Talk:3753 Cruithne

Not a moon!

I see that AStudent has recently changed this page so as to remove the "incorrectly" from "... sometimes incorrectly described as Earths second moon". Folks, I know it would be romantic to have another moon, but Cruithne is simply not a moon of the earth! It isn't even remotely close to being a moon of the earth! Any suggestions as to how we can put that idea into the article in such a way that the romantics won't remove it? Chrisobyrne 12:43, 18 October 2006 (UTC)

Saying it is "sometimes described as Earth's second moon" is true. Saying it is Earth's second moon would be different, and wrong. Inserting little disqualifiers like 'inaccurately' seems a bit prescriptive to me, but I won't remove it myself. I think something better would be a very concise explanation of (i) why it is called Earth's second moon and (ii) the fact that it is not a satellite of the Earth ("moon" has no strict astronomical definition anyway, I think.) Robin Johnson (talk) 11:26, 19 October 2006 (UTC)

I'm concerned that not having a qualifier like "incorrectly" could be interpreted as an endorsement of the "second moon" statement. As to the answer to your first question (why it is called Earth's second moon), I suspect that the answer is "because it's a romantic notion". The scientists words are being mis-interpreted by people who want to hear that we have another moon. Frankly, I don't think this article is a place for that discussion - I think that's a discussion that belongs on a human psychology page somewhere. Chrisobyrne 10:15, 20 October 2006 (UTC)

I disagree with "moon has no strict astronomical definition". According to Wikipedia :) "moon" means the same thing as "natural satellite". And, as an astronomer, that is also my understanding. And, I think the definition of "moon" would have to be stretched beyond breaking point before it could possibly include Cruithne. Chrisobyrne 10:23, 20 October 2006 (UTC)

Sorry for bringing this up again, but... It's not Earth's second moon, and scientists do not refer to it as such. I think that we are doing a disservice by saying that "some refer to it as Earth's second moon", because the only people who do so are popular science writers, and they (almost?) aways say that it is not. Even the reference cited in this topic is somewhat vague as to whether it should be called a moon or not. In short, I think "Earth's second moon" should be relegated to bad journalism. Personally, I liked the old intro that mentioned it was inaccurate to call it a moon. Lunokhod 00:03, 28 February 2007 (UTC)

Yes, but that's what's now written in the article, isn't it? Chruithne is just nicknamed "Earth's Second Moon"; I guess no scientist would ever consider this a valuable scientific statement. But I think, this fact is at least worth mentioning. — N-true 14:15, 28 February 2007 (UTC)

It would be handy if someone could provide evidence in either direction, because as I heard it it might be a moon of the Earth, but there is a split in the astronomical community, much like that over the classification of the term "planet". If anyone has any evidence rather than saying "No scientists say it is one so get over it" to paraphrase, then this debate gets nowhere, and ultimately neither side has any validity to their statements. I could say no scientists believe that monkeys exist but that doesnt consitute evidence to the suggestion that they dont exist, nor to the statement that no scientists think they do.

Indeed, while this is an article from 8 years ago, and may well be out of date, it does suggest that at one time scientists WERE calling it a second moon. http://sci.esa.int/science-e/www/object/index.cfm?fobjectid=11640

Indeed, here is a much more recent article (2005) that states it IS a "sort of" moon. http://www.rigel.org.uk/newsletter/200512/ EdB 101 02:15, 13 April 2007 (UTC)

A "moon" is both scientifically and colloquially accepted as meaning an object that orbits a planet. This fact is plainly obvious, and looking up any remotely reputable definition for the term "moon" will make this abundantly clear. It is not necessary to provide evidence of scientists calling it a moon or not. If a scientist did s/he was in error, or was not speaking literally. Because Cruithne does not orbit Earth it is misleading to refer to it as a moon. It orbits the sun! I fully agree that the original text: "sometimes incorrectly described as Earths second moon" is accurate and provides the best explanation of the facts. I realize this is now a rather old discussion, but obviously it needs to be reexamined. TragiCore (talk) 19:48, 3 March 2009 (UTC)

I like the description which was adopted in New Scientist 22 years ago: they nicknamed it "Earth's little sister". [As that publication often does, they were looking for a term which contained some popular appeal]. --DLMcN (talk) 08:29, 24 June 2019 (UTC)

2011 revisit

I have no axe to grind, but I find this discussion unsatisfactory. It seems obvious to me that the fact that an object orbits the sun is no argument against it also orbiting the earth; our existing Moon does both, as I think everyone will agree. Further, I am not at all certain that I know what criteria should be used to decide whether 'A orbits B' is a true statement. No-one has attempted to define this, and therefore to provide a reason for asserting one way or another whether Cruithne orbits Earth. Looking at the first animation (which I know is a 2-dimensional representation of a 3-D reality; the plane of Cruithne's orbit around the sun is inclined to that of the earth), it seems to me that the displacement vector from the Earth to Cruithne rotates monotonically through 360 deg during each period of the motion of the objects. Could this be used as a definition of 'A orbits B' (perhaps with the added condition that the vector should remain in a plane)? This definition would lead to the conclusion that the Sun orbits the earth, which might be an objection, but this could be overcome by acknowledging that 'A orbits B' is not in fact a scientific statement or concept. In reality both objects orbit a common centre of mass. So what I have proposed is actually a putative definition of 'mutual orbital motion' or some such concept. Can someone who knows something about this topic in depth please clear this up in a rigorous way ? — Preceding unsigned comment added by 82.32.48.177 (talk) 09:21, 11 November 2011 (UTC)

I do not think Cruithne every comes close enough to the Earth to even become a temporary satellite capture. I could claim that the Earth orbits the space station, but you already know that is a ridiculous statement "for general use", even if mathematically true. -- Kheider (talk) 12:52, 11 November 2011 (UTC)

Hey Kheider - thanks for your comment. What I am asking for is a formal definition of the meaning of 'A orbits B' so that we can answer the question 'Does Cruithne (C) orbit Earth (E)?' and give a reason for our answer. I have proposed a possible definition; if it is accepted then I would say that the first animation on the main page suggests that 'C orbits E' is a true statement. There might be an alternative definition which makes that statement false, but I would like to know what it is. How do you describe the kind of motion which makes the statement 'a space station orbits the earth' true ? Are you using the definition I have given, for example, or if not, what definition are you using ? Would you be happy with my definition if we include a requirement that the common center of mass is inside E (or B in the general case)? If we add this requirement we would not be able to say that the components of a double star orbit each other, and that might be unsatisfactory. (Dr Andrew Smith) — Preceding unsigned comment added by 82.32.48.177 (talk) 18:06, 13 November 2011 (UTC)

The first animation shows a 1:1 Orbital resonance and has nothing to do with Cruithne orbiting the Earth. Pluto does not orbit Neptune even though they are in a 2:3 resonance. -- Kheider (talk) 18:26, 13 November 2011 (UTC)

OK I see I will not get an answer to this. You continue to use terms without defining them. -- (Andrew) — Preceding unsigned comment added by 82.32.48.177 (talk) 22:25, 13 November 2011 (UTC)

Let me put this another way: When was the last time your saw Earth's moon on the other side of the Sun? When was the last time you saw the Earth's moon beyond Mars? A moon is suppose to orbit the primary body faster (EDIT: in less time) than it "orbits" any secondary body. -- Kheider (talk) 23:09, 13 November 2011 (UTC)

