Talk:Orbit/Archive 1

Example calculations

 * This section has been moved temporarily to another location while it is under development. -- Metacomet 05:51, 31 December 2005 (UTC)

Article Name
Shouldn't this article (Planetary orbit) be renamed Orbit (Astronomy) or Orbit (Celestial mechanics)? Planets are not the only thing that orbit. The star also orbits around the planet and two stars may orbit around eachother. Zhatt 16:40, 27 September 2005 (UTC)


 * Technically, that's not quite correct. The star does not orbit around the planet, nor does the planet orbit around the star.  In reality, both the planet and the star orbit around the center of mass of the planetary system.  In practice, however, the mass of the star is almost always many many orders of magnitude larger than the mass of the planet, so that the center of mass of the planetary system very nearly coincides with the center of mass of the star.  So as a practical matter, the planet revolves around the star, not vice versa.


 * As an example, in our own solar system, the Sun makes up 99.85 percent of the total mass of the solar system, and Jupiter accounts for another 0.10 percent. The remaining eight planets account for only 0.04 percent combined, and comets, asteroids, and dust account for the balance.  Source:  Abell, Morrison, and Wolff, Exploration of the Universe, fifth edition (Saunders College Publishing, 1987), p. 234.


 * In a binary system, the two stars may have masses of similar order of magnitude, so that it is correct to say that each star orbits around the other, or more accurately, each star orbits around their common center of mass.


 * -- Metacomet 05:49, 30 December 2005 (UTC)

I agree that the article name is wrong though. Much of the focus is on satellite orbits; the common theme is gravitational orbits. Orbit (gravitational) is my suggestion. Joffan 23:25, 17 July 2006 (UTC)


 * I suggest either Orbit (astronomy) or Orbit (physics). The Land 00:10, 18 July 2006 (UTC)


 * you guys never sorted this out, but a name change is needed here.. what are we supposed to do with articles like Satellite orbit? it apparently doesn't fall under this one.. Mlm42 14:30, 4 October 2006 (UTC)

Stability of planetary orbits
My understanding is that the stability of planetary orbits, being an n-body problem, is a open question. Wasn't there a prize offered for solving this that was never claimed? --Michael C. Price talk 19:50, 22 September 2006 (UTC)


 * The following discussion is an archived debate of the . Please do not modify it. Subsequent comments should be made in a new section on the talk page. No further edits should be made to this section. 

PAGE MOVED to Orbit (celestial mechanics), per discussion below. -GTBacchus(talk) 03:38, 5 November 2006 (UTC)

Old Requested move
Planetary orbit → Orbit (physics) — This is a long overdue nomination. From the first line of the article, it is clear the name needs to be changed, and "Orbit (physics)" seems most appropriate. Mlm42 12:47, 30 October 2006 (UTC)

Survey
Add  * Support   or   * Oppose   on a new line followed by a brief explanation, then sign your opinion using ~.


 * Support - Although the article is clearly focused mostly on the orbit of bodies around the Earth or around the Sun, the article's information has more general applications (and it should include more information about the orbits of stars around each other and stars and star clusters around the centers of galaxies). George J. Bendo 14:43, 30 October 2006 (UTC)
 * After reading the comments below, I now think moving this to Orbit (celestial mechanics) is better. George J. Bendo 12:17, 31 October 2006 (UTC)
 * Support (modified). Clearly not everything that orbits another entity is necessarily a planet (sorry Pluto). — CharlotteWebb 22:45, 30 October 2006 (UTC)
 * Orbit (celestial mechanics) was a more popular suggestion that I expected. Let's go with that. — CharlotteWebb 01:04, 1 November 2006 (UTC)
 * Oppose except for a brief note on Bohr's analogies, this deals entirely with the celestial mechanics sense of orbit. That may be primary; and orbit would be defensible; but orbit (physics) would have to include orbitals. Septentrionalis 22:47, 30 October 2006 (UTC)
 * Orbit (celestial mechanics) would still be a better title than the current one. I would not particularly oppose moving it to Orbit as a primary topic, however. — CharlotteWebb 22:55, 30 October 2006 (UTC)
 * What do you mean by "would have to include orbitals"? do you mean atomic orbitals? i believe to use the term orbit instead of orbital in that case would be incorrect. Mlm42 08:57, 31 October 2006 (UTC)
 * Oppose I would instead support the move to Orbit (celestial mechanics). WilliamKF 20:50, 31 October 2006 (UTC)
 * Oppose I would support a move to Orbit (celestial mechanics). There are many things in physics that are orbits that this article fails to even allude to; giving it an unjustified general title would be wrong. linas 04:10, 2 November 2006 (UTC)

Discussion
Add any additional comments:


 * Orbit already redirects here. Why not simply move to that? siafu 14:50, 30 October 2006 (UTC)
 * As you can see in Orbit (disambiguation), there are many other uses, including Orbit (anatomy), Orbit (group theory) and Orbit (dynamics), which are fairly well used. Mlm42 16:50, 30 October 2006 (UTC)
 * Orbit (disambiguation) should be moved to Orbit, in that case. — CharlotteWebb 22:53, 30 October 2006 (UTC)
 * Would a move to Orbit (celestial mechanics) include content that could be in orbit (astrodynamics)? that is to say, is the term orbit in astrodynamics synonymous with orbit in celestial mechanics? if somebody is looking for information about orbits of satellites, like the International Space Station, should they check orbit (celestial mechanics) for the answer? Mlm42 08:58, 1 November 2006 (UTC)
 * No. Astrodynamics is rather different than celestial mechanics; it deals with rockets and mass change/mass ejection. By contrast, celestial bodies do not change or eject mass as a rule, which is why its called "mechanics" and not "dynamics". linas 04:17, 2 November 2006 (UTC)
 * It appears we have consensus to move this page to Orbit (celestial mechanics); i'm unclear with the procedure in how to proceed.. do i just move it, or do we still need an admin for something? Mlm42 08:56, 2 November 2006 (UTC)
 * Better to wait a couple days to see if someone else comes along; but then the page can just be moved. Septentrionalis 20:18, 2 November 2006 (UTC)
 * The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made in a new section on this talk page. No further edits should be made to this section.

Requested move

 * The following discussion is an archived discussion of the . Please do not modify it. Subsequent comments should be made in a new section on the talk page. No further edits should be made to this section. 


