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== Issues with recent edits ==
==Gravitational potential and gravitational potential energy==


The material on supernovae seems to be quite out of place. Indeed, it's relevance to the subject of this article seems tenuous at best. I have removed it, pending further justification as to what it has to go with this article. Secondly, I have only ever seen the term "gravitoelectric potential" in connection with general relativity. It is certainly not a term that is in wide use deserving of a place in the lead of the article. If having it in the GR section is not agreeable, then the article doesn't need to mention it at all. ] (]) 19:58, 6 March 2012 (UTC)
Gravitational potential is NOT the same as gravitational potential energy. The writer has mixed these two things. Needs fixoring ASAP. <small>&mdash;''The preceding ] comment was added by'' ] (]&nbsp;&bull;&nbsp;]) on 06:59, 9 January 2006.</small><!--Inserted with Template:Unsigned-->
:You don't have a clue what you are talking about, which makes your tampering with the physics article irrelevant at best. ] (]) 20:15, 6 March 2012 (UTC)
::Well, the sources you give are unreliable for the content you have added. I have contacted the physics project here. We'll see what they say about it. ] (]) 20:21, 6 March 2012 (UTC)
::Also, if you have nothing constructive to add to this discussion (rather than ad hominem personal attacks), the default position is for us to restore the article to its original state (see ]). Quite frankly, this doesn't pass the smell test. While it's true that I'm not currently a practicing physicist, I do have a degree in physics. "Gravitomagnetism" has always been associated with fringe physics for me. Your section does little to alleviate this concern. If, as indeed you believe, this is supposed to be a mainstream interpretation of where the gravitational potential comes fr, then why are you referencing a self published source, and a book about supernovae that doesn't seem to address directly the point that you are making. Find a clear statement in the peer-reviewed published literature that supports your theory that the gravitational potential in the result of constructive interference on matter waves. Otherwise is is nothing more tgan ]. ] (]) 20:32, 6 March 2012 (UTC)
:::I had a look at https://sites.google.com/site/eschatopaedia, which is used a few times as a source here. Clearly this is not anywhere near a ]. Anything in the article that is referenced by this source, can be safely removed. I have reverted to an earlier version, and removed another statement in the image caption with eschatopaedia as a source. User {{user|U5ard}} warn on talk page. - ] (]) 20:50, 6 March 2012 (UTC)


== U=-mu/r is just an approximation ==
:What, specifically, do you believe is incorrect about the article as it presently stands? --] 07:46, 9 January 2006 (UTC)


My professor mentione in class today that U=-mu/r is just an approximation of Laplacian(U)=0. However, I failed at locating and information on this.
::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 {{unsigned|130.234.202.80|on 15:39, 31 January 2006}}
Does anyone know more and could add this? <span style="font-size: smaller;" class="autosigned">— Preceding ] comment added by ] (]) 19:13, 26 June 2012 (UTC)</span><!-- Template:Unsigned IP --> <!--Autosigned by SineBot-->


:The Laplacian of U is a multiple of a delta function. See ]. This corresponds to taking a unit mass and placing it at the origin. ] (]) 19:51, 26 June 2012 (UTC)
==Merge with ]==


== Definition of gravitational potential ==
Most of the material on this page is covered at ] 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. --] 07:59, 9 January 2006 (UTC)


I changed the definition of gravitational potential from work that is done per unit mass '''by the force of gravity''' to work that is done per unit mass '''by an external agent against the force of gravity'''. If it were to be work that is done by the force of gravity, then it would be positive since the direction of the gravitational force (towards the centre of the object) is the same as the direction of the displacement (towards the centre of the object as well). It is because gravitational potential is defined as the work that is done against the force of gravity (by something) so that the direction of the force is the opposite of the direction of the displacement and that gravitational potential is always negative.] (]) 08:58, 12 June 2015 (UTC)
== sign (+ or -) of the gravitational potential P ==


:Moving an object to infinity is against the force of gravity. ] (]) 16:55, 12 June 2015 (UTC)
L.S.,


== Sourced mathematical form ==
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.


Twice (, ) the opening sentence of the section ''mathematical form'' was changed. I changed it to the (triply) sourced version: , , , all litterally supporting the standing version. I think these sources speak for themselves, so I have the lead. Good point, {{u|JRSpriggs}} and {{u|Goodphy}}, but let's make sure we follow the cited sources as closely as possible {{smiley}} - ] (]) 06:39, 4 October 2016 (UTC)
Here follows the reason. For P=+GM/r the accelleration is indeed given by the gradient of P.
:Quite notably, those references (all based on the (British) A-level curriculum, and in that sense one source) neglect to say who is doing the work. For their definition to make sense this has to be taken as an external agent (this might be clear in the context of the A-level curriculum). Quite clearly the work done ''by the gravitational force'' in moving a unit mass from infinity to a point x is a positive number. I am going to hunt for some clearer references on this as the current state of affairs is most confusing for potential readers. (pardon the pun)]] 08:56, 4 October 2016 (UTC)
The components of the gradient of P are:(in ax the x is subscript, so the x-component)
::One thing that I dislike is that in defining it as the work done by an external agent no reference is made to gravity. I would much prefer (the clearly equivalent) definition as "the work done by the gravitational force on a unit mass at position x, if it were moved to infinity" (Besides having the advantage of stating clearly the relation with gravity, this also helps clarify the term "potential", which is short for potential to do work.]] 09:11, 4 October 2016 (UTC)
ax=-GMx/r3
::: Looks good now.
ay=-GMy/r3
::: {{ping|JRSpriggs}} I your , because ''F'' is not "''the force necessary to overcome the gravitational force, i.e. the negative of the gravitational force''". It is just the expression of the gravitational force as a function of location. The integration is taken from infinity to some ''x''. See F_G in the cited source . - ] (]) 09:26, 5 October 2016 (UTC)
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.