Right - now you are beginning to bite on the question. You are have added a condition to my initial definition (I suppose); namely your final sentence. However if we understanc 'faster' as meaning 'with a shorter period', then it appears that C's motion is a limiting case of allowed moons since it orbits E & S with equal periods (I think - based on the animation). I was about to ask "suppose the Moon's orbit were to increase; would there be a point at which 'M orbits E' would become untrue ?". You seem to have answered this. My second question is "Is the trajectory of C consistent with the situation which would exist if the period of a satellite of the earth were to be increased until it becomes equal to a year ?" If the answer to this is 'yes' then I would say that this is justification for saying that C is 'like' a second moon, but with an orbital period that is at the extreme limit of acceptable values for it to be said to be a moon. Andrew. — Preceding unsigned comment added by 82.32.48.177 (talk) 09:56, 14 November 2011 (UTC)

From the orbit article: "An orbit is the gravitationally curved path of an object around a point in space". As can be clearly seen in the pictures in the article the point in space Cruithne's orbit is curved around is the Sun/SS Barycenter, not Earth/Earth–Moon barycenter. Hence Cruithne is not a moon. --JorisvS (talk) 11:18, 14 November 2011 (UTC)

Hi JorisvS - Thanks for your contribution. You might accuse me of logic-chopping, but E does in fact occupy a point (or more than one point) in space around which C's path curves. That is the point I made in my original posting. There are many such points within the loop of C's trajectory. You will have to find a better definition than this in order to reach your conclusion. I'm afraid you have committed a non-sequitur; the correct logical conclusion is exactly the opposite of the one you reach. --Andrew

No, Cruithne's orbit is an ellipse with the Sun/SS Barycenter in one of its foci. This means its orbit is curved around the Sun/SSB, not the Earth. And here I mean Earth, not the orbit of Earth. This does not change when looked at from a corotating frame. --JorisvS (talk) 13:38, 14 November 2011 (UTC)

It takes 770 years for the series to complete a horseshoe-shaped movement, with the Earth in the gap of the horseshoe. It only takes only 1 year for Cruithne to go around the Sun. -- Kheider (talk) 14:04, 14 November 2011 (UTC)

I'm sorry JorvisvS, there are points which you make which I do not understand, and which seem obviously untrue: (a) the orbit of C is clearly not an ellipse; (b) the path of C does 'curve around the earth' (at least the animation shows that it does); perhaps it would help if you were to be more precise about what you mean by 'is curved around' - I have said how I understand this (see my first posting). But I don't want this to be a sterile argument. I am genuinely interested in knowing why, in conceptually rigorous terms, astronomers want to distinguish between an orbit such as C's and that of M. To say that C's orbit encompasses the sun does not satisfy me: the path of M, considered over a year, also encompasses the sun. It looks to me as though C is simply a case in which the 'month' has become the same as a year (but I might be wrong in this - it is just an impression). This is why I ask - 'what would happen if the orbit of a genuine earth-satellite were to increase ? - Would there be a point at which we would no longer say that it orbits the earth ?' I am sure that the answer to this must be 'yes', but is it possible to define that point or condition precisely ? Perhaps another approach would be to ask, "if the orbit were to increase, would there come a point of instability or discontinuity at which the the nature or the orbit would suddenly change so as to become significantly different from what it was at a smaller radius or shorter period ?. If there is no discontinuity, is the condition 'month=year' an arbitrary point of distinction in the sense that 'month'<year corresponds to 'moon' and 'month'=>year signifies 'non-moon'". -- Andrew — Preceding unsigned comment added by 82.32.48.177 (talk) 14:22, 14 November 2011 (UTC)

Earth's hill sphere extends about 1.5 million km from the Earth. Objects must orbit the Earth within this radius, or they can become unbound by the gravitational perturbation of the Sun. In terms of orbital period, all stable satellites of the Earth must have an orbital period shorter than 7 months. The Moon's orbit, at a distance of 0.384 million km from Earth, is comfortably within the hills sphere. Cruithne is way outside the Hills sphere. -- Kheider (talk) 15:31, 14 November 2011 (UTC)

Ok - this seems to be a step forward. Perhaps this is what you were referring to when you mentioned 'speed':- "A non-rigorous but conceptually accurate derivation of the Hill radius can be made by equating the orbital velocity of the orbiter around a body (i.e. a planet) and the orbital velocity of that planet around the host star. This is the radius at which the gravitational influence of the star roughly equals that of the planet." But I must say there is a danger of a circular argument here along the lines of "The Hill sphere is the region within which a satellite can be said to orbit a planet; 'orbiting a planet' means that the satellite is within the Hill sphere". I note that the Wikki page on Hill Sphere does not give an independent definition of "A orbits B". Perhaps is is sufficient to say that the concept of the Hill Sphere is used an an arbitrary criterion in the use of 'A orbits B'...... Andrew — Preceding unsigned comment added by 82.32.48.177 (talk) 15:55, 14 November 2011 (UTC)

The hills sphere is what determines if a body can be bound to another. Cruithne is not bound to the Earth, it is bound to the Sun. -- Kheider (talk) 16:06, 14 November 2011 (UTC)

A question

A question: this page states that the next time 3753 Cruithne will be gravitationally sling-shot by earth and have a series of close approaches will be around 2292 - but the page for 2285 writes that this will occur in 2285. Could someone clarify this?

"Cruithne shares Earth's orbit, but does not actually orbit the Earth. Instead, it follows a spiralling path that moves along the Earth's orbit in a horseshoe shape, the two ends of the horseshoe approaching either side of Earth but not quite reaching it. It takes Cruithne 385 years to complete one such horseshoe orbit."

- Not to sound stupid but I am not following this dicussion of Cruithne's orbit. Huh?  :-) (I think we need to specify: horseshoe-shaped as observed from where?)

Take a look at the diagrams and animation of Cruithne's orbit in the external link provided at the bottom of the page. If you can come up with a simple textual description of that, you are most welcome to replace the one above. :) -BD (Actually, since the images on the page are © Paul Wiegert, I'll email him and see if I can get permission to use them in Wikipedia. I don't think that a simple textual description is possible, period. :)

Good God! If I'm understanding that right, it IS horseshoe-shaped!!

Well, only from the perspective of the Earth. From the perspective of an observer who isn't viewing the situation from a point orbiting the sun at Earth's orbital radius, Cruithne is actually following a relatively conventional elliptical orbit around the sun. But since that elliptical orbit has almost exactly the same period as Earth's, it behaves as if it's orbiting around the Earth in this weird manner. I've just emailed Dr. Weigert for permission to use some of his diagrams here, when I get a response I'll see about trying to explain this more clearly. It's cool. :) -BD

"a relatively conventional elliptical orbit", Okay, thanks, that restores my faith in God and Newton.  :-)

Not forgetting Kepler, if you please! - Lee M 01:28, 4 Sep 2003 (UTC)

"But since that elliptical orbit has almost exactly the same period as Earth's, it behaves as if it's orbiting around the Earth in this weird manner."

NO IT DOESN'T! Have another look at the animation - even if you hold the Earth still, Cruithne KEEPS TO ONE SIDE of the Earth - it does not orbit AROUND the Earth. The horseshoe slowly migrates until it's edge comes close to the Earth, whereupon it reverses direction so that the effect can repeat itself with the other edge of the horseshoe after another 385 years (orbital inclination notwithstanding). There is a myth out there the Cruithne is a moon of the Earth, and I think everything possible needs to be done to kill this myth. (I know that Paul Wiegert says "The near-Earth asteroid 3753 Cruithne is in an unusual orbit about that of the Earth" - I think his choice of the word "about" is unfortunate, I think he probably means "in relation to").