 * Orbit (celestial mechanics) → Orbit —(Discuss)— This move was done out of process by an admin a month ago, but the talk page was not moved. I reversed it for now, so it can be relisted here. —The way, the truth, and the light 05:35, 4 May 2007 (UTC)

This proposal is essentially to see if Orbit should get a disambiguation page or Orbit (celestial mechanics); there was consensus on the former last year as can be seen above. The way, the truth, and the light 05:38, 4 May 2007 (UTC)


 * There are dozens (hundreds really) of Wikipedia articles that link to Orbit. Very few of them are wanting to send the reader to an article about eyeball sockets! Sending them to Orbit (disambiguation) might be "correct" in some theoretical sense, but doing so isn't serving average, every-day Wikipedia users at all well! (Please check out a sample of the links at Special:Whatlinkshere/Orbit.) (Sdsds - Talk) 21:51, 4 May 2007 (UTC)


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

This article has been renamed as the result of a move request. This is clearly the primary meaning of "orbit". --Stemonitis 09:13, 9 May 2007 (UTC)

Inequalities
In trying to edit the Pierre-Simon Laplace and George Biddell Airy articles I keep coming across references to "inqualities" in planetary motions. What is the exact definition of an inequality in this context?Cutler 19:53, 12 September 2007 (UTC)

Tilted Cannon?
I'm wondering what happens when the cannon is tilted up or down (is not fired parallel to a tangent touching the surface of the Earth).

Is it never possible to launch a circular orbit at an angle like this -- or will gravity correct the path to a circle, due to the speed and mass of the object?

Is is possible to launch any circumnavigating (elliptical) orbit at an angle, or will the curve always hit the Earth?

Does such a tilt influence what the escape velocity is for the object, and the parabolic vs. hyperbolic infinite orbit shape?


 * If you tilt the cannon one of two things can happen. 1) you tip the cannon up so much that you don't gain enough horizontal velocity to "miss" the Earth and you end up impacting the surface somewhere along your trajectory.  2) if you only tip a small amount and therefore manage to achieve a stable orbit your orbit will be elliptical, furthermore the same elliptical orbit could be achieved by simply placing a different cannon at the periapsis of your orbit and firing horizontal with faster than the circular orbital velocity for that altitude.  It might be worth working these concepts into the main article if they haven't been already.  As for the escape velocity I don't think it matters but I'm not 100% sure on this.  The escape velocity is computed by setting the kinetic energy of the object as it leaves the planets surface equal to the change in potential needed to make it fly off to infinity.  Since KE does not depend on direction it should not matter but I'm not certain of this. --AndrewBuck (talk) 06:57, 20 November 2007 (UTC)

Yet more on understanding orbits
I have just reverted one error in the last previous edit, because a closer reading of the examples cited shows that for that case (slightly slower than C, but faster than B), the periapsis (perigee for Earth) is actually opposite the firing point, per the original.

I also added a note that, (a) on the one hand, all Newtonian orbits are closed ellipses that repeat exactly, but (b) any non-Newtonian effects produce orbits that are generally not closed, though bound. I see now that this fussy point should probably be moved to the following section, which I will do shortly.

On an unrelated issue, just to explain, I have capitalized "Earth" within the section, according to the usage of astronomers (my personal background), being a proper name (of a planet), as decreed by the IAU. But I believe this may be one of those Wiki-specific conventions (as between English and American usage), suggesting consistency within an article as originally begun. I would advocate such capitalization in astronomical or related technical contexts, but am not rigidly committed to either; nor even to consistency, if it would be disruptive.

Also, does anyone have opinion or advice on the usage of orbit for the open-trajectory cases? I would tend to call those "trajectories", and reserve "orbit" for bound trajectories (which in practice are never precisely closed). As the section stands, "orbit" is used for all. Wwheaton (talk) 22:11, 15 February 2008 (UTC)

Section on Understanding orbits
This section, with the cannon ball diagram, is really great to have in the article. But it appears to have several technical misunderstandings. First: assuming the cannon ball is small compared to the Earth (and what cannon ball isn't?) the mass of the cannon ball does not change the velocity required to acheive orbit. (Does make a difference even if the cannon ball were the mass of the Moon?) Also, for any given firing point, there is only one velocity which will result in a parabolic orbit. Would fixing both of these be non-controversial? (Sdsds - Talk) 23:41, 8 May 2007 (UTC)


 * I think so. If the cannon ball were the mass of the moon, there would be a sizable reaction force on Earth. The way, the truth, and the light 00:32, 9 May 2007 (UTC)


 * Somebody fixed it .--Patrick (talk) 13:10, 20 November 2007 (UTC)

[Gibberish section deleted here] Wwheaton (talk) 22:16, 15 February 2008 (UTC)

Miscellaneous
where can i find information about earth's orbit around the sun? no link seems to lead to this information. -tom Are all planets orbiting the sun anti clock wise? -peg


 * Yes, all planets (and major moons) orbit in the same direction, and nearly in the same plane. This is now generally accepted to be due to the primordial rotation of the disk of gas and dust, out of which the Solar System formed.  Wwheaton (talk) 22:37, 15 February 2008 (UTC)

---

Most recent update was mine. My main intention was to fix the incorrect assertion in the previous version that inner planets has more circular orbits. This was in the introduction, so I placed the correction there. As a result the intro now looks a bit bloated with material duplicated below. -- Alan Peakall 17:03, 5 Sep 2003 (UTC)

---

This page was moved to orbit (physics) and turned into a disambig page for a bit; this does not really make sense, since almost all inbound links were in the gravitational orbit sense. I moved the disambig page to orbit (disambiguation), and moved orbit (physics) back here. -- The Anome 00:10, 30 Aug 2004 (UTC)


 * You could also ask User:BenjBot to solve such a problem. I would not say that orbit in physics is the first thing for orbit. Tosha 04:00, 30 Aug 2004 (UTC)

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It's also a brand of gum... Someone should add that.

---

Earth's orbit is neither clock wise nor counter-clock wise, and it is both. One cannot truely answer the question because it is relative to your perspective. The orbit is either clockwise or counter-clockwise depending on whether you look at it from the "top" (if it is truely the top), or if you look at it from the "bottom" (if it truely is the bottom).