::::To DVdm: TimothyRias's version appears to be correct and is equivalent to mine. Your version has the wrong sign on the term including ''F''. I suggest you look at your own source again. ] (]) 14:56, 5 October 2016 (UTC)
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.
::::: Tricky, these signes here. Better still, now. - ] (]) 15:27, 5 October 2016 (UTC)


==Chapter "Numerical values==
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).


Normally we don't talk about ''absolute'' value of gravitational potential, only the difference between two values. Also with "The potential is half the square of the escape velocity" a reader might get the impression that the potential increases deeper down in the gravitational well - (+) and (-) reversed. ] (]) 21:11, 10 February 2017 (UTC)
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.


::This entire section seems to be original work. If so, that is a problem. As I write this, Voyager 1 is 20.6 Gkm from the Sun and Earth (20.63E9 & 20.61E9 km resp.)(according to the NASA site) yet the table claims it is 17 Gkm from Earth. Add these two problems to the problem mentioned by Hilmer B, that the absolute gravitational potential isn't known, and this entire table is very misleading. One other problem I have with it. Do these numbers include the contribution of Dark Matter? I doubt it. This section should be removed or completely rewritten, with authoritative references.] (]) 23:14, 25 February 2017 (UTC)
] (]) 22:32, 21 September 2009 (UTC)


== Fundamental Problem with this article. ==
:This is a case of differing sign convention. Per ], the usual convention is to define a potential <math>U(\vec{x})</math> such that <math>F = - \nabla \cdot U(\vec{x}) \cdot Q</math>, where Q is the charge upon which the force is acting (in this case, mass). This convention gives the change in potential energy <math>\Delta E_p</math> over some path <math>P</math> as <math>\Delta E_p(P) = \int_P \nabla \cdot U(\vec{x}) \cdot Q \cdot d\vec{x}</math>. Because a force moves a particle in the direction of decreasing potential energy, a minus sign results in the expression for force. --] (]) 23:59, 21 September 2009 (UTC)


There seems to be a fundamental problem with this article. In order to calculate the absolute gravitational potential at a point, contributions from ALL matter would have to be included. Also, given that matter isn't distributed homogeneously, the potential differs by direction of travel (less work would be required to separate a unit mass from Earth if the Sun or Moon were in the direction of (initial) travel). I'm not familiar enough with GR to say, but I'd guess that the tensor doesn't suffer from this (pretty severe, imho) shortcoming. In all situations where I've seen the term used, it is the potential DUE TO A reference mass (or system of masses, or mass distribution) and IGNORES the other masses, even if they contribute MORE to the total (absolute) potential (eg in near Earth problems, we calculate the gravitational potential on Earth's surface, usually ignoring the Sun's (or the Milky Way's) contribution.) So the definitions are wrong (or fatally incomplete).<!-- Template:Unsigned IP --><small class="autosigned">—&nbsp;Preceding ] comment added by ] (]) 23:37, 25 February 2017 (UTC)</small>
L.S.,
:Also, the top diagram of the potential vs over an x-y cross-section has a problem. The text states that the potential varies LINEARLY with distance below the (object's) surface. This is clearly NOT the case in this diagram, where the potential is everywhere curved (arguably with the exception of AT the surface). This diagram seems to be very wrong, I challenge its inclusion here.] (]) 23:37, 25 February 2017 (UTC)
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.


::As the article says, the ''force'' varies linearly inside a ball of constant density. The potential varies quadratically. The article is OK. ] (]) 01:36, 7 November 2019 (UTC)
== Dimensions are very important ==


== External links modified ==
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. ] (]) 02:23, 27 February 2010 (UTC)


Hello fellow Wikipedians,
: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. ] (]) 11:11, 27 February 2010 (UTC)


I have just modified one external link on ]. Please take a moment to review . If you have any questions, or need the bot to ignore the links, or the page altogether, please visit ] for additional information. I made the following changes:
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. ] (]) 21:52, 27 February 2010 (UTC)
*Added archive https://web.archive.org/web/20110718143144/http://surveying.wb.psu.edu/sur351/geoid/grava.htm to http://surveying.wb.psu.edu/sur351/geoid/grava.htm


When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.
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. ] (]) 21:52, 27 February 2010 (UTC)


{{sourcecheck|checked=false|needhelp=}}
: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 ] article). ] (]) 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". ] (]) 00:17, 28 February 2010 (UTC)


Cheers.—] <span style="color:green;font-family:Rockwell">(])</span> 19:47, 22 October 2017 (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.