No, he means "an unusual orbit about the orbit of the Earth". HTH HAND --Phil | Talk 14:58, Dec 23, 2004 (UTC)

Temperatures

The article gives the average surface temperature of Cruithne as 378 Kelvin, that's well above the boiling point of water. How can that be for an object orbiting the sun at an average distance comparable to earths distance and without an atmosphere for any greenhouse effects? Does anyone have an explanation for this? 84.160.196.181 14:23, 27 Feb 2005 (UTC)

The low albedo is responsible. The temperature estimate is computed from the albedo and assumes the surface reaches thermal equilibrium over multiple rotations, using the semi-major axis distance.

Urhixidur 18:47, 2005 Feb 27 (UTC)

A good discussion of the physics involved is, for example, Marco Delbo's The nature of near-earth asteroids from the study of their thermal infrared emission Chapter 2: Sizes and albedos of asteroids: the radiometric method and asteroid thermal models.

Urhixidur 22:20, 2005 Feb 27 (UTC)

Thanks for the explaination. I'm not quite satisfied because when looking at the moon its albedo (0.12) is even slightly lower than Cruithnes but the everage temperature is much colder. Hm, when realylooking at the moon it is quite bright so the albedo of 0,12 seems wrong. 84.160.223.61 15:05, 5 Mar 2005 (UTC)

The calculation goes like this. Assume thermal equilibrium, which means there is as much energy being absorbed per unit of time (from the Sun's rays) as is being emitted. The energy flux absorbed is a fraction of the solar luminosity (L_o = 3.827×10²⁶ W) determined by the ratio of the asteroid's presented surface (πd²/4, where d is the asteroid's diametre) to the orbital sphere (4πR², where R is the orbital radius). The albedo intervenes at this point; the energy flux absorbed is the fraction (1-A). Obviously, an albedo of 1 (perfect reflector) means no energy flux is absorbed. The energy emitted is the asteroid's surface (πd²) times the all-wavelength energy flux per unit surface, given by (σT⁴), where σ is the Stefan-Boltzmann constant (5.670 399 102 108 67×10^-8 W/m²K⁴). This is true for a black body (perfect radiator); for asteroids, an emissivity ε of 0.9 is assumed. Thus we have:

$\sigma T^{4}\pi d^{2}\epsilon ={\frac {(1-A)L_{o}d^{2}}{16R^{2}}}$

hence

$T^{4}={\frac {(1-A)L_{o}}{16\pi R^{2}\sigma \epsilon }}$

For the Earth, this calculation yields an average temperature of 255 K (actual average: 287 K); for the Moon, it yields 277 K (vs 250 K). This gives an idea of the error inherent in these estimates.

By the way, thanks for having me take a look at these again; it allowed me to spot a mistake that has resulted in systematically too high estimated temperatures in the asteroid articles!

Urhixidur 15:53, 2005 Mar 5 (UTC)

Thanks again. Now I have a better understanding. The T⁴ causes the average temperature to fall when maximum and minimum temperatures differ more strongly. Thus heat transport on the asteroid as well as the rotation period might have a significant impact.

By the way, when in some decades the first human will set foot on Cruithne I will proudly be telling my grandchildren that it was me that gave the crucial hint on not going too lightly clothed and better be wearing a double pair of woolen socks ;-) 84.160.223.61 19:11, 5 Mar 2005 (UTC)

Note that in the case of a strongly eccentric orbit, the definition of "average" temperateure used here is wrong --we're using the semi-major axis, whereas the time-averaged orbital radius is actually a(1+e²/2) (see here). Considering the asteroid's actual thermal regime (i.e., thermal inertia) complicates the calculation even further.

Urhixidur 01:44, 2005 Mar 6 (UTC)

Pronunciation

Paul Wiegert's page about Cruithne gives a different pronunciation than that given here. He says it has just two syllables, with the stress on the first. Who's right? --agr 05:17, 20 Jun 2005 (UTC)

Wiegert is right. The word is definitely two-syllabled with the stress on the first syllable. Krü-nyeh is a pretty good approximation of the correct Gaelic pronunciation. I guess KREEN-yeh would be the easiest way for Anglophones to pronounce it. That's my two cents, anyway! Eroica 12:48, 13 August 2006 (UTC)

Hi! If that is the truth, please correct this article with IPA. But, I wonder "Correct Gaelic pronunciation will be the two-syllabled one, but as an English word, how astronomers pronounciate it?"

In ja.wikipedia, a discussion about pronounciation of this asteroid is going on. Because foreign names are spelled in Japanese according to its pronounciation.--NJT 09:29, 24 August 2006 (UTC)

Is there an acute accent in the Irish spelling? If not, there's no /u/ sound, as in duine /ˈd̪ˠɪnʲə/ "person", and the nearest English would be /ˈkrɪn.yə/. If there is, as in súil /suːlʲ/ "eye", then there's no /i/ sound, and the nearest English would be /ˈkru.nyə/ (at least according to Wikipedia). Based on the cited sources, it might be the latter. I'm going to go ahead and put that in, on the rational that I might be right and the current listed pronunciation isn't even English, so correct me if I'm wrong. As pointed out above, what we really need is how astronomers pronounce it, but I imagine they're as clueless as we are, and each likely has his own idiosyncratic pronunciation. kwami 22:24, 8 May 2007 (UTC)

It would be great if you did not change the pronunciation of the Irish when I correct it AGAIN. -- Evertype·✆ 22:41, 9 May 2007 (UTC)

(And sorry, it wasn't you. My mistake.) -- Evertype·✆ 22:42, 9 May 2007 (UTC)

Cruithne would also be pronounced /krihənə/ with a palatalised n. That's how I would say as a Munsterman although other Irish dialects would be less inclined to pronounced the intervocalic /h/. I believe the Scots would probably say /krunjə/ but I can't be sure. I don't know how the Manx would pronounce it. I expect English speakers will use their own (incorrect) pronunciation anyway, as seen in ogham and crannóg. An Muimhneach Machnamhach (talk) 22:15, 8 June 2008 (UTC)

Yes, afaik from my Irish friend who speaks Gaeilge, Irish still has dialects and some words are pronounced differently in different parts of the island, e.g. the "bh" in the name Aoibheann will be like English "v" some places and English "w" in others. Pascalulu88 (talk) 02:18, 18 August 2023 (UTC)

Quibble: "jə". Then you link to this "http://en.wikipedia.org/wiki/Wikipedia:IPA_for_English" page for pronunciation guide. Find me that symbol on that page, please... A guide which isn't one isn't a guide. "How do I get from Miami, Florida, USA, to New York City, New York, USA?" "Well, you head south for a bit, then east." :-/ 24.250.195.181 (talk) 22:05, 11 January 2009 (UTC)OBloodyHell

"Croothny" would seem to be an intuitive English pronunciation. Rothorpe (talk) 23:39, 13 November 2011 (UTC)

Someone added a spelling pronunciation with the "th" pronounced, cited to a BBC game show. Actually, the host was corrected at the end, over his earpiece, and said it was "kroo-EE-nyə". That's assuming he repeated it correctly, so it's hardly a RS, but it would be nice to know where the person correcting him got it from. Maybe just sounding it out with the knowledge the "th" is silent but little more?

Here[1] it's /'kru:j.njə/, but again that's an approximation of the Celtic, with a diphthong that does not occur in English. At Forvo[2] we've got an Irish pronunciation of ~ /'krʊnjə/. That would work easily enough in English. — kwami (talk) 00:29, 9 January 2014 (UTC)

Origin of Cruithne's name

"Cruithne was named after the first Celtic racio-tribal group to inhabit the British Isles. The Cruithne (aka Priteni or Picti) emigrated from the European continent and appeared in Britainnia between about 800 and 500 B.C. [3]."