 * Yes; in fact the standard convention is that "north" is the direction of the thumb when the fingers of the right hand point in the direction of the motion. According to this, all bodies revolve (and rotate) counterclockwise by definition, except when referenced to some larger external system, as eg, a contrary moon or asteroid w/r the Solar System. Wwheaton (talk) 22:37, 15 February 2008 (UTC)

--- The equation of the orbit described by the particle is thus:
 * $$r = \frac{1}{u} = \frac{l}{1 + e \cos (\theta - \phi)}$$,

Should the second :$$\frac{l}{...}$$ be a :$$\frac{1}{...}$$ ? Otherwise it doesn't make any sense, what would l be? DavidMcKenzie 16:00 21 July 2005

--

Remembered what the l was: it's the semi-latus_rectum. Added a link to that and cleared up the ambiguity between the 1 and the L. DavidMcKenzie 16:51 21 July 2005

Tidal effects near GSO
I'm watching "If there were no Moon" (produced by Discovery Channel and narrated by Patrick Stewart), which talks about tidal forces pushing the moon away gradually. I've found discussion on orbital decay due to tidal forces when an object is below synchronous orbit. Though it may be just the opposite, I'm not quite getting how it works when an object is in or slightly above SO. Could someone please add a detailed technical description to the main article? --- —Preceding unsigned comment added by Greenwikiengineeer (talk • contribs) 17:22, 30 December 2007 (UTC)
 * I've moved this from the head to the end of the article, where later discussion should normally go.
 * These tidal effects work by exerting a gravitational torque (roughly, a kind of twisting force), so there are two logical steps to necessary to make them act. They would not have any effect at all between bodies that were  perfect spheres, or spherically symmetric, say made of concentric spherical layers.  So the first thing is that one or both bodies have to be non-spherical (or at least, not axisymmetric around the axis perpendicular to the plane of the orbit).  Typically this happens because the tidal forces themselves pull stronger on the nearer sides and weaker on the further sides, which tends to draw the bodies out into a slightly teardrop shape, with the points of the tears towards each other.  For the Moon's effect on the Earth, this effect is roughly the size of the oceanic tides (plus a smaller bit due to tides actually raised in the rock, with amplitudes of the order of centimeters I think).  While the teardrop shape is typical due to the tidal forces, any irregularity will do: any bump say, like a mountain, or whatever.
 * Then, as the other part, to get the twisting effect, the axis of the typically tear-shaped distortion has to be out of alignment with the line connecting the centers of the two bodies. Then one body's gravitational field can try to force the other into alignment, pulling harder on the bump pointed in its direction.  Such misalignment occurs either because the orbit is not perfectly circular (so that the angular speed around the orbit is not constant), or because one or both bodies is rotating at a rate different than the orbital angular velocity.
 * The final element is inevitable if the first two conditions (asymmetry and misalignment) are fulfilled. Because Newton's Third Law requires the gravitational force on the twisted body to have an accompanying reaction back on the other, there will be a force on the other body (even if it is symmetrical itself), trying to move it to align with the axis of the teardrop.  This will cause the orbital velocity of that other body to change, either increasing or decreasing, as it tries to move into alignment.
 * So to answer your question: the tidal distortion of the Earth due to the Moon rotates with the orbital period of the Moon, once per month, and so it acts to speed up satellites that are slower (beyond the Moon), but to slow down those that are faster, inside the Moon's orbit. Because the lunar distortion is so small, for artificial satellites the effect alternates back and forth (as they pass the bump), and so almost cancels, and the result is negligible on human time scales.  (There is also an effect due to the Sun's tidal field that seriously affects lunar satellites, often crashing them in a year or two.)  But if the Moon were near GSO, the tides would be huge (GSO is ~10 times closer, so about 1000 times what they are today, since, if $$r$$ is the distance, the tidal distorting force is roughly proportional to $$1/r^3$$).  This would cause the Moon to spiral inward if it were inside GSO (because the axis of alignment of the teardrop on the Earth would lag behind the Moon), and the Earth's rotation to speed up, until they came into mutual rotational lock.  This situation is seen in many binary stars in close orbits, that are slightly (or sometimes extremely) tear-drop shaped, and rotate in synch with their points aligned (sometimes almost touching).  But if the Moon were a little outside GSO. the Earth would rotate faster than the Moon's orbital revolution, so the bump would always be ahead of the Moon, spiraling it outwards, and slowing the Earth's rotation, which is what seems to have happened in historical fact.
 * This explanation is longer than I meant! But I hope it helps.  Wwheaton (talk) 16:26, 20 February 2008 (UTC)

Newton's Cannonball question
In Newton's Cannonball experiment, am I correct in thinking that if the cannonball manages to pass the 'half-way mark' it will go into an uninterrupted orbit, and won't hit the Earth say 3/4 round? Marky1981 (talk) 10:06, 24 April 2008 (UTC)
 * Yes, with a couple of minor caveats. First of all, the mountain must be high enough that it is completely above the atmosphere, so there is no drag loss.  Second, the approximation of exact Newtonian physics, for an exactly spherical planet, must apply.  Then (assuming the barrel is precisely horizontal), the firing point will either be the lowest (perigee) or the highest (apogee) point of the orbit, and the orbit will be a closed ellipse, precisely repeating itself ad infinitum.  The critical issue is that the perigee must be high enough to clear the top of the atmosphere.  This "top of the atmosphere" is a bit fuzzy, but in practice 100 km is too low to remain in orbit for more than a short time, and 1000 km is high enough that such orbits last many years.
 * As a practical application, note that if two satellites collide and fragment into pieces, all the pieces will be left in orbits passing through the collision point, and will therefore have perigees no higher than that. Then the height of that point essentially determines the maximum possible lifetime of the fragments against atmospheric drag. (But since the pieces will generally all have different periods, they will typically not collide again.)

Thanks for the detailed explanation. Marky1981 (talk) 09:51, 25 April 2008 (UTC)

Historical maldefinition of 'orbit'
The definition of an orbit in this article as follows

“In physics, an orbit is the path that an object makes around another object or a barycenter while under the influence of a central force, such as gravity.”

is historically untenable for the very simple reason that it seems it was not until the 17th century well after Kepler that planetary orbits were conceived as in any part caused by a centripetal force such as gravity, possibly first by Roberval.(???), except perhaps for the Moon’s orbit around the Earth.

Certainly the article’s claim that

“The basis for the modern understanding of orbits was first formulated by Johannes Kepler whose results are summarized in his three laws of planetary motion.”

is historically false on this definition, since Kepler did not believe planetary orbits were caused by gravity nor any other centripetal force nor central force such as gravity, but by a combination of the Sun’s rotating sunspecks and a magnetic force that perturbed circular orbits into ellipses.