== Merger from ] ==
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?


Hi there!
:Here &rho;(''x'') is the distribution function, and d^3x is the volume element. ] (]) 02:20, 28 February 2010 (UTC)
I just stumbled over the article ] which was supposedly merged here last year. Now I want to point out that the merger should have in my opinion left some mention of the term/concept "gravity well" in this article.


Since I didnt participate in the merger and have not proper knowledge about the specifics of the concepts at hand I have to ask others to look into this.
:I believe this notation, using &rho; 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. ] (]) 03:15, 28 February 2010 (UTC)


Thanks! ] (]) 06:25, 12 February 2021 (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'')d<sup>3</sup>''x'' to d'''m''', I'm ambivalent: in some sense d'''m''' is more conceptual, on the other hand, the notation ρ(''x'')d<sup>3</sup>''x'' 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 ). ] (]) 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 ]. 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.--] (]) 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 ρ''dV'' 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 ''V''s with Φs and use ''dV'' as the volume element.--] (]) 05:39, 28 February 2010 (UTC)

*The 'Units and dimension' and section that was added, seems inappropriate per ] 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.
--] (]) 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. ] (]) 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'')d<sup>3</sup>''x'' 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'')d<sup>3</sup>''x''. Were one to actually compute an integral, one would, in most cases, immediately rewrite dm as ρ(''x'')d<sup>3</sup>''x''. ] (]) 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 <math>\int_{\mathbb{R}^3}dm(\mathbf{x})</math>. 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 ], then it is the integral of a distribution function (and so we should write the simpler &rho;(''x'')d''x''). If it is a ] 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 ] is significant, and should be mentioned, although that fact was removed in the recent round of edits. ] (]) 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. ] (]) 21:11, 1 March 2010 (UTC)

The expression, d<sup>3</sup>''x'', 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 d<sup>3</sup>''x''. 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. ] (]) 00:07, 1 March 2010 (UTC)

:The notation d<sup>3</sup>''x'' is completely standard in physics texts, by the way, and it is not meant to mean dx dx dx=(d''x'')<sup>3</sup>, 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 d''x''d''y''d''z''. RDBury above also suggested d''V'' instead which I have certainly seen a lot, but is not necessarily standard, so I might be reticent to use that. ] (]) 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, d<sup>3</sup>''x'' 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. ] (]) 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. ] (]) 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. ] (]) 21:11, 1 March 2010 (UTC)

:There isn't "a lot of extra explanation", we simply state correctly (and now with a reference) what "dm" refers to in the notation. Saying that "dm" is a "mass measure" is mathematically much more satisfactory than referring to fictional "differential elements of mass", and is not likely to lead to any greater confusion than the latter. (However, it still seems simpler to me to work with a distribution function instead.) The latest version now also includes a brief discussion of the role of Poisson's equation, which was strangely lacking from the earlier revision. Also, I have corrected the recently-introduced errors that put '''R'''='''r'''&minus;'''r'''<sub>i</sub> as incorrect and incoherent. ] (]) 22:06, 1 March 2010 (UTC)

Look at the definition of '''R'''. Try to understand it. One of the things we now need to do is add a figure showing '''R,''' '''x''', and '''r'''. To avoid ambiguity we need to talk in terms of point a and point b rather than just talk about the point, the point, ... .

<small><span class="autosigned">—Preceding ] comment added by ] (] • ]) </span></small><!-- Template:Unsigned -->

:Please stop adding this, it is both incoherent and incorrect. Also, you continue to remove sourced content. The potential is a ] of a point '''r''' in space. There is no need to talk about the center of mass of the system when defining it. Of course, if one picks a coordinate system that places that origin at the center of mass, then one recovers what you have written, but that does depend on choices that are irrelevant to the definition of the potential. ] (]) 01:32, 2 March 2010 (UTC)

::The current revision is wrong. Also, sourced content was removed, I don't know if you are aware of that. (I keep pointing this out, but you keep ignoring it, and just reverting every edit that I make, which is getting to be really aggravating.) ] (]) 02:01, 2 March 2010 (UTC)

::'''Comment'''. I tried to make various compromises in the article, including using RHB's preferred "dm" notation, but I also felt it important to include the case of a continuous mass distribution &rho;, and a discussion of the Poisson equation. My efforts to achieve compromise have been systematically reverted, often without any edit summary or talk page explanation, by RHB. On top of that, RHB has introduced conceptual errors into the article, as well as unnecessary and unexplained formulas (like the formula that pretends to be an integral in spherical coordinates, but fails to say what any of the variables are), and removed sourced content. I ask that we should either go back to the earlier consensus version of the section, or that a new consensus should emerge. The current version of the article is totally unacceptable. ] (]) 02:08, 2 March 2010 (UTC)

