Talk:VSOP model

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Indian astronomers

The following was just inserted into the History section:

Ancient astronomers like Aryabhatta II , bhaskara had done preliminary study and come up with fairly accurate orbits and forward orbital interpolations .

I have moved it here because there is no source. Also, the capitalization of the name(s) seems wrong, and it was just stuck into the history section without any meaningful discussion of the role of Indian astronomers in the area of secular variations of planetary orbits. --Gerry Ashton (talk) 20:40, 25 February 2008 (UTC)[reply]

Stable orbit

The following talk was in the discussion page of Kepler's laws of planetary motion. But an anonymous user suggested that this page is more appropriate for the talk :

According to Kepler's third law, the period of a planetary motion is propotional to the 3/2 th power of radius ( or semi major axis. ) But this is an idealised case. In reality, there is a very diffuse gas in the Solar system and the motion of the planets around Sun may be retarded by this gas. To be sure, the retarding effect is negligable. But the cumulative effect over millions of years may be considerable, which means that the delicate balance between the gravitational and cetrifugal forces is in danger. But luckily, we haven't observed any spirally inward motion of any planet. I think that the article must have a section to explain how the planets maintain their orbits over billions of years. Nedim Ardoğa (talk) 16:11, 16 October 2009 (UTC)[reply]

Maybe there should be a section, but it would have to be based on reliable sources, not speculation. --Jc3s5h (talk) 16:30, 16 October 2009 (UTC)[reply]

I have read several papers which discuss the evolution of planetary orbits and none have ever considered any diffuse gas retarding the planets. They have considered solar mass loss due to solar luminosity and solar wind, but this has increased Earth's orbital radius by the negligible amount of only the diameter of Earth over the last 4.5 billion years. See [1].

But the planets do not "maintain their orbits over billions of years". They don't even maintain their orbits over thousands of years because the planets perturb each others' orbits. Their orbits move in inertial space in essentially three ways: the line of their apsides (perihelion-aphelion) rotate, their inclinations to the invariable plane of the solar system change, and their eccentricities change. These changes are slow enough to allow any single orbit to be considered an ellipse, but even a few orbits produce noticeable changes in their "elliptical" orbits. Nevertheless, Newton's universal theory of gravitation coupled with mathematical techniques developed by Euler and others (embodied by VSOP over a few thousand years) can be used to calculate these orbits for at least several million years (if computational capacity was available). But many small bodies that orbit the Sun cannot complete even a single orbit without a significant deviation from an ellipse.

Only the four jovian planets (Jupiter, Saturn, Uranus, and Neptune) have orbits that can be rigorously calculated over the 10-billion year life of the solar system. The orbits of the terrestrial planets (Mars, Earth, Venus, and Mercury) are chaotic beyond about 30 million years. Venus and Earth are moderately chaotic, whereas Mars and especially Mercury are wildly chaotic. The eccentricity of Mercury can reach 0.9, causing its orbit to intersect that of Venus, possibly resulting in a collision. Furthermore, resonance with Jupiter can cause the entire inner solar system to destabilize about 3.3 billion years from now (1% probability), possibly resulting in the ejection of Mercury or Mars from the solar system, the collision of Mercury with the Sun, or the collision of any two of these four planets. See Mercury, Mars, Venus and the Earth: when worlds collide!. A good overview is Stability of the solar system. The red giant Sun will engulf Mercury, Venus and Earth (if they still survive) in 7.6 billion years. See Distant future of the Sun and Earth revisited. — Joe Kress (talk) 08:21, 17 October 2009 (UTC)[reply]

I would like to thank Joe Kress for his informative talk. (I will follow the links he suggested.) But I am afraid, such topics as effects of heavenly bodies on each other and future red giant stage of Sun are not exactly what I'd like see in this article. I merely ask for a paragraph which explains how the planets manage to maintain the stability of their orbits in the presence of interstellar gas. (By the way for the presence of diffuse gas see Solar System (Interplanetary medium) and Interstellar medium ) Nedim Ardoğa (talk) 13:52, 18 October 2009 (UTC)[reply]

Interplanetary medium discusses the solar wind and interplanetary dust. In addition, much larger meteoroids continually bombard all planets, preferentially on the side facing the direction of their orbital motion. But again, I've never seen any one consider these effects on the evolution of planetary orbits, so even discussing maintaining planetary orbits in their presence can only be discussed in the article if you can find a reliable source. — Joe Kress (talk) 23:02, 18 October 2009 (UTC)[reply]

I instead propose Kepler's laws of planetary motion for that topic. Rursus dixit. (^mbork³!) 21:01, 14 March 2010 (UTC)[reply]