A somewhat historically better definition which does not depend upon central forces and therefore includes the notion of a planetary orbit not caused by any central force(s), but by such as rotating celestial spheres, and which thus does not exclude the notions of planetary orbits for millennia before the 17th century, is to be found in the Shorter Oxford English Dictionary. But an adequate and accurate definition of 'orbit' is certainly extremely difficult.--Logicus (talk) 18:01, 20 April 2008 (UTC)


 * The definition in the lead should be the modern one. You might want to be editing the section on the historical developement of the concept. The way, the truth, and the light (talk) 18:19, 24 April 2008 (UTC)


 * Logicus: No the main definition should just be correct, whether modern or not. Defining 'orbit' such as meaning 'the path of a planet' in such a way that it excludes planetary orbits as conceived before the 17th century and even by Kepler is clearly unacceptable. The criterion of 'modernity' for a definition objected by TWTTTL is a red herring: the Shorter Oxford English Dictionary definition that TWTTTL deleted is perfectly modern in its definition, which is as follows:


 * “ In astronomy an orbit is the path of a heavenly body, the curved path described by a planet or comet round the sun and by a satellite about its primary. “


 * Moreover, contra TWTTTL and Wikipedia, the current modern Wiktionary definition of orbit is :


 * "A circular or elliptical path of one object around another object."


 * which also omits the current Wikipedia definition’s untenable requirement of orbits being caused by a central force.


 * However this Wiktionary definition is also untenable but for another reason, namely that orbits need not be circular nor elliptical, if indeed any orbits are, but may also be parabolic or hyperbolic as some comet orbits may be, or a rosetta like Mercury's orbit, or any other figure going around something. Thus the Wiktionary definition must be reduced to


 * 'The path of one object around another object.'


 * However, a valid objection to this definition is that in Aristotelian celestial physics planetary orbits were conceived as paths centred around a point, namely the centre of the universe, rather than around a body, and it seems this also applies to the alleged ‘modern’ conception as defined around a barycentre rather than around a body


 * Thus I propose the following minimal but historically inclusive adequate definition:


 * ‘The path of one object around a point or another object.’ —Preceding unsigned comment added by Logicus (talk • contribs) 18:14, 30 April 2008 (UTC)


 * I agree that the limitation to central forces is too restrictive. The gravitational field of Saturn is clearly non-central, for example.  Any potential force between two bodies will give bounded trajectories, which may or may not be periodic.  And even the restriction to potential forces is a bit tight.  For example, we might reasonably say the NEAR spacecraft orbited Eros, but it could gain or lose energy as it did so, due to the objects extreme asymmetry and rotation, giving a time-dependent potential.  I personally think the term should be limited to trajectories that are at least spatially bounded, at least for a moderate time, but they clearly do not have to be periodic.  I think the definition ought not exclude the bound trajectories of stars in disk or elliptical galaxies and star clusters, even though those may not remain bound forever.
 * I am tentatively reverting to User:Logicus's minimal form, pending a little more discussion, hopefully with input from others. Cheers, Wwheaton (talk) 21:52, 30 April 2008 (UTC)

After nosing around a bit, it seems to me that the Wiki Orbit (dynamics) article is a superset of our meaning here, in the sense that anything we consider an orbit here would be there too. I suspect we ought to check out that article (more carefully than I have done, yet) to see where we want to draw the line. It seems to me that stable bounded solutions of the gravitational many-body problem should be included here (so we get the Earth/Moon system), certainly, maybe even if only stable for a long time, not quite forever. But I think we should also include non-gravitational forces in the lead-sentence definition, even if we want to narrow the article's scope down to the gravitational case shortly after. Here I am thinking about orbits in general relativity (which even applies to Mercury's orbit as a practical case), orbits close to black holes, the orbits of charged particles in a magnetic field such as orbits in a particle accelerator, the Van Allen Belts, the orbit of a particle in a harmonic potential, etc, etc. My guess is that we should have links out to the more specialized cases, and limit ourselves to celestial mechanics here, but try to include the realistic cases that occur in the astronomical context, at least by linkage. Cheers, Wwheaton (talk) 22:56, 30 April 2008 (UTC)


 * This article used to be named Orbit (celestial mechanics) and Planetary orbit; see the RMs above, and it was always recognized that this should be about the astrodynamical concept, while the other uses should be indexed by orbit (disambiguation).
 * Also, it seems that User:Logicus is here to promote Aristotelian physics and has a fundamentally wrong argument: namely, that our definition of orbit must include all historical concepts that have now been superseded. I'm not responding to him any more until he gets a clue. The way, the truth, and the light (talk) 23:29, 30 April 2008 (UTC)


 * I agree that historical usage is of limited use here, as there are many more meanings than I would have imagined.

Fundamentally I think we should scope and title articles so that a naive but reasonably intelligent reader/user can find his way to what he wants as quickly, easily, and surely as possible. And also be comprehensive enough that someone on a more esoteric quest has a reasonable hope that finding his goal is possible following our pointers. The single sentence introductory paragraph does seem a bit sparse to me, but do you (TWTTTL) agree that restriction to central forces is too strict? I would like to see all cases that actually come up often in an astronomical context included, even though some (eg, n-body problem) are too specialized to deal with in detail here, and I think we could require that the trajectories in question be bounded (at least for a reasonably short time interval). Orbits of stars in galactic potentials, and also of charged particles in magnetic fields, I would propose to admit via the first sentence, but reroute later in the lead paragraph. I also think the disambiguation page needs some additions, as does our "See also" list. Being the main entry for "Orbit" seems to me to carry some responsibility to be comprehensive in helping folks to find the right track. I do think Logicus's version is sufficiently inclusive, but some additional words to map out the territory in more detail might be good. An alternative would be to leave all this to the disambiguation page, but a little more info than we give now could save the reader some false steps. Wwheaton (talk) 03:08, 1 May 2008 (UTC)

Orbits neither always gravitational nor restricted to planets or astronomy
User Wolkeeper changed the definition of 'orbit' to restrict it to gravitationally caused orbits and also removed important material on atomic orbits and quantum mechanics. But the article is neither just about gravitationally caused orbits nor just about planetary orbits and I suggest nor should it be. So Logicus has restored the previous more general definition of 'orbit' and also the material on atomic orbits. But do other editors think the article should be restricted just to planetary orbits or just astronomical orbits more generally, or even more restricted to just gravitational astronomical orbits ? I think the article should be expanded with a much more extended treatment of atomic orbits and quantum mechanics. --Logicus (talk) 21:53, 6 July 2008 (UTC)