I believe this is incorrect. In Scottish pseudo-history, Cruithne was the name of the first king of the Picts:

Pictish Kings:

"Mythical kings of the Picts are listed in the Lebor Bretnach's account of the origins of the Cruithnians. The list begins with Cruithne son of Cing (see Cruithne), and his sons Fib, Fidach, Foltlaig, Fortrend, Caitt, Ce and Circinn."

It is my understanding that the discoverer of Cruithne, Duncan Waldron, is of Scottish descent. It is also customary to name asteroids after individuals, not racial groupings.

Eroica 12:40, 13 August 2006 (UTC)

You are probably correct, but the main reference source (Schmadel's Dictionary of Minor Planet Names is uncertain whether the tribe or the king was intended. I have qualified the sentence in the article. Thanks for the suggestion. The Singing Badger 18:21, 19 August 2006 (UTC)

YouTube links

This article is one of thousands on Wikipedia that have a link to YouTube in it. Based on the External links policy, most of these should probably be removed. I'm putting this message here, on this talk page, to request the regular editors take a look at the link and make sure it doesn't violate policy. In short: 1. 99% of the time YouTube should not be used as a source. 2. We must not link to material that violates someones copyright. If you are not sure if the link on this article should be removed, feel free to ask me on my talk page and I'll review it personally. Thanks. ---J.S (t|c) 06:58, 7 November 2006 (UTC)

UFO Rumors

This rock has been stated on some websites as being a UFO, and UFO Casebook, Re.:Alien Races state that the reptile aliens are using a asteroid as a ship to get to Earth. 65.163.112.107 06:51, 9 March 2007 (UTC)

Now, how may this be placed ? Several websites do mention that this rock, others are UFOs in disguise awaiting the right time to hit this planet. What would YOU do if you saw a alien battleship/carrier in Earth orbit, yet at one that military assets can't get to it ? 65.163.112.107 06:55, 9 March 2007 (UTC)

Placed "UFO" in article, due to this matter. 65.163.115.203 (talk) 10:27, 17 February 2008 (UTC)

Seen those rumors myself on the indicated website indicated here. Is that shit for real ? If so, I'll eat hot sauce, so that a lizard will get ulcers. 65.163.115.203 (talk) 10:29, 17 February 2008 (UTC)

Are any of these web sites remotely reliable sources?--Bedivere (talk) 22:48, 22 February 2008 (UTC)

The word "UFO" is involked in a pseudo-serious context. Is that an even vaguely serious question? :oP 24.250.195.181 (talk) 22:11, 11 January 2009 (UTC)OBloodyHell

UFO's and sentient beings from outer space remain a completely unknown part of the universe. I don't want this in the wiki — Preceding unsigned comment added by 201.241.238.57 (talk) 22:01, 25 August 2016 (UTC)

Removing of "misleadingly"...

I had added to the statement of Cruithe being sometimes called a moon the word "misleadingly" (I admit, I had spelled it wrong twice, but I'm no native speaker, sorry). It was twice removed, with the reason that it's a) misspelled, b) a loaded word and c) unnecessary. I agree on a, of course, but not on b and c — I mean, it's clear that 3753 Cruithe is not a moon by definition, but that it's called "Earth's second moon" by various sources. To avoid that people who don't know as much about astronomy take up that term "second moon" or even believe that Cruithe is a moon of Earth, I added the word "misleadingly", to show that the statement is actually not quite correct and even unscientific. This statement should be marked as pseudoscience; maybe someone can find an adverb that's more appropriate? — N-true 18:31, 4 September 2007 (UTC)

Orbiting Lagrangian point L4? Oh no, it's not!

From the Earth-POV animation, it seems the orbit encloses L4. But by the text, this configuration won't last. The orbit will move away from Earth, through L3 and back towards the Earth on the other side, enclosing L5 before moving back away again. Bean-spirally horseshoe shape ...

I guess an animation reflecting this would be too much to ask for, right?  :)

But without any indication in the captions that this configuration is temporary, my first impression was that this asteroid indeed was in a stable orbit around L4. So, could someone please have a look at those captions, so that the very nice animations don't mislead us poor ignorant readers? (I'd make a suggestion, but I'm coming up short.)

Thanks! — the Sidhekin (talk) 20:33, 9 February 2008 (UTC)

Sorry, folks -- I don't believe this is in either the L4 or the L5 positions.

-- 1) L4 and L5 are roughly immobile with regards to the Moon, just located ahead or behind it in the same orbit. You don't "orbit" a lagrange point (mostly) you "sit" in it.
-- 2) L4 and L5 are "semistable" -- stable like a ball at the bottom of a bowl. It is L1, L2, and L3 which only nominally stable (like a ball balanced on an unsecured pin), and those also don't "move" in relation to a line through the centers of the earth and moon. This thing is all over the place. My guess is that it's probably a chaotic attractor. I don't have the time or the immediate skills to evaluate that assumption, though.
-- More here: Lagrangian point —Preceding unsigned comment added by 24.250.195.181 (talk) 23:48, 11 January 2009 (UTC)

Yeah, but... Tadpole orbits. They go around the L4 and L5 points, and can even very nearly nudge L3 at their trailing edges. And that shape in the current animation showing the orbit "as seen from Earth" sure as heck looks like a somewhat fat, blunt tadpole. And from a cosmic standpoint, librating around a certain orbit or relative point in space essentially counts as "sitting in it". If that wasn't possible and allowable, all the Jupiter Trojans and such would have to cram closely together to form a single accreted mass centred on the main planet's lagrangian points, with anything that couldn't do that ending up spinning wildly off into space. But of course the trojans are actually more clustered around those points, in non-static positions that oscillate around the L4 and L5 (and if you count the Hildas, and account for the extrastellar barycentre between Jupiter and Sol that may actually put them at the Jovian L3...), some of them being pretty wild, stretching out towards Neptune and in towards Mars and Earth.

Therefore, there seems to be some validity in the notion that it may be tadpoling around L4 right now, but with the chance of being peturbed into horseshoe relationship that slides back around towards L5, and maybe stabilising there for quite some time also. Unless of course it really is detatched from Earth other than having a very-nearly-but-not-quite (to within some parts in a thousand or even million) 1:1 resonance, and its otherwise independent orbit merely *looks* conveniently like a lagrangian tadpole. But then as orbital mechanics don't really care for "intent" or human-convenient categorisation, what exactly is the difference between that and anything else in a similar looking orbit? A track is a track...

Oh, and, also... you're getting confused with the Earth-Moon (Earth-Moon-Sun?) Lagrangian points, and the Earth-Sun set. Cruithne quite obviously isn't anywhere close to, or orbiting in harmony with the Earth-Moon LP's - for one thing, it would have to circle earth once every four weeks. The set of objects we have in mind are co-orbital with Terra herself, NOT Luna, and thus have a period of approximately one solar year, not one lunar month. Does this change your arguments at all 209.93.141.17 (talk) 02:53, 25 September 2017 (UTC)

Cruithne certainly seems to be in a tadpole orbit around Lagrangian point L4, just as much as 2010 TK7 is. And 2010 TK7 is clearly described as an Earth Trojan, even though it "oscillates about the Sun–Earth L4 Lagrangian point (60 degrees ahead of Earth), shuttling between its closest approach to Earth and its closest approach to the L3 point (180 degrees from Earth)", and originally "may have been oscillating about the L5 Lagrangian point (60 degrees behind Earth), before jumping to L4 via L3." So what is the big difference between 3753 Cruithne and 2010 TK7 that make the latter a Trojan at L4 and not the former? George Fergus (talk) 21:59, 16 May 2020 (UTC)