Let me add that this formula
:<math>V(\mathbf{r}) = -\sum_i \frac{GM_i}{|\mathbf{R}-\mathbf{r}_i|} \, \rm where \ \mathbf{r} = |\mathbf{R}-\mathbf{r}_i| \ </math> and where '''R''' is a vector from the center of mass to point b.
is extremely unclear, since the vector '''r''' appears on the left-hand side as the argument of the function and on the right as a scalar (which is one reason I changed these '''r'''s to '''x''': they were persistently being misunderstood by an editor). The equation '''r''' = |'''R''' &minus; '''r'''<sub>''i''</sub>| is also questionable, because on the left is something that does not involve ''i'' and the right clearly depends on ''i''. Happily, I see that my preferred (correct) revision has been restored that has none of these problematic issues. ] (]) 11:49, 2 March 2010 (UTC)

:I have to add that I don't see how any formula involving the center of mass can be anything non-trivial. I thought about this last night, and I have an example that I'd like others here to think about: Suppose I'm standing at the origin. There are two point masses, each 1&nbsp;kg. One point mass is 1&nbsp;m directly to my left, and the other point mass is 1&nbsp;m directly to my right. I'm at the center of mass of the system of the two point masses. But the potential is not singular there; instead it is singular at the locations of the two point masses. So the center of mass really doesn't appear naturally in the potential; you can always change your coordinate system, as I think RHB100 wants to do, but there's no reason why the center of mass is a better place than any other (from a mathematical perspective). ] (]) 12:44, 2 March 2010 (UTC)

::I had a similar problem as well, and initially tried to post it, but my explanation failed utterly to convey the sense of it. For me the bottom line is that the potential is currently defined in a totally coordinate-independent manner, which is how it should be. ] (]) 13:00, 2 March 2010 (UTC)

'''I think terms such as my left and my right are ambiguous. You need to talk about point a and point b. Another thing I rely on vectors. Vectors are independent of any coordinate system in which they happened to be expressed. I like to rely on vectors since it often eliminates the need for consideration of a coordinate system. It is important to give consideration to the center of mass when expanding the potential in terms of Legendre Polynomials as I have done below.''' ] (]) 03:14, 3 March 2010 (UTC)

:Your bold text is using up all my electronic ink.

:Here is a more formal statement of what I would like: Suppose that there is a point mass of 1&nbsp;kg located at (1&nbsp;m, 0, 0) and a point mass of 1&nbsp;kg located at (1&nbsp;m, 0, 0). For each point (''x'', ''y'', ''z''), what is the gravitational potential at (''x'', ''y'', ''z'')?

== Which revision? ==

We need to develop a consensus. I propose my most recent revision as a suitable starting point. I have attempted to take into consideration the comments of the preceding section, including RHB's preference of the "dm" notation, as well as RDBury's suggestion of using "dV" and what seems to be a consensus that a distribution function should be presented. (Not to rehash old arguments, but most of the physics books that I checked which used "dm" in an intuitive setting almost immediately explained this with a distribution function.) In addition, I had made a number of edits to address some of RHB's misunderstandings of the text as it had stood. The other revision, which I feel to be substantially inferior, is (here is a between the two revisions). I would ask that some consensus should develop on which revision should be the "stable" one. ] (]) 02:21, 2 March 2010 (UTC)

:Hmm. While you wrote this, I was working on a new revision myself. It's pretty similar to yours; as of now it's on the page itself, but in case the article changes my version can be seen at . ] (]) 04:47, 2 March 2010 (UTC)
::Looks fine to me, clear progress over the version I had suggested. ] (]) 11:22, 2 March 2010 (UTC)

'''Sławomir Biały, you are not qualified to accuse me of misunderstanding anything. I am a Licensed Professional Engineer in the field of control systems engineering. I hold advanced engineering degrees from two of the better quality engineering schools in America. I have had a career designing autopilots for American missiles. I don't believe you could get an undergraduate degree from one of the better quality American Universities. You are not qualified to accuse me of misunderstanding anything. The errors I have pointed out are due to sloppy writing and errors on your part not any misunderstanding on my part.''' ] (]) 23:43, 2 March 2010 (UTC)

:Wow, that's some bold text.

:I don't understand why you're even interested in qualifications. Isn't it more important to be correct? I for one plan to never reveal my identity or my qualifications. If I'm wrong, I want to be told I'm wrong, and I don't care whether the person doing it is a certified genius or a bored teenager.