 * The path of an electron around an atom is not an orbit, it's an orbital, so it's clearly off-topic. The use of the word 'orbit' for anything other than gravitationally bound objects is neither common, nor referenced.- (User) WolfKeeper (Talk) 22:48, 6 July 2008 (UTC)


 * While I support the desire of Logicus to expand wikipedia's coverage of things called "orbits" I also support the view of Wolfkeeper that this article is not the place for that. Logicus, please take a look at Orbit (disambiguation), which is the most general wikipedia page about all things called "orbits." This discussion we're having should probably be taking place on the talk page for that article! After all, the human anatomy experts (for example) have something they call "orbits" too! (sdsds - talk) 01:01, 7 July 2008 (UTC)


 * I agree it should be limited to gravitational orbits. This is a huge subject, especially when "box orbits" in galaxies, extensions to general relativity, etc are considered--way too much for a single article.  Also, quantum mechanical objects do not even have orbits or trajectories, things there are fundamentally different.  I can see no virtue in lumping them all together, except possibly in a single top-level disambiguation page.  And even there, if there is one "much-the-most-common" usage, I think we should make it easy on the reader by taking him there first. Wwheaton (talk) 18:49, 7 July 2008 (UTC)


 * Logicus responds to Wolfkeeper, Sdsds & Wwheaton: Thanks for your comments. It is of no concern to Logicus whether this article is only to be about planetary orbits, but thus retitled as such, or more generally about gravitational orbits, but again appropriately retitled as such. But orbits in general are neither merely planetary nor merely gravitational, the most important orbits in 20th century physics arguably having been those of electrons in quantum mechanics, which were normally referred to as orbits, notwithstanding any currently fashionable Humpty Dumpty linguistic fascism to rename them 'orbitals'. And as the Wiki article on 'atomic orbitals' opens, 'orbital' is the name of the mathematical function that describes the orbit, which is not the same as the electron orbit itself: "An atomic orbital is a mathematical function that describes the wave-like behavio[U]r of an electron in an atom"
 * As for limiting an article about planetary orbits to gravitational orbits, it is surely preposterous to exclude discussion of the pre-17th century millenia of non gravitational planetary orbits.
 * Gravitational planetary orbital theory only started AFTER Kepler's non gravitational theory of planets orbits. It started with the celestial mechanics of Galileo and his students such as Borelli, and also such as Roberval I think.
 * As for Wolfkeeper's 'Royal We' restoration comment "WE'RE not writing a 17th century encyclopedia, and orbitals are very, very clearly off-topic here.", whoever WE may be, on the contrary to Wolfkeeper's writing team and whatever they may be writing, this article currently does write about 17th century celestial mechanics in its 'History' section, such as its nonsense about Kepler's non-gravitational orbital analysis, which must thus mercifully be deleted if 17th century history is to be excluded.
 * And contra Wolfkeeper, electron orbits are very, very, very clearly on topic here, and indeed the article once included a small section about them.
 * Why should magnetic attractive force orbits and also nuclear force orbits be excluded from an article on kinetic orbits in general ?


 * Seems to me if Wolfkeeper and his writing team are to have their way, then at least the article needs retitling 'Gravitational planetary orbits', or maybe the more general 'Gravitational celestial orbits' to include non-planetary orbits such as stellar orbits.
 * Given Wwheaton's pertinent observations on the massiveness of just that topic, I suggest the latter retitling. --Logicus (talk) 16:27, 10 July 2008 (UTC)


 * I flatly disagree with every single part of this. First, just because the 17th century concept of orbits didn't involve gravity doesn't mean that that isn't the current understanding- that is what we are trying to cover, the knowledge of the current understanding, including the current understanding of what people used to think on this topic. It's perfectly fine that the orbit article should include the history, including parts which, at the time, were not considered (erroneously) to be gravitational.- (User) WolfKeeper (Talk) 02:18, 13 July 2008 (UTC)
 * Secondly, I disagree with the idea that the title is wrong. If you say the word 'orbit' to somebody, they think gravity, they think planet, spacecraft etc. etc. They don't think subatomic particle; that ended 80 years ago. If you read the guidelines of the wikipedia, an article of this name has to be about gravitational orbits, not about anything else because that's what the name most commonly suggests to people. Moving the article and adding a redirect from here serves no purpose. The current name advertises what the article is about perfectly well.- (User) WolfKeeper (Talk) 02:18, 13 July 2008 (UTC)
 * Thirdly, I completely disagree with the idea that an electron orbits around a nucleus. They don't. They are in a stable quantum wave around the nucleus that does not involve anything rotating in any normal way. Your description of an orbital as a mathematical fiction probably isn't entirely accurate, but it's still not an orbit either.- (User) WolfKeeper (Talk) 02:18, 13 July 2008 (UTC)


 * I continue to believe that "orbit" should be strongly discouraged in the atomic or nuclear context, as particles in quantum situations simply do not follow "trajectories" or orbits in the classical sense of the word. Using the same word simply perpetuates a misleading picture, obsolete for nearly eighty years.  And I think that to bring the typical reader most directly and efficiently to his desired target, it is getter to take him directly here, with the link to the disambiguation page for the many other possible meanings. Wwheaton (talk) 07:58, 13 July 2008 (UTC)

Note the creation of Kepler orbit at 21:33, July 8, 2008 by User:Stamcose. (sdsds - talk) 01:24, 13 July 2008 (UTC)


 * Logicus to Wolfkeeper:And I disagree with all you say, but instead of refuting your invalid arguments in tedious detail, here I just cut to the chase and point out no dictionary definition of 'orbit' I know of includes the notion of orbits being gravitational. The Popular Oxford just has "curved course of planet, comet, satellite, etc", for example. So I shall flag your invalid gravitational qualification of the definition I provided to request a justifying source, and delete it when you cannot find one and realise your definition is an idiosyncratic POV (-: --Logicus (talk) 18:09, 14 July 2008 (UTC)


 * So are you seriously claiming that in the definitions that a body goes around a celestial body in an 'orbit', and that this trajectory is not due to the physical phenomena commonly called gravity?- (User) WolfKeeper (Talk) 18:34, 14 July 2008 (UTC)