Is the section titled "Similar Minor Planets" a typo?

http://en.wikipedia.org/wiki/3753_Cruithne#Similar_minor_planets

I think it should read "Similar NEO's", or something like that. —Preceding unsigned comment added by Chuck starchaser (talk • contribs) 18:08, 11 October 2009 (UTC)

Since this section discusses the moons of Saturn, and the last paragraph is about co-orbital asteroids, I think it is probably better to refer to them as "minor planets" since Jupiter trojans are not NEOs... -- Kheider (talk) 19:18, 12 October 2009 (UTC)

orbit

the article states that the orbit period is less than the earth's, but that isn't a stable relationship ... over a very long period, the orbit is (unless i'm missing something) the same as the earth's. both of these seem to be accurate values for the period (depending on your time frame). shouldn't the article reflect this? when i see a difference i immediately wonder how there can be a 1:1 resonance

All orbits vary due to perturbations. Cruithne has an orbit that is unstable over a long period of time, and on astronomical time scales is only briefly a Quasi-satellite in a 1:1 resonance with the Earth. Basically it is little asteroid that has the same basic orbital period as the Earth. -- Kheider (talk) 15:17, 9 August 2010 (UTC)

Bean-shaped orbit

The animation showing Cruithne's orbit from the perspective of the Earth depicts the Sun as never being between Earth and Cruithne. This contradicts the animation that depicts Cruithne's orbit for real.--Jarhed (talk) 14:55, 16 June 2011 (UTC)

Between 1950 and 2050, Only on 1976-Jan-27 did 3753 Cruithne come within 0.5° of an alignment with the Sun. On 2032-Jan-21 it will be 8.74° from the Sun. -- Kheider (talk) 19:46, 16 June 2011 (UTC)

What contradiction? Both animations show that Cruithne is sometimes further from Earth than the Sun is; neither shows Cruithne passing behind the Sun. —Tamfang (talk) 20:25, 16 June 2011 (UTC)

Sorry, I stand corrected, thanks.--Jarhed (talk) 06:00, 17 June 2011 (UTC)

Quasi-satellite or not?

Cruithne is called a quasi-satellite. From the perspective of the dominant body quasi-satellites appear to orbit it in a retrograde direction. Yet the description of its orbit is that of a body in a horseshoe orbit. So which is it? --JorisvS (talk) 11:32, 16 December 2011 (UTC)

Removed these related editorial bits from the running text of the article:

It is a minor planet that orbits the Sun in a horseshoe orbit{ { fix|text=Then it would not be a quasi-satellite; the image below shows a bean shape|date=October 2012 } } relative to Earth.

and

It has been incorrectly called "Earth's second moon" but it is a quasi-satellite{ { dubious|reason=Quasi-satellites appear to orbit the planet from its perspective, Cruithne does not|date=October 2012 } }

Feel free to edit the article to reflect the correct answer or talk about it here, but don't just muck up the mainspace without coming down one way or the other. — LlywelynII 10:33, 7 December 2012 (UTC)

Hey, I'm pretty new to editing wikipedia. Based on the articles horseshoe orbit and quasi-satellite both using Cruithne as examples, I removed the questioning tags mentioned above, making the article a lot more readable. I also copied over a reference used in the horseshoe orbit article. Clarification for OP: horseshoe orbit refers to how the orbit looks from earth's point of view, not a bird's eye view.Semitones (talk) 04:20, 27 December 2012 (UTC)

The description of its orbit was quite messy. Removing such tags without addressing the problem is generally bad practice. Luckily, I've finally managed to correct the problem myself. --JorisvS (talk) 17:24, 27 December 2012 (UTC)

Have we cleared this up yet, or is it still open to debate that e.g. it might be a wide-ranging Trojan? 209.93.141.17 (talk) 02:54, 25 September 2017 (UTC)

Reference no longer available

Lloyd, Robin. "More Moons Around Earth?". Space.com.

This reference no longer exists, but is cited from multiple times in the article. Very good data is available from the JPL sources, so I propose editing out any information the missing source that is not found in anouther source. I will wait a couple weeks before changing the article, so anyone who has another source or has an argument against this edit can make a case. --Kaiomai (talk) 06:25, 24 June 2012 (UTC)

Is it archived? — LlywelynII 10:30, 7 December 2012 (UTC)

Cruithne is not a moon, no matter what Stephen Fry claims.

...I belive Alan was klaxoned for saying "two" when it came up again. So Stephen corrected himself. Six Sided Pun Vows (talk | contribs | former account) 20:50, 14 February 2013 (UTC)

That's no moon. But where is a problem with the article, indeed? Incnis Mrsi (talk) 07:55, 15 February 2013 (UTC)

Left over from the creation of the Moon

Given the theories on the creation of the moon being that early stage solar system had two bodies colliding with a wobble effect the expelled the mass needed to create the moon -- I find it very strange that there appears to be no discussion about whether Cruithne is a left over of that processes. Any mass which was not pull back to either earth or moon would enter into a parallel orbit to the two which is exactly what we see -- Is there any references which discuss such hypothesis? — Preceding unsigned comment added by Sorenriise (talk • contribs) 03:56, 14 September 2013 (UTC)

Because a) its orbit is too unstable for it have remaind for that long, b) any remnant body would not be ejected into such an orbit. --JorisvS (talk) 11:14, 15 September 2013 (UTC)

Spike

In case anyone is curious about the spike in page views on and around December 19-20, 2014, it's because Cruithne was mentioned on the popular website thechive.com here. Matt Deres (talk) 14:21, 20 December 2014 (UTC)

Moon question revisted

Phys.org has just run an article calling it the second moon explicitly (though still in quotation marks in the headline) here, and this has been picked up by Huffington Post. I'm putting these here just in case there's been any revisions of official opinion. Remember Pluto was considered a planet until 2006 so it cannot be said that categories can't be changed, though I do think the official recognition of a second moon would generate some major headlines beyond HuffPo! 68.146.52.234 (talk) 16:54, 26 February 2015 (UTC)

• As Cruithne is currently in a heliocentric orbit around the Sun, any claims that it is currently a 2nd moon of Earth are pure bs. (As of 1 March 2015, Cruithne has an insanely Hyperbolic trajectory with an orbital eccentricity of 1500000 with respect to Earth. Cruithne "only" has eccentricity of 8000 w.r.t. Jupiter.) You might as well claim Pluto orbits Neptune. -- Kheider (talk) 17:01, 26 February 2015 (UTC)
• There is no chance in hell of that ever happening. It written that way because either the author is ignorant about the situation, being sensational, or both. A moon (natural satellite) is a body that does not orbit the Sun directly, but instead another body. Cruithne orbits the Sun directly, just like all other minor planets, but just happens to have its orbit configured in a specific way relative to Earth (this configuration is called a quasi-satellite). --JorisvS (talk) 17:05, 26 February 2015 (UTC)

Motion of 3753 Cruithne is not an instance of the Coriolis effect?

I notice that User:Seattle Skier has removed the comment I made some time ago that 3753 Cruithne' curious orbit (as seen from earth) is an instance of the Coriolis Effect. His reason is that it is "not relevant" to 3753 Cruithne. In a note to me on my Talk page he says "They are completely unrelated effects, other than the fact that both are seen in rotating reference frames, they have no other connection".