:RHB100, your version of the article is wrong. The formula V = -&Sigma; ''GM''<sub>''i''</sub>&thinsp;/&thinsp;|'''R''' - '''r'''<sub>''i''</sub>| is incorrect. I gave an example above: Suppose that you are standing at the origin and that there is a 1&nbsp;kg mass 1&nbsp;m to your left and a 1&nbsp;kg mass 1&nbsp;m to your right. What is the potential? ] (]) 01:37, 3 March 2010 (UTC)

'''In the example above you had V(r), now you have V without an argument. V without an argument is correct. The notation with V(r) is incorect since r is a dummy variable of summation. I have added a diagram below for the continuous case which should also make it clear for the discrete case if you keep in mind that x in the continuous case replace the discrete, r<sub>i</sub>.''' ] (]) 02:46, 3 March 2010 (UTC)

:Could you explain for me how my example would look in your fomulas? ] (]) 02:59, 3 March 2010 (UTC)

:V('''r''') means V at point '''r'''. By the way, an additonal notation b is not needed for this point.--] (]) 11:50, 3 March 2010 (UTC)

::You still have not answered my question. In my example: ''V''('''r''')&nbsp;=&nbsp;? Please be specific. I don't know how to interpret your formula in this context. ] (]) 23:24, 3 March 2010 (UTC)

== Mathematical form is poorly written ==

The mathematical form section is poorly written at present. Expressions such as "where r is a vector of length r pointing from the origin" indicate the general sloppiness with which the article is written since the origin is not even defined. The article below indicates some of the ways the article could be improved. A diagram has been added to this new version to clearly show the relationship of '''R''', '''r''', and '''x''' to supplement the verbal definition. Also the integral for the continuous case has been expanded into a series of Legendre Polynomials in the new version. The comments on mass measure serve only to add confusion and should be removed.

<small><span class="autosigned">—Preceding ] comment added by ] (] • ]) </span></small><!-- Template:Unsigned -->

==Mathematical form, New==

See section titled, Gravitational potential expanded in series of Legendre Polynomials. ] (])

:Perhaps it is better to put the power series in a separate section, choosing here the origin at the center of mass, and to work out the first few terms: main term n=0. term n=1 which vanishes due to the center of mass being at the origin, and n=2, the main deviation from the main term.--] (]) 11:59, 3 March 2010 (UTC)

Patrick, I have already worked out the first few terms in a Taylor series expansion. ] (]) 21:31, 4 March 2010 (UTC)


::The Laplace series is valid whether or not the origin coincides with the center of mass (in contrast to what RHB asserted in an earlier post). I do think this deserves a place in the article, though, but I think it is better to introduce spherical coordinates a little more explicitly than is done here. ] (]) 12:05, 3 March 2010 (UTC)

Here we again see the vague and ambiguous writing of Sławomir Biały. The accusation that I made a statement regarding Laplace series is totally untrue. If you want to accuse me of saying something wrong then quote exactly what I said rather than make vague allegations with regard to something I did not say. I said absolutely nothing about Laplace series. Your failure to make clear and precise statements causes a lot of confusion. ] (]) 19:40, 3 March 2010 (UTC)

:There is no need to get defensive. I agree with what you wrote below, but I misinterpreted your statement in an earlier thread regarding the center of mass. ] (]) 22:58, 3 March 2010 (UTC)

The fact is that in order to put the Legendre Series expansion in the proper form for applications, the vectors '''R''' and '''x''' should emanate from somewhere close to the center of mass. This helps to assure that x < R, a '''necessary''' condition for the convergence of the infinite series expansion. ] (]) 19:40, 3 March 2010 (UTC)

:May I ask what the point is of introducing a vector ''r'' and even drawing a diagram for it, which does not appear in any of the equations used? ] (]) 20:39, 3 March 2010 (UTC)

:<math>V = - \int \frac{G}{r}\ dm = - \int \frac{G}{|\mathbf{R}-\mathbf{x}|}\ dm, </math> where '''r''' is a vector from the differential element of mass to point b. '''r''' is very important since it is a vector from the mass element to the point at which the potential is being computed. The potential is inversely proportional to r. ] (]) 01:38, 4 March 2010 (UTC)

Note: an improved diagram has replaced the old diagram to more clearly show the meaning of '''r'''. ] (]) 01:38, 4 March 2010 (UTC)

== Notational question ==

Is anybody opposed to using <math>\vec{x}</math> instead of <math>\mathbf{x}</math> for vectors. Due to the difference in font-weight between the normal text and the rasterized TeX it is sometimes hard to distinguish bolded from non-bold TeX. No such confusion is possible with the overhead arrow. Both notations are fairly common in the literature. (I've never quite been able to figure out which communities use what notation. Is it a math vs. physics thing? Or a US vs. EU thing? Or is it purely personal preference?)