 * This discussion is becoming ridiculous. "Orbit" has many meanings (go look it up under group theory, for example), but for the purposes of this article we do not have to cover every possible meaning, and I believe most of the editors here agree that orbits due to gravity are a sufficiently comprehensive, and yet compact, subject to define the boundary in this context.    There are standard ways to deal with disputes here besides edit warring, and we can resort to them if necessary. Wwheaton (talk) 18:54, 14 July 2008 (UTC)


 * What's the matter, exactly? The first line of the article makes it clear that there are many different meanings of orbit, and it correctly points to a disambiguation page. The only reasonable change would be to make Orbit point to the disambiguation page, rather than the gravitational orbit page, but is it really that important, given that the first line of the article points to it anyway? Fpoto (talk) 07:27, 15 July 2008 (UTC)
 * Apologies for being a bit grumpy above. This discussion has been going for weeks (see Historical maldefinition of 'orbit'  section above), and I am tired of it, I guess.  Logicus (talk)'s position is (forgive me for putting words in your mouth, sir!  Feel free to correct me if I misspeak) is that we should broaden the article to cover other kinds of orbits.  I think the gravitational case deserves an article all its own, and I like for the names of articles to get the "typical" reader where they most likely want to go, in as few steps as possible.  I just modified the "otheruses" tag to restrict us to the gravitational case here.  Perhaps I was overbold, but I was hoping to close off the debate; others are of course invited to chip in. Wwheaton (talk) 14:14, 15 July 2008 (UTC)


 * There's a good reason why we don't do that in encyclopedias. Unlike dictionaries, an encyclopedia article is on a single topic. So if you look up orbit in the dictionary, there's usually a bunch of definitions numbered 1 to n. For an encyclopedia article, you can pick just one of those and use it for the article. That's the difference between a dictionary and encyclopedia- an encyclopedia is on a single, unitary, topic whereas a dictionary has all of them in one place.- (User) WolfKeeper (Talk) 14:35, 15 July 2008 (UTC)


 * But there is a sense in which Logicus may be somewhat right- gravity isn't the only force in the solar system, there are also photons, magnetic fields and the solar wind, which have an effect also. But in every inertial case (i.e. ignoring rockets actually under thrust) I can think of, gravity is by far the strongest.- (User) WolfKeeper (Talk) 14:35, 15 July 2008 (UTC)

Logicus: The article currently starts

"In physics, an orbit is the gravitationally curved path of one object around a point or another body, for example the gravitational orbit of a planet around a star.[1]"

But the justifying reference currently given for this definition of 'orbit' as gravitational, namely to a JPL teaching text on Basics of Space Flight, does not in fact justify this definition of orbit at all, and apparently nowhere defines 'orbit' even. I therefore delete it and yet again flag this idiosyncratic definition for some justifying reference, though of course it is almost certain none will be found. To define orbit in such a perverse way that means planets were not conceived of as having orbits in physics before the 17th century, because they were not thought to be gravitational before then, is so clearly ludicrous that it is highly unlikely any reliable source will be found that commits this blunder.

The article then claims:

"Historically, orbits were FIRST understood in terms of epicycles, which are the sums of numerous circular motions."

FALSE. (i) Before epicycles were first introduced by Heracleides and Apollonius, at least since Aristotle apparent planetary orbits were explained by planets being embedded in transparent nested concentric rotating spheres made of a fifth element. (ii) Nor were epicycles "sums of numerous circular motions". Rather orbits were explained as the result of compounded spherical rotations, which came to include epicyclical spheres/rotations.

It then claims:

"This predicted the path of the planets quite well, until Johannes Kepler was able to show that the motion of the planets were in fact elliptical motions."

FALSE. (i) Epicyclical astronomy continued to predict planetary orbits quite well long after Kepler and even better than Kepler's tables. (ii) Kepler never showed planetary orbits are elliptical. In no published work did Kepler ever demonstrate the ellipses he hypothesised for 11 celestial bodies agreed with Tycho Brahe's orbital data, nor any others.

It then claims

"Sir Isaac Newton was able to prove that this was equivalent to an inverse square, instantaneously propagating force he called gravitation."

Illiterate nonsense. Elliptical motion and gravitation are not equivalents in any sense.

I provisionally flag all these mistaken claims, to be rewritten.

--Logicus (talk) 16:22, 28 July 2008 (UTC)

Mangled sentence

 * The radial force is &fnof;(r) per unit mass is ar, then[...]

The phrase above appears in this article, with the repetition of the word "is". Can someone say what it means? Michael Hardy (talk) 00:56, 24 December 2008 (UTC)


 * Maybe: "The radial force per unit mass, &fnof;(r), is the radial acceleration, ar.  Then the elimination of the time variable from the radial component of the equation of motion yields:" ??  After I get some sleep I might even be able to say if it makes sense, besides being syntactically plausible.  Wwheaton (talk) 06:27, 24 December 2008 (UTC)


 * The phrase should be written as: "The radial force &fnof;(r) per unit mass is ar", which is quite simple, because radial force is mass (unity, in this case) times radial acceleration. The phrase could be rewritten for clarity as


 * The radial force &fnof;(r) per unit mass is the radial acceleration ar; eliminating the time variable from the radial component of the equation of motion yields:
 * Done--Pot (talk) 16:01, 11 January 2009 (UTC)
 * Better yet, one should make reference to the two previous formulas that are used to obtain the subsequent one. In books, formulas are typically labelled with numbers, like (3). How is it done on Wikipedia?--Pot (talk) 19:41, 25 December 2008 (UTC)
 * Apparently, this is not normally done on Wikipedia, so I did not do it--Pot (talk) 16:01, 11 January 2009 (UTC)

What still remains to be clarified is how eliminating the time variable from the radial component of the equation of motion is done. --Pot (talk) 16:24, 11 January 2009 (UTC)

open orbits
Is it common for astronomers to call hyperbolic and parabolic motion orbits? To the layman, this is confusing. Orbits in common language implies periodic motion. If this is a common way for astronomers to speak, there should be an introductory sentence that explains this. Like this: "Astronomers commonly refer to any motion of one body relative to another as an orbit, even if the motion is not in a circular or eliptical path." It seems this article could use some translation into common English! -- Samuel Wantman 06:01, 30 July 2005 (UTC)