The Coriolis effect is a deflection of moving objects when the motion is described relative to a rotating reference frame. This rotating reference frame can be a turn table in your home, a rotating bowl of water in a laboratory, or the motion of water, air, or long-range ballistic missiles over the earth rotating on its axis. It also applies to the geographic paths seen to be taken by artificial satellites that orbit the earth, and it is a Coriolis “force” that keeps geostationary satellites above a fixed position on the earth’s surface. The curious motion of the planets that intrigued the ancients, but are now known, thanks to Copernicus, Galileo and Newton, to be due to Coriolis effects caused by using the earth's orbiting motion around the sun as the frame of reference. When the sun is used as the frame of reference the planets' motions are far more straight forward. The same can be said (and is emphasized in the is article, and on this Talk Page) about 3753 Cruithne’s strange orbit, as seen from earth. But, from what I gather User:Seattle Skier says (unless I am completely misunderstanding his very brief remarks), it seems that Coriolis mathematics does not apply, or is inappropriate at some arbitrary altitude above the earth’s surface. I’m obviously missing a very fundamental principle here. As far as I understand the Coriolis effect, it applies as much to an ant on a turn table watching a fly fly straight across that turn table, as it does to our observations of the motions of the objects in our solar system using our rotating and orbiting earth as the frame of reference.

Could someone please clarify whether or not 3753 Cruithne's motion as observed from earth is an instance of the Coriolis Effect or not. I'm very curious to know the readship's opinion on this. Cruithne9 (talk) 06:36, 22 July 2015 (UTC)

Cruithne9, you appear to be misunderstanding some basic physics here, such as the extent of what the Coriolis effect is and what it applies to, and you are thus misapplying it to cases which really have nothing to do with it. Take your statement that "it is a Coriolis “force” that keeps geostationary satellites above a fixed position on the earth’s surface." That is completely untrue: the Coriolis force ${\boldsymbol {F}}_{C}=-2\,m\,{\boldsymbol {\Omega \times v}}$ on a geostationary satellite is zero, because its velocity in the rotating frame is zero. In the rotating frame, it is entirely the centrifugal force ${\boldsymbol {F}}_{c}=-m\,{\boldsymbol {\Omega \times (\Omega \times r)}}$ which is nonzero and keeps the satellite in place versus plummeting downward, not the zero Coriolis force.

Your next statement that the "curious motion of the planets that intrigued the ancients, but are now known, thanks to Copernicus, Galileo and Newton, to be due to Coriolis effects" is also completely untrue, although for different reasons than the prior statement. The "curious" apparent retrograde motion of the planets can be explained without any reference to Coriolis effects or to any fictitious forces at all, it is a simple case of geometry and does not even need Newton's laws or any physics at all to explain. See the diagrams in that article which should make this quite clear. Similarly, the motion of 3753 Cruithne can be explained by simple geometry in the rotating frame as shown in the animated image File:Horseshoe_orbit_of_Cruithne_from_the_perspective_of_Earth.gif, without needing Coriolis effects or any physics at all.

Your statement that "I’m obviously missing a very fundamental principle here" appears to be quite true. Hopefully these examples provide some of the very simple explanation which you have overlooked, and will make it clearer where the Coriolis effect actually applies, and where it does not.

By the way, it is irrelevant what the readership's opinion on this is, because what is important for Wikipedia is that any information added to articles be verifiable in reliable sources (and also be correct!). There are no reliable sources which state that 3753 Cruithne's motion as observed from earth is an instance of the Coriolis effect, because that is simply not true. --Seattle Skier (talk) 08:54, 24 July 2015 (UTC)

Hi Seattle Skier. Thank you for this extensive explanation. I will need to ponder over it for a while to let the implications sink in, particularly in the light of the remarks about the apparent motion of distant stars as seen from the rotating earth in the "Distant stars" section in the Coriolis effect article, which seems to suggest that any motion (which I would imagine would include objects with an apparent velocity of zero) observed from a rotating frame of reference can be referred to as a "Coriolis effect". (No reference is provided in that section, so I cannot check whether astronomers are comfortable with the term or not, and what they would apply it to, if the term is used by them.) Cruithne9 (talk) 13:04, 24 July 2015 (UTC)

PS. I don't want this to sound as if I am arguing with you. I'm looking for information and enlightenment. So I hope you will bear with me here. As you say above, the Coriolis force is an entirely fictitious "force", as is the Centrifugal "force". Both effects can be explained in terms of simple geometry and physics. I therefore struggle with the dismissal of one fictitious force (the Coriolis effect) in favor of another fictitious force (the centrifugal force) to explaining the apparent behavior of a geostationary satellite. These comments probably sound ridiculous to you, but I would desperately like to know what types of motion viewed from a rotating frame of reference can and cannot be termed "Coriolis" effects. Cruithne9 (talk) 14:01, 24 July 2015 (UTC)

PPS. I think I may have discovered why we seem to be talking at cross purposes. When an object moves over the earth's surface (and is partially or wholly detached from that surface) it seems to follow a curved path. For someone observing that curved motion, and who is unaware that the earth is rotating, it would seem as if the object is subject to a sideways force causing it to deviate from traveling in a straight line. One can calculate the force that would account for this motion, and call it a "Coriolis Force". But it is an entirely fictitious force. The formula you use applies to this situation, which a special case of the Coriolis effect. When a straight-line motion across the solar system is viewed from our orbiting perspective, the path would also appear curved. The formula needed to calculate the "force" that might be responsible for that curved motion would be different from the one you present above. Things become mathematically horrendously difficult if the "real" motion is circular or elliptical round the sun. But that does not mean that the distorted motion as viewed from the orbiting earth is not an instance of the Coriolis "effect".

3753 Cruithne's bean shaped orbit in the vicinity of the earth is not due to Coriolis Forces (or, let's say, it would be foolishness to calculate them, as they would be unique to Cruithne, and applicable nowhere else in the universe). But that does not mean that its motion as seen from earth is not an instance of the Coriolis Effect. I hope this makes sense. Cruithne9 (talk) 20:29, 24 July 2015 (UTC)

Cruithne9, I will try my best to patiently re-explain things, as I've done this sort of thing many times in the past with students (I don't currently teach physics, but had to do so often in the past during several years of graduate work prior to my PhD and then several years working as research faculty after that). I apologize in advance if my comments seem snippy or curt, that is not my intent, but it is hard to convey tone properly in online writing. However, a real problem here is that you're just making up a lot of things out of thin air to fit your pre-existing beliefs, things which are not true, and some of this may be due to failing to read various statements carefully. Please be willing to read carefully and learn, while not clinging to your pre-existing beliefs about this subject. From your statements above:

"As you say above, the Coriolis force is an entirely fictitious "force", as is the Centrifugal "force"." I never said this in what I've written to you, you're putting words in my mouth. See above, I say "without any reference to Coriolis effects or to any fictitious forces at all", I do not ever say that the Coriolis force is an entirely fictitious force. The use of that term "fictitious" leads to a lot of needless trouble, perhaps it's best to call them pseudo forces or inertial forces instead, as they are very real effects in the rotating frame.

"Both effects can be explained in terms of simple geometry and physics." Not true at all, where did you get this idea? Simple geometry cannot explain or derive either the Coriolis or centrifugal force, you must use physics in a rotating frame to derive them. But as I stated, simple geometry CAN easily explain the apparent retrograde motion of the planets and the motion of 3753 Cruithne, without needing any physics. This is the most fundamental issue that you are having, by failing to understand this key point. You're trying to turn problems which need only simple geometry into physics problems, when they are not.

"I therefore struggle with the dismissal of one fictitious force (the Coriolis effect) in favor of another fictitious force (the centrifugal force) to explaining the apparent behavior of a geostationary satellite." As the equations show, the Coriolis force is dismissed in this case because it is ZERO. The centrifugal force is not dismissed because it is non-zero. That is it. There is nothing to struggle with. The Coriolis force turns out to be zero in this case, so it is not relevant to the behavior of a geostationary satellite.