Also to me <math>\hat\mathbf{x}</math> for a unit vector seems like a pleonasm. ] (]) 15:27, 3 March 2010 (UTC)

:I was under the impression that the manual of style discouraged using notation that would be forcibly rendered inline as a PNG image (like <math>\vec{x}</math>). At least with my settings, this aligns very poorly with the surrounding text. The article doesn't use mathbf inline, as <math>\mathbf{x}</math>, but rather the html bold '''x''', which should be easily distinguishable from the surrounding unbolded text. ] (]) 18:26, 3 March 2010 (UTC)

== Explanation of edit ==

I have the article for a number of issues. First of all, the notation of the new section was not consistent with the notation of the previous section (detailed discussion about what notation to use appears in an earlier thread&mdash;if you can manage to ignore all of the insults). I also removed some extraneous details on the construction of the Taylor series of the generating function of the Legendre polynomials, this is a well-known expansion and is already amply dealt with in the dedicated article ]. I got rid of the diagram as confusing and unnecessary (this seems to have already been pointed out by other editors above). I also made other tweaks, including an explicit remark on the change to spherical coordinates, and I have corrected to the explanation of why the first moment vanishes. ] (]) 14:22, 11 March 2010 (UTC)

Sławomir Biały, your editing has degraded my well written section. I am a licensed professional engineer in the field of control system engineering. I hold advanced engineering degrees from both the University of Arkansas and UCLA. What are your qualifications? Just because you by your own admission do not understand the diagram does not mean other people have the same shortcomings as you. Any professional quality person knows that a diagram is absolutely essential in explaining a topic of this type. Note that Meirovich includes a diagram for this topic in the book, "Analytic Dynamics". You need to learn that other people are better able to comprehend and understand than you. Other people do not have the same shortcomings as you. ] (]) 02:33, 13 March 2010 (UTC)

:Ok, so from the above post, the reason you prefer your revision is that there is a diagram in a book. But as I have already pointed out, Patrick has remarked briefly about the lack of need for additional notation (b,r,R,cm), and TimothyRias remarked on the lack of necessity of the diagram. The diagram and additional notation simply make the treatment more complicated, not less so. ] (]) 12:12, 13 March 2010 (UTC)

I like it better for many reasons, the clarity with which it is written, the generally better quality writing, ... . ] (]) 21:08, 13 March 2010 (UTC)

Sławomir Biały has the arrogance to destroy my writing by replacing it with his own poor quality writing. But he refuses to tell us the basis of his arrogance. He damages the Misplaced Pages with his destructive activities but I see nothing in the way of solid accomplishments. ] (]) 21:08, 13 March 2010 (UTC)

Sławomir Biały is guilty of taking comments out of context in his paragraph above. Neither of the comments Bialty referred to above had any relevance to the diagram, dated 5 March 2010 removed by Bialty, since they were made before the diagram. Furthermore I answered both of the comments and had a useful dialogue with Patrick. ] (]) 21:16, 13 March 2010 (UTC)

:(edit conflict) My modest contributions to the project are a matter of public record, although they are not especially pertinent to the present discussion. Obviously which revision constitutes better writing is a somewhat subjective matter that would benefit from further outside input. ] has already weighed in favor of (well, one fairly close to that). But subjective issues aside, there are a number of things that can be said quite objectively about , which I would not consider to be a model of good writing. There are unattached sentence fragments, and the formatting is of substandard quality&mdash;e.g., <math>cos\beta\,</math> instead of <math>\cos\beta\,</math>, <math>(\frac{x}{R})</math> instead of <math>\left(\frac{x}{R}\right)</math>. The style of referencing is quite homespun. Finally, the notation should at least be made to conform to that of the preceding section, which was ultimately a compromise if you recall. There are also other more subjective things that I had attempted to correct, including: (1) the issue of the diagram (that others at the very least have commented on here), and (2) a mathematically correct explanation for the vanishing of the first-order correction term in the series. ] (]) 21:26, 13 March 2010 (UTC)

Sławomir Biały, your statement that, others have commented on the diagram, is just an outright lie, just a complete fabrication. The diagram that you in all your arrogance chose to remove thereby depriving others of the benefits of using is dated 5 March 2010. Others have not commented on this diagram. ] (]) 22:07, 13 March 2010 (UTC)

:TimothyRias' comment: . Patrick's comment on the irrelevance of the proposed "b" notation: . Seems pretty clear to me what they were referring to, but I suppose I might have misunderstood their intentions. At any rate, it is not my intention at all to be dishonest in this discussion. ] (]) 22:14, 13 March 2010 (UTC)

== Bad writing of Sławomir Biały 1: A vector does not designate a point==

There are many things wrong with the writing of Biały. One place we can start is by pointing out that a vector does '''not''' designate a point. Biały makes the mistake of referring to the point, '''x''', where '''x''' is a vector.

A vector has only a direction and a magnitude. It does not have a location. A vector beginning at the point (x,y,z) = (0,0,0) and ending at the point, (x,y,z) = (2,0,0), is exactly the same as a vector beginning at the point (x,y,z) = (5,0,0) and ending at the point, (x,y,z) = (7,0,0). This is true since they both have the same magnitude and direction.