For astronautical engineers, spacecraft engineers and astronomers, I think it is common. Looking at the definition of "orbit" states that it is a "path" and I cant really see an implication of periodicity. The Greeks are probably the ones who coined the term "orbita" (path) for the wanderers (planets) as they probably did not observe open orbits (how could they have?). Open orbits were probably a mathematical result first before they were observed, hence the misnomer. Wicak 09:19, 3 August 2005 (UTC)


 * It isn't common, but seems OK in the context of a discussion of closed orbits. One does not speak of a hyperbolic flyby trajectory as an orbit, however, and escape from orbit around a body is... well... escape from being in an orbit. However, the term "infinite orbit", used later, isn't at all standard and should be removed. Harold f (talk) 21:54, 16 May 2009 (UTC)

David Tombe's history edits
David, you've really messed things up, adding the planetary orbital stuff to the history section, supported by sources with nothing to do with history. Why not leave it in the planetary orbit section or some such? And please, do not introduce a second reference style into the article; for this along, you need to be reverted. I'll see how far back have to revert to fix some of this mess. Please try again more carefully. Dicklyon (talk) 22:01, 12 July 2009 (UTC)


 * Dick, it followed on from the stuff that was already there about Newton. But you are correct that the whole article needs to be reorganised. As you can see, I put it in the planetary orbital section first time. But it was then out of flow with what was already in the history section. What I'll do is revert your reversion to get the stuff back, and I'll then reorganise it and bring the whole thing down to the planetray orbital section. David Tombe (talk) 23:51, 12 July 2009 (UTC)

What is a "hyperbolic solar system escape orbit"?
...and if it is a valid orbit, could someone who knows about such things, consider adding a description of it to this article on Orbit?

A "hyperbolic solar system escape orbit" is mentioned at New_Horizons (4th paragraph) but I cannot locate a description of it anywhere. Cheers. N2e (talk) 20:51, 19 October 2009 (UTC)


 * The previous section on 'open orbits' may be useful to keep in mind in answering the question as the lay reader and space physicists are likely to have a rather different understanding of the vernacular English word orbit.

It is more accurately described as a "hyperbolic escape trajectory" ("orbit" implies a repeating non-escape pattern, though I recognize that usage may vary). Long story short, in Newtonian gravity, paths of light objects near (isolated) heavy objects are conic sections (circles, ellipses, parabolae, hyperbolae). Closed paths represent orbits, open paths represent flyby/escape trajectories. I hope this helps to clarify what is meant by this term. --Christopher Thomas (talk) 21:18, 19 October 2009 (UTC)


 * Yes, thanks, it does. And the mods that have been made to both articles are great improvements, and include links to the salient next level of detail.  N2e (talk) 22:42, 19 October 2009 (UTC)

Fact tags in lead section
Hi, I'm new to this article and its development. Why are there two citation needed tags in the lead? Don't the Kepler and Newton articles already explain and cite to heart's desire? Are these statements that could be "reasonably challenged"? Franamax (talk) 21:39, 20 October 2009 (UTC)
 * Well I think there are two ideas I could offer. My understanding is that in well-written, not-excessively-long ledes it is not necessary to cite each assertion, PROVIDING that the lede is merely summarizing information that is clearly articulated (and verifiably cited in the main body of the article.  I have no idea if that is true in this article or not so cannot answer your question about why the CN tags are there; I'll leave that analysis to other editors.  However, to your point that citations may not be needed for statements that are "explain"ed in another WP article, I don't believe that is quite correct.  The WP policy is quite explicit that WP cannot source assertions with other WP articles.  So I would think that if those claims are in fact made in the body of the article text then they would need to be cited.  Cheers.  N2e (talk) 01:25, 21 October 2009 (UTC)


 * You'd need to ask Logicus that- he put them there.- (User) Wolfkeeper (Talk) 06:54, 5 November 2009 (UTC)

Table of orbital data

 * This section has been moved temporarily to another location while it is under development. -- Metacomet 05:51, 31 December 2005 (UTC)
 * You might want to change this redirect if it comes out of development.88.159.72.240 (talk) 15:38, 16 December 2009 (UTC)

The picture Orbit2.gif
This animation is misleading.

The radius of the larger body is about twice the radius of the smaller body. Its mass should therefore be about 8 times the mass of the smaller body. The distance from the smaller body to the common centre of mass should therefore be about 8 times the distance from the larger body to the common centre of mass. But on the animated picture this ratio is about 1.4 instead of about 8 as should be!

Stamcose (talk) 12:31, 14 August 2008 (UTC)


 * You're assuming the density of the bodies is the same, which isn't necessarily so.- (User) WolfKeeper (Talk) 12:55, 14 August 2008 (UTC)

A sensible image should assume (about) the same density! I assume it is just a matter of setting configuration parameters to the animation a bit more cunningly!

Stamcose (talk) 10:04, 15 August 2008 (UTC)


 * I agree - the animation should be changed so that it corresponds to objects with the same density. It is said to be similar to charon-pluto, but Pluto is significantly more dense and thus in that case the figure is even further off.  --NealMcB (talk) 15:25, 19 September 2010 (UTC)

Kepler
I wonder if the statement "Kepler analyzed mathematically" is correct? As I recall reading, he made many many measurements over years, before arriving at a mathematical result. Empirical deductions would be a more accurate description. Wicak 09:12, 3 August 2005 (UTC)
 * The text has changed, but Kepler was a mathematician who largely relied on Tycho's observations, so indeed this was correct. See http://snews.bnl.gov/popsci/tycho-kepler.html --NealMcB (talk) 15:37, 19 September 2010 (UTC)

Schizophrenic lead
I find the lead to be quite strange. On one side it wants to be very rigorous, and says that orbits are not computable by classical mechanics, but only by general relativity. On the other side it gives a definition which applies rigorously to almost no celestial body ("around a point in space"). Solar system, for example, has many bodies, so that e. g. the Sun-Earth barycenter has not a fixed position (even neglecting the revolution aroud the center of Galaxy), and planets pertub one another (recall the discovery of Neptun and Pluto). The errors made by neglecting the many-body nature of the solar system are small, but many, many orders of magnitude greater than that caused by using Newtonian mechanics instead of general relativity.

