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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)

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