Thus a vector certainly does '''not''' designate a point and the writing of Biały shows a failure to understand very basic fundamentals on the nature of vectors and points. ] (]) 21:55, 13 March 2010 (UTC)

:Perhaps this is something of a difference of cultures, but the potential as we have defined it is a function of the ''point'' designated by '''x''' = (''x'',''y'',''z''). As you say, this is not a vector. Once an origin is chosen, however, then of course '''x''' also denotes a ]: the displacement from the origin to '''x'''. There doesn't seem to be much benefit in belaboring this point, although perhaps a link to ] in the article at the appropriate place would be helpful. ] (]) 22:07, 13 March 2010 (UTC)

==Article needs improvement and is not well written==
The article is not well written at present. If you think it is good then you are kidding yourself. Sławomir Biały has managed to destroy the research and original writing of the section, "Gravitational potential expanded in series of Legendre polynomials". ] (]) 23:17, 14 March 2010 (UTC)

== Deliberately introduced confusion or poor quality writing ==

I think it is becoming obvious that the lack of clarity in the article is to a significant degree due to deliberately introduced confusion. Sławomir Biały (alias Slawekb) has removed the diagram which depicted the vectors. If you look at the version in the history of RHB100 on 13 March 2010, you will see that the presence of the diagram certainly makes it clearer and easier to understand.

It therefore becomes pretty much completely obvious that Sławomir Biały (alias Slawekb) has the goal '''not''' of clarifying and making more understandable '''but instead of making the article more confusing and difficult to understand'''. We don't know the reason for this destructive activity. There are some people who like to send out computer viruses just for the joy of causing problems. There are also people who would like to make less information available on the Internet in order to sell more books.

The statement, "The denominator in the integral can be expanded in terms of the dot product to give ...", is misleading and confusion. The statement, "Expanding the denominator by taking the square root of the square, carrying out the dot product, and factoring R out of the denominator we get the more useful expression,", is much more understandable.

Quoting from the article, "where in the last integral we have changed to ] (''r'',&theta;,&phi;) in which ''r'' is the distance to the origin and &theta; is the axial angle with respect to the axis in the direction of '''x''' ". This is ambiguous. "''r'' is the distance to the origin", from where to the origin? And why use the indirect language speaking of the origin rather than the center of mass. "axial angle" is a meaningless expression. "with respect to the axis in the direction of '''x''' " is meaningless.

] (]) 21:38, 14 March 2010 (UTC)

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Archives
Archive 1

Issues with recent edits

The material on supernovae seems to be quite out of place. Indeed, it's relevance to the subject of this article seems tenuous at best. I have removed it, pending further justification as to what it has to go with this article. Secondly, I have only ever seen the term "gravitoelectric potential" in connection with general relativity. It is certainly not a term that is in wide use deserving of a place in the lead of the article. If having it in the GR section is not agreeable, then the article doesn't need to mention it at all. Sławomir Biały (talk) 19:58, 6 March 2012 (UTC)

You don't have a clue what you are talking about, which makes your tampering with the physics article irrelevant at best. U5ard (talk) 20:15, 6 March 2012 (UTC)
Well, the sources you give are unreliable for the content you have added. I have contacted the physics project here. We'll see what they say about it. Sławomir Biały (talk) 20:21, 6 March 2012 (UTC)
Also, if you have nothing constructive to add to this discussion (rather than ad hominem personal attacks), the default position is for us to restore the article to its original state (see WP:BRD). Quite frankly, this doesn't pass the smell test. While it's true that I'm not currently a practicing physicist, I do have a degree in physics. "Gravitomagnetism" has always been associated with fringe physics for me. Your section does little to alleviate this concern. If, as indeed you believe, this is supposed to be a mainstream interpretation of where the gravitational potential comes fr, then why are you referencing a self published source, and a book about supernovae that doesn't seem to address directly the point that you are making. Find a clear statement in the peer-reviewed published literature that supports your theory that the gravitational potential in the result of constructive interference on matter waves. Otherwise is is nothing more tgan original research. Sławomir Biały (talk) 20:32, 6 March 2012 (UTC)
I had a look at https://sites.google.com/site/eschatopaedia, which is used a few times as a source here. Clearly this is not anywhere near a wp:reliable source. Anything in the article that is referenced by this source, can be safely removed. I have reverted to an earlier version, and removed another statement in the image caption with eschatopaedia as a source. User U5ard (talk · contribs) warn on talk page. - DVdm (talk) 20:50, 6 March 2012 (UTC)

U=-mu/r is just an approximation

My professor mentione in class today that U=-mu/r is just an approximation of Laplacian(U)=0. However, I failed at locating and information on this. Does anyone know more and could add this? — Preceding unsigned comment added by 82.139.125.186 (talk) 19:13, 26 June 2012 (UTC)

The Laplacian of U is a multiple of a delta function. See Newtonian potential. This corresponds to taking a unit mass and placing it at the origin. Sławomir Biały (talk) 19:51, 26 June 2012 (UTC)

Definition of gravitational potential

I changed the definition of gravitational potential from work that is done per unit mass by the force of gravity to work that is done per unit mass by an external agent against the force of gravity. If it were to be work that is done by the force of gravity, then it would be positive since the direction of the gravitational force (towards the centre of the object) is the same as the direction of the displacement (towards the centre of the object as well). It is because gravitational potential is defined as the work that is done against the force of gravity (by something) so that the direction of the force is the opposite of the direction of the displacement and that gravitational potential is always negative.121.6.218.21 (talk) 08:58, 12 June 2015 (UTC)