"but I would desperately like to know what types of motion viewed from a rotating frame of reference can and cannot be termed "Coriolis" effects." The only types of motion are those for which the Coriolis force ${\boldsymbol {F}}_{C}=-2\,m\,{\boldsymbol {\Omega \times v}}$ is nonzero. Anything else does not involve Coriolis effects. And anything which can be explained using simple geometry (not requiring physics) is definitely not an example of the Coriolis effect either. These are the 2 key points for clearing up this misunderstanding.

"remarks about the apparent motion of distant stars as seen from the rotating earth in the "Distant stars" section in the Coriolis effect article, which seems to suggest that any motion (which I would imagine would include objects with an apparent velocity of zero) observed from a rotating frame of reference can be referred to as a "Coriolis effect"." Where did you get that idea from reading that section? Does it state that ANY motion observed from a rotating frame of reference can be referred to as a "Coriolis effect"? No, it does not say that. That section (which is somewhat confusing, totally unreferenced, and probably worthy of deletion) is entirely about the spinning motion of stars around the poles (see the circumpolar star article for more info on this). And as the equations in that section show, by the 3rd line the Coriolis term completely vanishes and the total ${\boldsymbol {F}}_{f}=m\,{\boldsymbol {\Omega \times (\Omega \times r)}}$, which is only a centrifugal (centripetal) force with no Coriolis component remaining (there is no ${\boldsymbol {\Omega \times v}}$ term left). Therefore there is no Coriolis effect in the simple circumpolar rotational motion of the stars. The last line of that section says exactly as much ("therefore recognizable as the centripetal force that will keep the star in a circular movement around that axis"). Since there is no Coriolis effect in that motion, that section really does not belong in that article, and I may delete it after further thought on the matter.

"3753 Cruithne's bean shaped orbit in the vicinity of the earth is not due to Coriolis Forces . . . But that does not mean that its motion as seen from earth is not an instance of the Coriolis Effect" Your first statement is true, the second one is false. The first statement implies that it is NOT an instance of the Coriolis effect. The bean-shaped motion relative to the Earth is derivable from simple geometry alone without needing any physics or Coriolis or whatever, and the animated image File:Horseshoe_orbit_of_Cruithne_from_the_perspective_of_Earth.gif demonstrates this derivation nicely. Please don't go looking to desperately call it a Coriolis effect, when it's just a simple geometric effect caused by the relative orbits of Earth and 3753 Cruithne around the Sun. --Seattle Skier (talk) 06:12, 25 July 2015 (UTC)

PPPS. Hi Seattle Skier. I would like to make just another point. The formula you provide for the Coriolis Force applies to objects moving horizontally over the earth's surface, and is used extensively in meteorology. That force is maximal at the poles and zero on the equator. But consider a bullet shot absolutely vertically upwards. Ignoring the influence of air currents, that bullet will come down slightly to the west of where it was fired from (both north and south of the equator), except at the poles, where it would fall down back into the barrel from which it was fired. The deflection is maximal on the equator. So here the Coriolis forces that account for this phenomenon have the opposite effect to the ones predicted by your formula. I only mention this to emphasize that the Coriolis Forces are instance specific, and do not define the Effect. My apologies for my ramblings on like this. Cruithne9 (talk) 03:54, 25 July 2015 (UTC)

"But consider a bullet shot absolutely vertically upwards. Ignoring the influence of air currents, that bullet will come down slightly to the west of where it was fired from (both north and south of the equator), except at the poles, where it would fall down back into the barrel from which it was fired. " This is completely untrue in the absence of air resistance. A bullet shot vertically upwards at the equator (or anywhere else on earth) in a vacuum chamber with no air resistance will fall back down at the location of the barrel from which it was fired, not just at the poles. A real bullet fired upward in the air will certainly end up deflected westward overall, but that is not the case you mention. I will explain why below.

"The formula you provide for the Coriolis Force applies to objects moving horizontally over the earth's surface" It is not the formula I provide, it is THE formula, and it applies in any direction, not just horizontal. It applies perfectly to the case of the vertical bullet, anywhere on earth, equator or pole or elsewhere. And it can be used to easily show that the bullet will fall back down at the location of the barrel of the gun anywhere on earth (in a vacuum chamber with no air resistance). That is because the non-zero Coriolis forces on the bullet as it ascends will be exactly equal and opposite to the non-zero Coriolis forces as it descends, since its velocity profile will be symmetric on the way up and the way down (in a vacuum chamber with no air resistance). The bullet will not stay vertically above the gun at all times as it ascends and descends (except at the poles), it will be somewhat west of the gun during its flight, but it will fall back down at the location of the gun because of that symmetric velocity profile.

"The deflection is maximal on the equator." This is actually correct, but the Coriolis deflection on the way up (westward) is exactly matched by the Coriolis deflection on the way down (eastward), so the bullet will fall back down at the location of the barrel of the gun (in a vacuum chamber with no air resistance). A real bullet fired upward in the air will certainly end up deflected westward overall, since it will be moving much faster on the way up than it does on the way down due to air resistance, and so the westward Coriolis deflection on the way up will be much greater than the eastward Coriolis deflection on the way down.

"So here the Coriolis forces that account for this phenomenon have the opposite effect to the ones predicted by your formula." Nope, this is not true, they are not opposite in any way. And again, it's not "my" formula, it's THE correct and only formula.

"I only mention this to emphasize that the Coriolis Forces are instance specific, and do not define the Effect." Nope, this statement is completely wrong, sorry. The Coriolis forces ARE the effect.. --Seattle Skier (talk) 06:12, 25 July 2015 (UTC)

Hi Seattle Skier. You present the image File:Horseshoe_orbit_of_Cruithne_from_the_perspective_of_Earth.gif as a sort of "proof" that Cruithne's bean-shaped motion relative to the Earth is derivable from simple geometry, and geometry alone, without needing any physics or Coriolis "forces" or whatever. But exactly the same can be said of all the following examples of the Coriolis effect taken from the following clips in the Coriolis effect article:

In the inertial frame of reference (upper part of the picture), the black ball moves in a straight line. However, the observer (red dot) who is standing in the rotating/non-inertial frame of reference (lower part of the picture) sees the object as following a curved path due to the Coriolis and centrifugal forces present in this frame.

Object moving frictionlessly over the surface of a very shallow parabolic dish. The object has been released in such a way that it follows an elliptical trajectory.
Left: The inertial point of view.
Right: The co-rotating point of view.

and this animation clip of a cannon ball being fired from a rotating platform.

In each case the motion seen by an observer on the rotating non-inertial frame of reference can be explained even more obviously, simply, and in its entirety, by geometry, without recourse to any physics, or related sciences, than your example of Cruithne's orbit, when viewed from an inertial (stationary) frame of reference. I see absolutely no difference between your example of the (File:Horseshoe_orbit_of_Cruithne_from_the_perspective_of_Earth.gif) and the examples given in the Coriolis effect article (and other sources) of the "genuine" instances of the Coriolis effect.