Dubious paragraph

The second paragraph of History seems to be in grave grave error: it currently claims that Tycho, Kepler and Newton couldn't make predictions on their work, but instead extrapolated earlier observations. Seems like contrafactual to me, the real story going about as following:

Copernicus made a full heliocentric system based on epicycles, including computations and predictions, which however was better than the geocentric system based on Ptolemy and updated medieval tables of Toledo, only because the medieval tables of Toledo weren't fresh, and Copernicus'es tables were fresh;
Kepler was the first to introduce elliptical orbits, among others using the very computational Kepler's Equation which together with spherical trigonometry and orbital elements of the planets — computed by Kepler himself — is quite enough to compute planetary orbits better than any epicycle-based system;
Newton made so much maths and physics, up to and including founding mathematical analysis, so that one could derive Kepler's Equation from his classical general theory of gravity, and also parabolic and hyperbolic motion with unprecedented precision; it was with this maths that Halley connected a number of comet occurrences to be one comet, later named Halley's Comet after him. This feat he performed already in 1705.

Rursus dixit. (^mbork³!) 21:01, 14 March 2010 (UTC)[reply]

The gist of that paragraph is from a VSOP article IIRC. "Higher mathematics" refers to the first solutions of the multibody problem (three or more bodies) by Leonard Euler, Tobias Mayer and other mathematicians about 1750. Newton was unable, using only his gravitational theory, to find the position of the Moon, which is a three-body problem, Moon-Earth-Sun. Elliptical orbits for planets and predicting the orbit of a comet like Halley are both two-body problems. — Joe Kress (talk) 07:07, 20 March 2010 (UTC)[reply]

Expanding spacetime theory

I'm not a cosmologist so I can't give a professional judgement, but this theory smells of fringe science. The article cowritten by Kolesnik & Masreliez looks legit on superficial inspection, but predates the self-published (?) book and seems to have no clear relation to it. Unless reliable sources can be found that demonstrate that 1) Masreliez's expanding spacetime theory is mainstream science and 2) this is relevant to the current article the links do not belong in this article. Martijn Meijering (talk) 10:10, 20 May 2010 (UTC)[reply]

Hi Martijn,

How come you don't like the smell? Maybe you are just mixing fringe science up with pseudo science? As for the predating, I do not get your point. Kolesnik published his first ideas on the secular accelerations in 1995/-96, which Masreliez is referring to in his first (1999) peer reviewed paper on his SEC model and his popular book account (2000), as one possible evidence of his predicted new drag effect. Kolesnik finalized his analysis of planetary data and had it published with Masreliez in 2004.

Before crying for mainstream perhaps you should take a look at non-standard cosmology. The outcome should have a bearing on ephemeris up-datings. Cheers / Kurtan (talk) 13:57, 21 May 2010 (UTC)[reply]

Looks dodgy to me, too William M. Connolley (talk) 19:38, 9 February 2011 (UTC)[reply]

I've moved this to talk for now, since I don't trust it.

Planetary secular acceleration of cosmological origin

^{[dubious – discuss]}

Traditionally, the secular bias in residuals of differential optical observations of the Sun and planets results from the following four factors:

constant error in the proper motions of a reference catalog (residual rotation with respect to the dynamical reference frame);
the effect of the tidal acceleration of Earth;
secular errors of the longitudes in a comparison ephemeris;
systematic observation errors.

Masreliez cosmological model SEC of (1999), being a conformal time FLRW solution of Einstein's field equations of general relativity, predicts an alternative explanation that planets secular acceleration is also of cosmological origin. The net result is that the planet accelerates in its orbit, while slowly falling toward the sun. The relation for the change in angular velocity given by SEC is

{\frac {d\omega }{dt}}=3\omega {H_{0}}

where 1/ ${H_{0}}$ is the Hubble time and ω is the increasing angular velocity. This tiny change will cause the Earth to fall roughly 22 meters closer to the Sun per year.

About 240,000 worldwide optical observations of the Sun, Mercury, and Venus, accumulated during the entire era of classical astrometry from James Bradley up to the present, were compiled by Kolesnik et al during the 1990s and used to analyze the secular longitude variations of the innermost planets. A reduction method relating historical planetary observations to the Hipparcos reference frame is presented. Secular trends in the longitudes of the Sun, Mercury, and Venus with respect to the ephemeris DE405 are estimated for the time span 1750-2000.<ref name=Kolesniketal/> It was concluded that

the apparent equinox motion resulting from the 250 year interval of optical observations cannot be interpreted as an actual rotation of the Hipparcos system. More likely, it is caused by systematic errors in the right ascensions of the 19th century observations. In order to properly investigate the residual rotation of a reference catalog, only 20th century observations should be used.

