Talk:Semi-major and semi-minor axes

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Text and/or other creative content from Semi-minor axis was copied or moved into Semi-major axis with this edit. The former page's history now serves to provide attribution for that content in the latter page, and it must not be deleted as long as the latter page exists.

Confusion or me being dumb

Forgive me, it's late, I may be missing something obvious, but it seems like the mathematical and astronomical definitions given in this article are contradictory. If the semi-major axis is half the largest diameter of the ellipse ie. the largest radius, then surely this is the same as the aphelion point of an orbit, not a sort of 'average orbital radius'? Trent 900 23:12, 9 April 2007 (UTC)[reply]

The semi-major axis is measured from the center of the ellipse, while the aphelion and perihelion distances are measured from the focus. The foci are offset from the center of the ellipse by an amount directly proportional to the eccentricity ( i.e offset=e*a). Norbeck (talk) 08:16, 13 July 2010 (UTC)[reply]

time of year

Is it true that the earth and sun are 1 AU apart at the same two antipodal points of the calendar year? If so then when, would be a good piece of information here. MotherFunctor 17:23, 27 April 2007 (UTC)[reply]

Sort of

If you ignore the precession of the equinoxes (which define the tropical year), precession of the axial tilt (which affect sidereal year) and the precession of perihelion (which affects the anomalistic year)... which I think are reasonable assumptions to make in the short term...

... then no, the distance of 1 AU is achieved at some point in time, T days into the year, and again at -T (that is, T days before the start of the year). Anomalistic year, that is (since Im using perihelion as a reference point). The same is true for any arbitrary distance you want to pick, not just 1 AU. These points T and -T are not 180 degrees apart (neither by ellipse center nor by foci) due to the fact that the orbit is not a perfect circle.

75.172.40.73 (talk) 17:34, 27 April 2012 (UTC)[reply]

derivations instead of relations please

There are no references on how to derive these relations, neither are they derived here, only presented i.e. for ellipse a=-mu/2epsilon ... —Preceding unsigned comment added by 157.193.9.186 (talk) 13:42, 22 April 2011 (UTC)[reply]

Average Distance??

If the average distance is the distance as measured between the orbiting body and the primary focus... then how does the average depend on the angle (what, angle?, where'd that come from) you measure over? — Preceding unsigned comment added by 75.172.40.73 (talk • contribs) 17:23, 27 April 2012 (UTC)[reply]

Error in equation

Error in equation

The equation for angular momentum is incorrect.

(I will try to find a source for the correct equation, simply removing the division in the sqrt should fix it.)

This is only my second edit (prompted by trying for hours to get the wrong equation to work in my computer program) so I do not yet know how to change equations, and do not have a good source for my equation in the meantime I will add a note below the equation. — Preceding unsigned comment added by Paul Torry (talk • contribs) 00:05, 2 December 2012 (UTC)[reply]

http://www.physicsforums.com/showthread.php?t=393715

further correction

H is not in fact angular momentum but rather specific angular momentum. — Preceding unsigned comment added by Paul Torry (talk • contribs) 00:14, 2 December 2012 (UTC)[reply]

Image thumbnail not readable

While the image itself (if you click on the link to it) is perfectly readable, the thumbnail size in this page is not. I have 0 experience with images on wikipedia - is there a good way to fix this? Like a smaller image to begin with, or an SVG instead? I may be able to do the heavy lifting if someone points me in the right direction. I've perused Wikipedia:Extended_image_syntax, which led me to the belief that increasing the thumbnail size to 2.5x is sometimes OK, and I "Be'd Bold" to make that change, but it's quite a size difference so if there's a better way, let me know. RobI (talk) 15:40, 29 April 2013 (UTC)[reply]

Astronomy Section

I don't want to come off sounding harsh, but I am rather perplexed reading these pages dealing with with orbital geometry. This particular page and specifically this section of this page comes to epitomize my disgust. Whoever is writing this stuff does not appear to come from a background of physics, astrophysics or astronomy and it makes following these pages a magnitude more difficult.

Gravitationally defined (astronomical) orbits are created by the warping of space-time by massive objects (yeah-yeah fancy talk but that is as simple as it gets), in each system the most massive of these objects are the closest object to, and typically cover one, orbital focal point (see introduction illustration; exceptions are balance binary star systems). Because of the perturbations that exist in most space (i.e three body problems) even the most perfect circular orbits become elliptical over astronomical time frames. Within systems, smaller objects periodically advance and retreat on primary focal points. When one assumes the perspective of the massive center, there are two natural positions (nodes) within these elliptical orbits. The first node, called the periapsis (Pe) , is the point of closest approach to the systems center. At this point the orbiting object is no longer advancing on or retreating away from the systems center, but Pe also has the highest orbital and angular velocities. In addition the proxi-periapsis region primarily defines the stability of the orbit, because if at periapsis the object can interact with the atmosphere (e.g. Aerobreaking as an example), liquids (e.g. moon/earth tidal effects) or terrain of the massive center, then orbit is subject to rapid change . The second apsis, Apoapsis (Ap) has opposing statistics, being furthest away and having the lowest velocities. Since Ap has the lowest kinetic energy perturbations of the Pe (e.g. Aerobraking) can have assymetrically large affects on Ap. Because of its low kinetic energy at Ap, for highly eccentric orbits the Ap is the point in an orbit where it is easiest to alter inclination (all other parameters being held equal), periapsis and eccentricity. If the Ap is near the boundary of influence of system other objects can result in ejection from the system. For these reasons stable orbits are frequently denoted by Pe, and Ap as well as period as these parameters are 'reasonably' static (for discussions of how these change see Precession). Since Pe lies along the axis from the elliptical center through the focal point (being the closest point to the primary focal point) it is at the end of the semi-major axis. Likewise Ap being furthest away is by definition closest to the secondary focal point and is on the same line through the elliptical and system center as Pe. Consequently Ap to Pe length define the longest axis (by definition the major-axis) of the orbit. Therefore it is quite natural and simple to define the major axis in terms of these two nodes.

