Talk:Gravitational binding energy

message: The first sentence. "The gravitational binding energy of an object consisting of loose material, held together by gravity alone, is the amount of energy required to pull all of the material apart, to infinity", doesn't make a whole lot of sense. What goes to infinity? There are no units or measurements, is it the energy required? In that case the last comma is useless, if not then the sentence should be better structured so its clearer what the infinity being refered to is. 123.243.215.92 (talk) 11:16, 26 September 2012 (UTC)
thread_title: Crappy first sentence

message: : Would you, Vsmith, please explain why you feel to remove without any explanation the remark:
Well, doubled mass and a total different mass distribution. But what is the gravitational potential energy, to separate to infinity two half spheres which form a sphere? Then we consider each half-sphere as an object in the gravitational field of the other half-sphere!
I think at least you should also remove the remark This is 20% greater than the energy required to separate to infinity two such spheres touching each other.
Curious of a founded answer. I hope we started not a flame. :-/
I hope everyone agrees about the qualitative improvement by my Ersatz-statement. It is local-topic and not local-off-topic! BTW: I dislike private talks in contrast to open discussion in this Wikipedia -- so everyone can see the arguments respectively sentences of everyone involved. Regards, Achim  —Preceding unsigned comment added by Achim1999 (talk • contribs) 14:49, 18 June 2009 (UTC)
thread_title: unreasoned removal

message: As pointed out by user DVdm in Carl Sagan's Discussion Page "the source really does not qualify for Wikipedia" Deep Atlantic Blue (talk) 22:56, 3 June 2010 (UTC)
thread_title:  Derivation for a uniform sphere 

message: I have serious problems with the derivation -- it does not strike me as very rigorous. I've also found with my calculations that the precise result for the Earth is wrong -- it's actually around 1.08 * the uniform-density case. I'll give what I believe to be a better derivation. I'm sure that this derivation can be found in some textbook of celestial mechanics or planetary/stellar structure; does anyone know of any good ones to refer to?
Start with two particles and Newton's law of universal gravitation. Their gravitational binding energy is
:U_{12} = - \frac{G m_1 m_2}{r_{12}} = - m_1 V_2 = -m_2 V_1 
for masses m1 and m2, separation r12, and potential V. For several particles, we add up their contributions:
:U = - \sum_{i < j} \frac{G m_i m_j}{r_{ij}} = - \frac12 \sum_{i,j} \frac{G m_i m_j}{r_{ij}} = \frac12 \sum_i m_i V(\mathbf{x}_i) 
Note the 1/2 that appears; it keeps particle interactions from being counted twice.
Turning sums into integrals gives us
:U = \frac12 \int \rho(\mathbf{x}) V(\mathbf{x}) d^3 x 
We can turn it into a more convenient equation for the spherically-symmetric case by using vector calculus and Poisson's equation, \nabla^2 V = 4\pi G\rho, and integrating by parts. Using the acceleration of gravity \mathbf{g} = - \mathbf{\nabla} V, we get
:U = - \frac{1}{8\pi G} \int |\mathbf{g}|^2 d^3 x
In the spherical case, we find this simple form:
:U = - \frac12 \int_0^\infty \frac{GM(r)^2}{r^2} dr
It is evident that central concentration increases the binding energy above its uniform-density value.
Lpetrich (talk) 04:38, 1 February 2011 (UTC)
replies: text: Just from taking a look, I can tell that the mathematics in your formula are seriously flawed.  — Preceding unsigned comment added by Tonathan100 (talk • contribs) 17:59, 3 October 2015 (UTC)
thread_title:  Problems with the derivation