Talk:Orbit equation

Central inverse-square law force incorrect equations?

Angular momentum is conserved. I fail to see how l, which is defined to be the angular momentum (specific or not), can possibly be a function of theta. But, there it is, plain as day... --2601:8:A200:5DC:654F:9CAF:C091:1180 (talk) 10:16, 19 April 2015 (UTC)[reply]

Three-dimensional orbit equation?

The equation given in this article seems to deal exclusively with orbits in two dimensions, which is all well and good in basic theory, but in astrodynamics an orbiting body moves in three physical dimensions. Is there an all-encompassing equation which can be graphed to show an orbital path in three dimensions? If so, what is it? Should it be added to this article?

AlmightyFjord (talk) 20:46, 29 November 2007 (UTC)[reply]

This equation describes a two-body situation, and all two-body situations are planar. The 3D solution simply places the plane of the ecliptic within 3-space. Darekun (talk) 09:54, 30 June 2008 (UTC)[reply]

Given any two bodies, we can define a 2-D coordinate system. The orientation of the plane of an orbit with respect to another arbitrary plane is, well, arbitrary. Isaac Newton proved that in a two-body system all orbits stay within a single constant plane. You dont have to consider a third dimension unless you want to talk about things outside of the orbital plane. And yes, whereas real orbits are far more complicated than that, subject to perturbations and do in fact change in all 3 dimensions over the course of eons, its insignificant in the short term and no one has ever solved the n-body problem anyway, so there is no help anyone can provide. --2601:8:A200:5DC:654F:9CAF:C091:1180 (talk) 10:13, 19 April 2015 (UTC)[reply]

Merge proposal opposed

This is to oppose the recent merge proposal: discussion is offered here. Terry0051 (talk) 00:04, 29 November 2009 (UTC)[reply]

Change equations to be in terms of the semi-parameter (p) + Remove unneeded sections

Currently, this article has all the equations in terms of ${\textstyle {\frac {l^{2}}{\mu m^{2}}}}$ , which personally I have never seen any sources use this value. Firstly, people use the specific angular momentum (h) instead of simply the angular momentum (as the mass of an orbiting object is irrelevant to its trajectory), which is equal to equal to ${\textstyle {\frac {l}{m}}}$ . This gives the much simpler relation of ${\textstyle {\frac {h^{2}}{\mu }}}$ . Additionally, this is also equal to the semi-parameter of the orbit, ${\textstyle p}$ , (also called the semi-latus rectum ${\textstyle l}$ ) which gives the final simplified version of the orbit equation: ${\textstyle r={\frac {p}{1+e\cos \left(\theta \right)}}}$ , which is by far the most common version of this equation.

Currently the article does mention the specific angular momentum, but only in a footnote. Personally I see no reason not to list this simpler version of the equation and just provide the method of obtaining the semi-parameter, but I still wanted to ask for other's opinions on this matter here.

Additionally, both the "Low-energy trajectories" and "Categorization of orbits" sections seemingly do not relate to the topic of the article, and I fail to see the purpose of them at all. The purpose of this article is to explain the meaning of the orbit equation, give the formulation (and possibly derivation), and explain its use. Those two sections have nothing to do with any of these. Again, I still want to ask for other's opinions on this matter.

god this article is a mess... (ughhh I'm gonna have to rewrite the whole thing aren't I?) Fusion (talk) 00:50, 21 February 2025 (UTC)[reply]