Major-axis (2a) = r_Pe + r_Ap and semi-major axis = ^2a/₂

Simple enough. No need to introduce values that are defined 'behind the curtain'. The semi-major axis is simply the arithmetic mean of the radii at closest and furthest nodes from the systems gravitationally defined center. Since radii of these two apsis is generally taken as their default values the equation can be simplified.

a = ^{(Pe + Ap)}/₂

This makes defining the semi-minor axis so much easier. The semi-minor axis is the geometric mean of the same two radii.

b = (Pe * Ap)^0.5

This [Astronomy-section] ill-defined value for eccentricity, e, is quite simply the relative half-range of radii deviation,

e = (Ap - Pe)/major-axis

Notice that I did not need to use l, a or b to define e. latus-rectum like e definitions are often obscure to the people who examine natural orbital statistics. These values are twice removed from the most basic statistics and should be defined last. IN this case on l requires the apriori definition of a or b, and that is for solely for ascetics.

l = b²/a

it could have been written as:

l = 2 (Pe * Ap)/(Pe + Ap)

Done.

Here's is the point: either out of ignorance or sophistry the editors of these astronomy sections for geometric definitions have apparently obfuscated very simply defined orbital statistics, defacto have hidden the very simplist definitions behind parameters that often hardest to extract. Most oddly, the terms periapsis and apoapsis are not even mentioned. The same problem exists for many of the geometry pages in which gravitationally defined orbital mechanics are mentioned. I don't have the time to edit all these various pages and I'm not going to engage in edit wars with mathematical ex-spurts. So take this advise or leave it.--PB666 ^yap 13:52, 10 June 2014 (UTC)[reply]

Agreed and I doubt it's a problem specific to astronomy either. As a form of proof of this, I generally ignore wiki pages that present technical definitions in google for this very reason. I'm only looking at this one because I'm trying to find an obscure equation that doesn't involve apoapsis and thought to myself: "Hmm, I bet wikipedia will have some bizarre ones.". I was not wrong. 118.210.47.72 (talk) —Preceding undated comment added 09:30, 17 September 2016 (UTC)[reply]

Requested move 4 January 2016

The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review. No further edits should be made to this section.

The result of the move request was: not moved. Andrewa (talk) 17:47, 11 January 2016 (UTC)[reply]

Semi-major axis → Elliptical axis – This article describes all axes of an ellipse, not just the semi-major axis. Are you freaking kidding me (talk) 03:53, 4 January 2016 (UTC)[reply]

Oppose. Article also talks about semi-major axis of hyperbolas, so elliptical axis is inappropriate. Also, this is common terminology and elliptical axis is not. Bill Cherowitzo (talk) 05:59, 4 January 2016 (UTC)[reply]
Oppose. It's a standard parameter in orbital elements, used widely in Template:Infobox planet. Tom Ruen (talk) 08:53, 4 January 2016 (UTC)[reply]
Oppose Tom said it better than as I could. TREKphiler ^{any time you're ready, Uhura} 20:18, 4 January 2016 (UTC)[reply]

The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page or in a move review. No further edits should be made to this section.

Merge Semi-major axis and Semi-minor axis

As written here and indicated by the merge banners, with no feedback from anyone except User:Joel B. Lewis who favored the merge, I will do it later today (or tommorow). M ∧Ŝ c²ħε И_τlk 11:01, 23 April 2016 (UTC)[reply]

Grammar

Why are they "semi-major axis" and "semi-minor axis" instead of "major semi-axis" and "minor semi-axis"? The prefix "semi-" should modify the noun "axis" rather than adjectives "major"/"minor" because these terms are about the largest and smallest half-axes, not the (full) axes that are "partly largest" and "partly smallest". — Mikhail Ryazanov (talk) 21:14, 23 October 2016 (UTC)[reply]

While in general I would not attempt to justify the quirky structure of the English language that at times defies reason, in this case I believe that it gets it right. "Semi" is not modifying major/minor but rather the full noun "major axis"/"minor axis". Major and minor here are not really modifiers, but rather part of the proper names of the two specific axes. Bill Cherowitzo (talk) 21:27, 23 October 2016 (UTC)[reply]