Usually (and also in dictionaries) "orbit" means motion of a body around another (or, anyway, around some material thing), rather than around an abstract point, and this should be substantially the definition here. Which does not exclude that one can explain that the motion actually is around the center of mass, that the second body orbits, too, and so on. And it should be told that the orbits are usually calculated by Newton's laws, not only "for ease of calculation", but because they are a perfectly good approximation of the general relativistic theory, except in particular cases. I refer to Newton, rather than (as told in the lead) to Kepler, whose laws were written only for the planets of Sun, and not, for example, for Moon, artificial satellites or stars. --GianniG46 (talk) 19:18, 21 November 2010 (UTC)


 * I think the center of mass is a good thing to mention. - Sheer Incompetence (talk) Now with added dubiosity! 20:55, 21 November 2010 (UTC)

Hyperbolic comets

 * To date, no comet has been observed in our solar system with a distinctly hyperbolic orbit. - removed because other Wiki articles refute this? C/2006_P1 C/1980_E1 GBM (talk) 17:02, 27 January 2011 (UTC)

Entering orbit
Does, or should, one of the Wikipedia articles answer this question?:

If a small object traveling in a straight line enters the gravitational field of a much larger object and goes into orbit, is the first orbit an exact ellipse? If not, what is it? Does the ensuing sequence of orbits more and more closely approximate an ellipse, and if so, in what sense? And what determines the eccentricity of the ellipse that is asymptotically approached? Duoduoduo (talk) 15:16, 31 March 2011 (UTC)

Year-old mistake about magnitude of eccentricity
In this edit: http://en.wikipedia.org/w/index.php?title=Orbit&diff=320076098&oldid=320065491 User_talk:BobKawanaka asserted without reference that the "eccentricity of the planetary orbits is often not large. A circle has an eccentricity of zero, Earth's orbit's eccentricity is 0.0167 meaning that the ratio of its semi-minor (b) to semi-major axis (a) is 99.99%...." This is way off - e.g. the ratio of b/a for earth is more like 96.9%, and is much higher for most other planets. I don't know what "not large" was intended to mean, but the eccentricities have quite significant effects, so I've removed the paragraph. I'm surprised that this has been in the article unchallenged for nearly a year. It seems that more careful review is needed, especially for articles of "top importance" WikiProject Space/Importance ratings. --NealMcB (talk) 16:30, 19 September 2010 (UTC)


 * While it's true that any non-zero eccentricity is important, eccentricities of .0167 (Earth), .0068 (Venus), .0934 (Mars), .0483 (Jupiter), .0560 (Saturn), .0461 (Uranus), and .0097 (Neptune) [source: The Cambridge Planetary Handbook, 2000, p. 18] can reasonably be described as "not large". Moreoever, the originally given ratio of Earth's semiminor axis to semimajor axis, 99.99%, was correct, and the above given 96.9% is the one that is "way off". The formula is $$e=\sqrt{1- \frac{b^2}{a^2}}$$ so that $$\frac{b}{a} = \sqrt{1-e^2}.$$ Using Earth's e = .0167 gives b/a = .999860545.... Duoduoduo (talk) 15:04, 31 March 2011 (UTC)


 * Upon further investigation: the article Earth's orbit gives perihelion as 0.98329134 AU and aphelion as 1.01671388 AU, giving a ratio of $$r_{per}/r_{ap}=.9671....$$ By the formula (see ellipse article) $$e={{r_\mathrm{ap}-r_\mathrm{per}}\over{r_\mathrm{ap}+r_\mathrm{per}}},$$ this gives an eccentricity of .016711226...(in agreement with the Cambridge Planetary Handbook), which in turn gives a ratio of the semiminor to semimajor axis of b / a = .999860358..., or again 99.99%, confirming BobKawanaka's assertion. Presumably Nealmcb's mistake was in computing the ratio of perihelion to aphelion rather than the ratio of semiminor to semimajor axis.  Duoduoduo (talk) 16:48, 1 April 2011 (UTC)

trans-Martian injection orbits
I've looked, but been unable to find any info on Wikipedia about the nature of trans-Martian injection orbits. Anyone know if this is covered somewhere? Should it be? Cheers. N2e (talk) 23:25, 31 July 2011 (UTC)

Hierarchical pairwise simulations
At the end of the Newton's laws section, there's a statement about simulations followed by the sentence 'This is false.' Not useful. I don't know enough to to try validating or otherwise, so I'm adding a dubious statement tag. Lozzabates (talk) 10:22, 5 October 2012 (UTC)
 * The "this is false" is a piece of vandalism by user Fvfvdc that got left behind when people tried to revert the vandalism. I'll remove it. Martijn Meijering (talk) 10:31, 5 October 2012 (UTC)

Dubious statement
'It can be shown that a radial impulse given to a body in orbit doesn't change the orbital period (since it doesn't affect the angular momentum)'

This seems wrong to me. A strong enough impulse will give the body enough energy to move away from the central attractor forever. A slightly weaker impulse will give a huge orbit that might have any large period.

Can somebody show I'm wrong, find a reference backing the statement, or remove the statement. Thanks. —Preceding unsigned comment added by 80.229.247.11 (talk) 23:57, 10 April 2009 (UTC)

This statement does, in fact, seem to be incorrect! It seems to have been copied word for word from another website which didn't cite any sources.50.42.142.232 (talk) 14:51, 10 May 2013 (UTC)

Please clarify the definition of 'orbit'
I'm a novice with questions about the definition of 'orbit' presented in this article:

First, I was unable to figure out, from reading this article, whether an orbit is a path through space, or a path through space and time. In other words, is an orbit a purely geometric concept, or does it also describe motion? There are clues in the article, but they point in both directions. I think the ambiguity is unnecessary, and should be cleared up with a better definition in the very first paragraph. If the definition of 'orbit' is actually ambiguous -- sometime used to describe geometry only, other times used to describe motion -- then please say so up front. (Note that I've engaged in a related discussion on the Orbital Elements talk page.)

Second, I'm confused by the statement "around a point in space" which appears in the definition of 'orbit'. I know what it means, but is it really definitional? The mathematical expression for an idealized orbit establishes special significance to the focus of the ellipse, parabola, or hyperbola used to model the orbit, but isn't that special significance a consequence of the model, and not a fundamental property of the orbit itself? I don't understand why 'orbit' isn't defined simply as the path of any object subject solely to gravitational forces, and the existence of the barycenter presented not as part of the definition, but as a demonstrable consequence under certain modeling conditions.

Note that I read the earlier discussion Historical maldefinition of orbit, but it didn't clarify either issue for me.

184.187.180.7 (talk) 18:17, 19 June 2015 (UTC)

Assessment comment
Substituted at 01:56, 30 April 2016 (UTC)