Talk:Gravitational two-body problem

Merge proposal opposed
This is to oppose the recent merge proposal: discussion is offered here. Terry0051 (talk) 00:06, 29 November 2009 (UTC)

Caption Suggestion
It might be helpful to indicate in the 2nd orbit image that the orbit just happens to be a lot less eccentric, i.e. that the circular appearance is not due to the dissimilar masses. — Preceding unsigned comment added by 135.214.42.54 (talk) 21:39, 31 January 2013 (UTC)

What about non-orbits?
The article should describe the case where there is no orbiting, where the objects are instead colliding.SciGeek2016 (talk) 05:55, 11 November 2015 (UTC)

List of problems with this article
There are so many problems with this article, that it needs a complete rewrite, imho. I'm definitely not an expert in this area, please feel free to add (or correct) any of my listed issues.

1."The gravitational two-body problem concerns the motion of two point particles that interact only with each other, due to gravity." A) the comma is not necessary and should be removed. B) this awkward sentence confuses point masses and point particles. C) this sentence fails to clearly state what the gravitational two-body problem is about: the equation of motion of the system composed of two point masses whose sole interaction is gravitational attraction. (note the interaction is not "due to" gravity, it is (a) gravitational interaction. D) Going out on a limb here, but isn't the G2B problem a problem in Classical (not relativistic) mechanics? ONLY? and (even further out on the limb) doesn't the G2B problem solutions assume instantaneous action at a distance? If it is so limited (clearly this article is so limited), then that is a basic assumption and should be mentioned.

2."This means that influences from any third body are neglected." From any "third" body or from any "other" body? Is "body" the same as point mass?

3."For approximate results that is often suitable." This sentence implies that "exact" results are possible, that is that approximate results are only due to simplified assumptions rather than real limitations of our abilities. How about substituting ", for less precise results that is often suitable." ?

4."It also means that the two bodies stay clear of each other, that is, the two do not collide, and one body does not pass through the other's atmosphere. Even if they do, the theory still holds for the part of the orbit where they don't." The SUBJECT of this paragraph has been switched here. Point masses do not have atmospheres, they do not collide (except in the most rare of circumstances)

5."Apart from these considerations a spherically symmetric body can be approximated by a point mass." This implies that non-spherically symmetric bodies can NOT be approximated by a point mass. And for anyone who understands that no real astronomical bodies are spherically symmetric, it implies that point masses aren't suitable approximations!

6."Common examples..." No. "One common example is..."

7. "...spaceflight where ... a single celestial body overwhelmingly dominates the gravitational influence." No, arguably. The problem is that the gravitational interaction (between two bodies) isn't an "influence". (Its already been made clear (or should have been) that only gravitational interactions are being considered.) If we remove "gravitational", we have "a single celestial body overwhelming dominates the influence." which is incoherent.

8."The reduced mass multiplied by the relative acceleration between the two bodies is equal to the gravitational force." So, when acceleration is zero the gravitational force is zero????? What is "relative acceleration"??

9."The latter is proportional to the product of the two masses, which is equal to the reduced mass multiplied by the sum of the masses." You first use reduced mass without defining it, and then use this mess?? Why? To do what?

10."Thus in the differential equation the two occurrences of the reduced mass cancel each other, and we get the same differential equation as for the position of a very small body orbiting a body with a mass equal to the sum of the two masses." WHAT DIFFERENTIAL EQUATION?!?!? This is a risible example of an attempt to use English narrative sentences to do math.

11. I've spent about as much time as I can tolerate on commenting on this. One last set of comments. Concerning the part of the article after "Assume:" r is a position vector RELATIVE to one point mass. OK. Then r is not defined. a is not adequately defined: solutions to G2B problems are circles, ellipses, parabolas, hyperbolas and the semi-major axis generally is only used with ellipses (although have definition with circles and hyperbolas as well) h is defined twice, unnecessarily. θ is not defined. u(θ) and r(θ) are also not defined (although one would assume r(θ) means r as a function of theta, whatever r is...) and e isn't negative but is it real? integer? (this is being really picky, e is probably clearly enough explained). Also, why in the world aren't m1 and m2 defined FIRST? They need to be used for most subsequent definitions. Finally: T, ω, ε all also aren't defined.71.29.173.173 (talk) 19:28, 13 July 2016 (UTC)

To the above list I want to add "12." that the article totally ignores Newton's solution of the problem in Principia, Book I, Sect. 11 (Propositions 57-69), headed "The motion of bodies drawn to one another by centripetal forces". If Newton is right, then already the article's computer simulation of two bodies orbiting a common center in overlapping ellipses is mistaken, as it is impossible in nature. According to Newton, the true orbits in this case are always concentric, and therefore no collision of the two bodies can ever happen (cf. Prop. 58 Corol. 1). This stability of even a n-body problem is guaranteed by Corollary IV to Newton's laws of motion, the principle of concentric rotation of n bodies around a common center of gravity, which principle is also ignored in the article. Ed Dellian 84.144.128.120 (talk) 10:26, 15 May 2017 (UTC)