I would agree if they were written as "semi-majoraxis" and "semi-minoraxis", but they are written and pronounced as separate words "semi-major"/"semi-minor" and "axis". Even the current article title "Semi-major and semi-minor axes" (rather than "Semi-major axis and -minor axis", see "hanging hyphen" in WP:HYPHEN) suggests that the noun is "axis", not "major axis"/"minor axis". — Mikhail Ryazanov (talk) 02:43, 24 October 2016 (UTC)[reply]

By the way, here is some usage analysis. "GB" means the number of search results in Google Books, "GS" — in Google Scholar:

Adjective	Form
Adjective	some semi-axis	semi-some axis
major	GB: 2670 GS: 4530	GB: 37900 GS: 42400
minor	GB: 1360 GS: 2930	GB: 7520 GS: 14300
principal	GB: 67 GS: 128	GB: 11 GS: 165
principal (axes)	GB: 679 GS: 642	GB: 61 GS: 509
horizontal	GB: 303 GS: 377	GB: 2 GS: 19
vertical	GB: 361 GS: 457	GB: 1 GS: 30

As can be seen, "major/minor semi-axis" are also widely used, although less than these weird "semi-major/semi-minor axis". But as the adjectives become longer and more usual, the silliness of this idea to modify a whole noun phrase with a prefix becomes more and more evident; very few people dare to write "semi-horizontal axis" instead of "horizontal semi-axis". :–) — Mikhail Ryazanov (talk) 00:13, 5 November 2016 (UTC)[reply]

Wouldn't the proper way to refer to both be "semi-major/minor axis"? "semi" modifies the whole term "major axis" and "minor axis", but the two of those could be shown together with "major/minor axis". Aaronfranke (talk) 07:47, 14 April 2019 (UTC)[reply]

Why the hyphens?

Is anyone interested in trying to justify the hyphenation of these terms? My impression is that the normative spelling throughout the English-speaking world is without hyphens. See, e.g., Wiktionary, OneLook Dictionary (semi-major vs semimajor) or the Oxford Dictionary. (Please cite literate sources only.) WolfmanSF (talk) 01:53, 21 November 2017 (UTC)[reply]

I am the person responsible for the glossary section of the Astronomical Almanac published jointly by USNO and HMNAO (UK).

This year, it was decided that the spelling of certain astronomical terms should be updated in accordance with the existing lingual norms. Among other things, it was decided to abandon the long-outdated hyphenated spelling ``semi-major'' in favour of the universally accepted ``semimajor''. This nonhyphenated spelling has long become a norm on both sides of the pond.

So, while the 2023 version of the glossary still has semi-major and semi-minor hyphenated, in the 2024 version hyphen will be dropped. 214.9.101.5 (talk) 23:19, 15 March 2023 (UTC)[reply]

Both seem common in recent academic literature. A Google scholar search implies that the version with the hyphens is still slightly more common than the version without. What do you mean by "universally accepted" or "long-outdated"? I'm sure readers have no problem interpreting either variant. –jacobolus (t) 00:08, 16 March 2023 (UTC)[reply]

Equation and explanation for relationship between the semimajor axis and period is incorrect

In the section Astronomy/Orbital period, the equation for the orbital period is incorrect and the author makes a serious mistake in their assumption. The article states:

" $T^{2}={\frac {4\pi ^{2}}{G(M+m)}}a^{3}\,$

where $G$ is the gravitational constant, $M$ is the mass of the central body, and $m$ is the mass of the orbiting body. Typically, the central body's mass is so much greater than the orbiting body's, that $m$ may be ignored."

The mistake is in the fact that the mass of the orbiting body is invariant with respect to the period. If you follow Kepler's Third Law, the mass of the orbiting body cancels out. This is easily shown by setting the force of gravity equal to the centripetal force. Therefore, the correct equation should be:

$T^{2}={\frac {4\pi ^{2}}{GM}}a^{3}\,$

where $G$ is the gravitational constant and $M$ is the mass of the central body.

Therefore, the author's assumption that the central body's mass is so much greater ( $M\gg m$ ) than the orbiting body's is irrelevant. — Preceding unsigned comment added by Chris.d.odom (talk • contribs) 15:56, 31 January 2019 (UTC)[reply]

The text is not very explicit about the

a

in both equations. I think, only when the smaller mass is negligible, then the contribution of the elliptic orbit of the larger mass to this

a

is also negligible, and only then the second formula holds with

a

denoting the semi-major axis of the orbital ellipse with the host in a focus. Too many ellipses with axes all called

a

around. Purgy (talk) 17:36, 1 February 2019 (UTC)[reply]

Actually, after a more careful reading, I see that the author is talking about orbits around the barycenter, or center of mass, of a two-body system. So, my original complaints were unfounded. — Preceding unsigned comment added by Chris.d.odom (talk • contribs) 19:10, 4 February 2019 (UTC)[reply]

Missing defintion for L

In the Ellipse section, in the equation following "Now consider the equation in polar coordinates", it contains "l", but this is not defined or explained. More information is needed here. Aaronfranke (talk) 09:26, 14 April 2019 (UTC)[reply]