Furthermore, if I understand you correctly, you maintain that the formula for the magnitude of the Coriolis Force, ${\boldsymbol {F}}_{C}=-2\,m\,{\boldsymbol {\Omega \times v}}$, defines the Coriolis effect. But consider this situation. A spot of light from a laser pointer is moved at a uniform speed, in a straight line across a rotating turntable (the spot of light does not need to move across the center of the turntable). If the surface of the turntable is light-sensitive, the spot will leave a trail on the surface which is curved to exactly the same extent as the trail left by a ball rolled across the turn table at the same velocity. It is difficult to conceptualize a real physical force that will have such a profound effect on a spot of light. Now move the spot of light in an ellipse across the turntable. The ellipse’s dimensions are a scale model of Cruithne’s orbit around the sun, with the turntable’s axle in the position of the ellipse’s “sun”. It is timed so that the ellipse is completed in exactly the same time as one rotation of the turntable. A bean shaped trail will be formed on the turntable, which is a miniaturized version of the orbit of Cruithne as seen from earth. If you acknowledge that this is an instance of the Coriolis effect, then the one we see in the sky must also be due to the Coriolis effect resulting from our orbit round the sun. Cruithne9 (talk) 09:39, 2 August 2015 (UTC)

More on the Coriolis effect

Hi Seattle Skier. Very many thanks for the time and trouble you have taken to extensively respond to my concerns and misconceptions. I entirely agree that I got the bullet shot vertically upwards wrong. I should have realized that it would indeed come back down straight into the barrel of the gun from which it was fired, whatever part of the earth it was launched from. It was 3 a.m. in the morning when this idea occurred to me. My apologies. Though the bent trajectories bullets follow upwards and downwards are fascinating examples of the effects of the rotating earth.

Although I have no idea of how much of this discussion should be continued on the Talk pages of Wikipedia, because, much of this discussion could be resolved very quickly and efficiently through a face-to-face interaction, and then posted on this page in a few sentences, I feel I have to respond to some of the comments you have made.

Firstly, all of the texts explaining the Coriolis effect, including the Wikipedia article on the subject, start with the example of a rotating turntable or carousel, across which a pencil line drawn with a ruler (by a person outside the turntable) or balls tossed across the carousel either by a person on the carousel or by a person outside the carousel seem to follow curved trajectories when viewed by the person on the carousel.

Consider a rotating carousel (or merry-go-round), which, seen from above, is rotating clockwise. We will call the person on the carousel the “rotating” person, and the one on the ground outside the carousel as the “stationary” person. Any ball thrown across the carousel by either person follows a straight line as seen by the stationary person. But the rotating person will always see a curved trajectory. From the rotating person’s point of view it therefore seems that there is a force that acts (horizontally) perpendicularly to the ball’s motion to cause it to deviate from the Newtonian straight-line motion. This in not a real force, but an artifact of the observation relative to a non-linear rotating reference frame. (This is a direct quote form a Physics text book. The Wikipedia article on the Coriolis effect calls it a fictitious force, as do several other sources at my disposal). The entire effect can best be explained in terms of simple geometry, which, in your terms, if I understand you correctly, means that it is NOT an instance of the Coriolis Effect.

Where a “real” force comes into play (and cannot be explained in terms of simple geometry) is if the rotating person tries to move from point A to point B on the rotating carousel. If point A is close to the center of the carousel, and point B is near the periphery, then, if this person sets out in what he imagines is the shortest distance between the two points, he ends up to the left of his target. In order to reach point B he has to exert a sideways acting force to move him more and more to the right as he moves outwards towards B. On the carousel he will have traced a straight line trajectory, but according to the stationary person on the ground outside the carousel he will have moved along a curved path which can only have been caused by a sideways force. This force (or acceleration) is indeed real, because it required the expenditure of energy from both the rotating and stationary observers’ points of view. Is this the only instance of the Coriolis effect you would recognize as such?

If the turntable and carousel examples provided in all the introductions to the texts on the Coriolis effect are genuine, prototypical instances of the Coriolis effect then, by extension, any Newtonian motion beyond the carousel, viewed by the rotating individual, will also subject to Coriolis effects. Thus a ball thrown away from, or beyond, the carousel’s rim will also follow a curved as seen from the carousel. Indeed if it stays in the air for several turns of the carousel it will appear to follow an outwardly spiraling trajectory. In all cases the motion can be explained in terms of simple geometry from the point of view of the stationary observer. But if Newtonian motion across the carousel is correctly described as Coriolisean by the rotating observer, then the motion beyond the carousel must also be due to the Coriolis effect. It then ineluctably follows that motion observed from our orbiting earth of the planets and other objects in the solar system are also affected by the Coriolis effect. The fact that the complicated motions observed from earth are best resolved by translating them into the motions that would be seen by an individual in a stationary position in relation to the sun does not negate the fact that from the earth these motions are due to Coriolis effects, even though the stationary observer would ascribe them to simple geometry. The Coriolis effect does not exist for a stationary observer. But they are very real for an earth-bound observer unaware that he is on a huge 3 x 10⁸ km diameter carousel centered on the sun.

I know that you have said above that this nonsense, but you have not explained why it is nonsense, nor given any examples of when and how the Coriolis effect applies. For instance, are you suggesting that the turntable and carousel examples used in all the texts explaining the Coriolis effect are simply “lies to children” (to quote Terry Pratchett)? What would your interpretation of these examples be? In the “Visualization of the Coriolis effect” section of the Coriolis effect article in Wikipedia a puck of dry ice is slid across a bowl of spinning water. This puck follows an elliptic track (as seen by a stationary observer) across the parabolically curved surface of the rotating water in the bowl, although it bounces back and forth off the rim of the bowl. The Coriolis motion as recorded by a camera mounted on the rim of the rotating bowl is uncannily reminiscent of the orbit of Cruithne as seen from earth. Cruithne9 (talk) 12:39, 30 July 2015 (UTC)

This reply addresses both what you've written above, and your August 4 post on my talk page. Please understand that this will be my final comment on this topic, as I definitely don't have the time to continue this discussion any further. Sorry about closing it off, but you seem quite stubborn about this subject, which is frustrating for me and not enjoyable to deal with, and in some cases you also try to extend the scope of my comments too far beyond what I've actually written. I realize by now that whatever I say is unlikely to shift your views closer to the limits of what professional physicists consider to be Coriolis effects (versus the vast broad overextension that you prefer where Coriolis effects are seen everywhere in all situations that could be viewed in a rotating frame). So we'll just be going in circles here (!) if we continue this.

Key points to remember to unravel and understand the Coriolis effect:

• Only the most simple (trivial) examples used to demonstrate the Coriolis effect can be solved using simple geometry. In general, to solve any problem, physicists prefer to use the most simple description / method / frame of reference which gives a valid solution, so if you can solve a problem with simple geometry or by physics in the stationary frame, then great, do it that way, and don't bother using the rotating frame or Coriolis. You're confusing trivial demos which can be used to demonstrate what the Coriolis effect is (some of the simplest cases from the turntable / carousel demos) with problems which actually require using Coriolis effects in a rotating frame for their solution. The simple demos are great for an educational purpose, because they can be solved in both the stationary frame and the rotating frame.
• Real non-trivial examples of the Coriolis effect can NOT be solved by simple geometry, nor can they be solved in the stationary frame. It is simply not practical or possible to solve for the motion of the winds in the atmosphere, long distance artillery shells, Foucault pendulum, or various other classic real-world examples, using simple geometry or the stationary frame. These problems can only be handled in the Earth's rotating frame, leading to Coriolis effects. These are the cases that professional physicists would normally refer to as examples of Coriolis effects.

Returning to the original issue at hand here: in order to include anything in Wikipedia, it must be verifiable in reliable sources. There are no reliable sources which state that 3753 Cruithne's motion as observed from earth is an instance of the Coriolis effect (nor the motion of any other astronomical bodies), and so it can not state that in the article. Thanks. --Seattle Skier (talk) 18:12, 4 August 2015 (UTC)

Thank you very much. That makes it a it a lot clearer and understandable, and I am happy to close the discussion. Cruithne9 (talk) 05:26, 5 August 2015 (UTC)

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