and beyond). However, ρ(x)dx is much more likely to be understood by anyone who has taken some calculus, without necessarily moving on to higher level physics courses. Another matter is that dm is really mostly a shorthand for ρ(x)dx. Were one to actually compute an integral, one would, in most cases, immediately rewrite dm as ρ(x)dx. RobHar (talk) 22:41, 28 February 2010 (UTC)

I have several problems with "dm". First, the integral is still over physical space, but the notation does not emphasize this. It should at the very least be ${\displaystyle \int _{\mathbb {R} ^{3}}dm(\mathbf {x} )}$. Secondly, I do not like the way in which the integral with respect to "dm" is treated as though it were something well-defined in its own right. If this is an ordinary Riemann integral, then it is the integral of a distribution function (and so we should write the simpler ρ(x)dx). If it is a Lebesgue integral of a mass measure, then that should be indicated instead. But it is not explained at all what the "integral over the extent of the differential mass elements, dm" means. Also, the fact that this is a convolution is significant, and should be mentioned, although that fact was removed in the recent round of edits. Sławomir Biały (talk) 23:08, 28 February 2010 (UTC)

The problems you have with dm are due to your own lack of understanding and education. You should go back and repeat undergraduate dynamics for rigid bodies. RHB100 (talk) 21:11, 1 March 2010 (UTC)

The expression, dx, is not a meaningful expression for a differential volume. dx dy dz is a proper expression for a differential element of volume, a differential cube. I think that a student who had studied calculus would be confused by dx. The elements of dx dx dx are not orthogonal, they are all in the same direction and it is thus not a meaningful expression of a differential element of volume and it is confusing to say the least. RHB100 (talk) 00:07, 1 March 2010 (UTC)

The notation dx is completely standard in physics texts, by the way, and it is not meant to mean dx dx dx=(dx), but rather the 3 symbolizes the fact that the integral is over three dimensions. It is true that from the point of view of making this article at least accessible to people who have done calculus, it would be better to use dxdydz. RDBury above also suggested dV instead which I have certainly seen a lot, but is not necessarily standard, so I might be reticent to use that. RobHar (talk) 00:28, 1 March 2010 (UTC)

I have not read all physics books but I did take a survey of 4 physics books that I own. All 4 used the differential element, dm, in connection with angular momentum and moments of inertia. I did not observe the notation, dx in these particular books but again I confess I have not read all physics books. The books I surveyed are "Elements of Physics" by Shortley and Williams, "University Physics" by Sears and Zemansky, "Fundamentals of Physics" by Haliday and Resnick, and "Physics for Science and Engineering" by McKelvey and Grotch. RHB100 (talk) 01:52, 1 March 2010 (UTC)

I have added an explanation of the unexplained notation, since from the earlier version, is was not even clear that the integration was over ordinary physical space. I also felt the need to explain what "dm" is, and link to the appropriate notion of integral. Sławomir Biały (talk) 12:01, 1 March 2010 (UTC)

Physics and engineering books use integrals with dm as the differential element and manage to make it clear to the intelligent student without a lot of extra explanation. We should use mathematics to explain not to confuse. RHB100 (talk) 21:11, 1 March 2010 (UTC)

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