Moving an object to infinity is against the force of gravity. Sławomir Biały (talk) 16:55, 12 June 2015 (UTC)

Sourced mathematical form

Twice (, ) the opening sentence of the section mathematical form was changed. I changed it back to the (triply) sourced version: , , , all litterally supporting the standing version. I think these sources speak for themselves, so I have accommodated the lead. Good point, JRSpriggs and Goodphy, but let's make sure we follow the cited sources as closely as possible - DVdm (talk) 06:39, 4 October 2016 (UTC)

Quite notably, those references (all based on the (British) A-level curriculum, and in that sense one source) neglect to say who is doing the work. For their definition to make sense this has to be taken as an external agent (this might be clear in the context of the A-level curriculum). Quite clearly the work done by the gravitational force in moving a unit mass from infinity to a point x is a positive number. I am going to hunt for some clearer references on this as the current state of affairs is most confusing for potential readers. (pardon the pun)TR 08:56, 4 October 2016 (UTC)
One thing that I dislike is that in defining it as the work done by an external agent no reference is made to gravity. I would much prefer (the clearly equivalent) definition as "the work done by the gravitational force on a unit mass at position x, if it were moved to infinity" (Besides having the advantage of stating clearly the relation with gravity, this also helps clarify the term "potential", which is short for potential to do work.TR 09:11, 4 October 2016 (UTC)
Looks good now.
@JRSpriggs: I undid your edit, because F is not "the force necessary to overcome the gravitational force, i.e. the negative of the gravitational force". It is just the expression of the gravitational force as a function of location. The integration is taken from infinity to some x. See F_G in the cited source Arfken and Weber on page 72. - DVdm (talk) 09:26, 5 October 2016 (UTC)
To DVdm: TimothyRias's version appears to be correct and is equivalent to mine. Your version has the wrong sign on the term including F. I suggest you look at your own source again. JRSpriggs (talk) 14:56, 5 October 2016 (UTC)
Tricky, these signes here. Better still, now. - DVdm (talk) 15:27, 5 October 2016 (UTC)

Chapter "Numerical values

Normally we don't talk about absolute value of gravitational potential, only the difference between two values. Also with "The potential is half the square of the escape velocity" a reader might get the impression that the potential increases deeper down in the gravitational well - (+) and (-) reversed. Hilmer B (talk) 21:11, 10 February 2017 (UTC)

This entire section seems to be original work. If so, that is a problem. As I write this, Voyager 1 is 20.6 Gkm from the Sun and Earth (20.63E9 & 20.61E9 km resp.)(according to the NASA site) yet the table claims it is 17 Gkm from Earth. Add these two problems to the problem mentioned by Hilmer B, that the absolute gravitational potential isn't known, and this entire table is very misleading. One other problem I have with it. Do these numbers include the contribution of Dark Matter? I doubt it. This section should be removed or completely rewritten, with authoritative references.40.142.183.194 (talk) 23:14, 25 February 2017 (UTC)

Fundamental Problem with this article.

There seems to be a fundamental problem with this article. In order to calculate the absolute gravitational potential at a point, contributions from ALL matter would have to be included. Also, given that matter isn't distributed homogeneously, the potential differs by direction of travel (less work would be required to separate a unit mass from Earth if the Sun or Moon were in the direction of (initial) travel). I'm not familiar enough with GR to say, but I'd guess that the tensor doesn't suffer from this (pretty severe, imho) shortcoming. In all situations where I've seen the term used, it is the potential DUE TO A reference mass (or system of masses, or mass distribution) and IGNORES the other masses, even if they contribute MORE to the total (absolute) potential (eg in near Earth problems, we calculate the gravitational potential on Earth's surface, usually ignoring the Sun's (or the Milky Way's) contribution.) So the definitions are wrong (or fatally incomplete).— Preceding unsigned comment added by 40.142.183.194 (talk) 23:37, 25 February 2017 (UTC)

Also, the top diagram of the potential vs over an x-y cross-section has a problem. The text states that the potential varies LINEARLY with distance below the (object's) surface. This is clearly NOT the case in this diagram, where the potential is everywhere curved (arguably with the exception of AT the surface). This diagram seems to be very wrong, I challenge its inclusion here.40.142.183.194 (talk) 23:37, 25 February 2017 (UTC)
As the article says, the force varies linearly inside a ball of constant density. The potential varies quadratically. The article is OK. JRSpriggs (talk) 01:36, 7 November 2019 (UTC)

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Merger from Gravity well

Hi there! I just stumbled over the article gravity well which was supposedly merged here last year. Now I want to point out that the merger should have in my opinion left some mention of the term/concept "gravity well" in this article.

Since I didnt participate in the merger and have not proper knowledge about the specifics of the concepts at hand I have to ask others to look into this.

Thanks! Nsae Comp (talk) 06:25, 12 February 2021 (UTC)

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