A back of the envelope calculation using a change in semi-major axis of 22 meters per year yields a change of 7 ms in the length of the year per year. This may seem small, but is actually quite huge compared to the known precision of the length of the solar year-- if this is true, then I don't doubt that someone must have noticed this anomaly before and published about it. siafu (talk) 04:10, 18 March 2011 (UTC)[reply]

Discussion of the above

(note that the above is a version *after* a few mods I made. See [2] for the "original").

This section relies heavily on the Masreliez model, yet that link is to a family name not a person. So a bare minimum for re-insertion has to be identifying the author of this theory William M. Connolley (talk) 13:06, 10 February 2011 (UTC)[reply]

No more, he is now on the family article. If you understand French (I don't), you can follow the links to a person article there. I did a short version on the Japanese wp some time ago, as I find his ideas quite viable. Mariguld (talk) 15:41, 27 February 2011 (UTC)[reply]

The Masreliez model, Expanding Spacetime Theory, beeing a non-standard cosmology inviting disputes, you should not expect to find it, or a person article, on all wp versions. So if this prank is for reaching some kind of consensus, I suggest the passage be reinstated without delay. Mr Gearloose (talk) 12:20, 9 March 2011 (UTC)[reply]

Arbab / Intro

The intro ends

Lesser secular accelerations of cosmological origin in the solar system have been verified by Arbab (2008)[1]. Arbab is relying on an additional theory that emerged 1999-2004 from compiling planetary observations by Russian astronomer Yuri B. Kolesnik and theoretical predictions in a cosmological context by Swedish-American physicist C. Johan Masreliez.[2]

But there is no mention of Arbab in the article. This needs to be resolved, by either deleting him from the intro or adding to the article William M. Connolley (talk) 14:59, 11 March 2011 (UTC)[reply]

Which article is supposed to mention Arbab? If I recall correctly, Arbab (2008) is citing Masreliez (2004) and I take it that's why the additional, missing fact was added. If you are going to have a substantial chunk of "secular accelerations of cosmological origin" in the article, as I too claim you should, it must certainly be mentioned in the intro. Stop making a mess of this once quite informative article. Kurtan (talk) 20:01, 11 March 2011 (UTC)[reply]

I don't know what you're talking about. "Stop making a mess" is rather combative of you: if you care to point out which of my edits you think was messy, we could discuss it William M. Connolley (talk) 11:00, 16 March 2011 (UTC)[reply]

I actually skimmed over the paper in question today, and I think "verified" is an overstatement. He suggests these explanations, but they haven't been verified at all, by anyone. siafu (talk) 17:54, 18 March 2011 (UTC)[reply]

A more thorough leads me to conclude that this paper should not be considered an RS at all. It has 8 references, and 3 of them (!) are self-references, and as it turns out Mr. Arbab I. Arbab is a professor at the University of Khartoum (another !), and is the sole author of this paper, which presents no data, merely "theoretical" work using absurdly simple exponential models of the form x = x_0 * (t_0/t) ^ n to show the change in parameter x over time (t). If this isn't enough to be convincing that is definitely fringe, here's a quote from the introduction:

We have recently shown (Arbab 2003) that the present acceleration of the universe is due to the ever-increasing gravity strength.

Apparently, this is what passes for "verification" in some circles. siafu (talk) 19:15, 18 March 2011 (UTC)[reply]

Another note: Arbab relies on Well, J.W. as the sole source of actual data, which was a study of the length of day throughout geologic time, not the length of the year. Arbab even states that one of his assumptions is that the number of seconds in a year remain invariant (end of page 37), but then goes on to present his theory of how the Earth's mean motion increases, implying a variable number of seconds in a year (p. 38). This paper is plain rubbish, and needs to be excluded. Those supporting Maserliez's cosmology would do well to distance themselves from this paper, and Mr. Arbab in general. siafu (talk) 19:38, 18 March 2011 (UTC)[reply]

RfC: Does the Masreliez theory of expanding spacetime merit inclusion in this article?

Removed RfC tag. Martijn Meijering (talk) 21:23, 20 March 2011 (UTC)[reply]

Does the Masreliez theory of expanding spacetime merit inclusion in this article? None of us are cosmologists, it would be helpful to get an expert opinion. Martijn Meijering (talk) 20:18, 11 March 2011 (UTC) Added a sentence to make the central question show up on the Maths, science, and technology list. Martijn Meijering (talk) 22:35, 15 March 2011 (UTC)[reply]

I'm not sure what an expert would provide in this discussion. It seems rather premature to include this theory here, rather than at a page for its author (there doesn't seem to be one on the English wikipedia), or at its own page. Wikipedia is not the place for original research or for putting forward fringe theories, so the way to move towards inclusion would be to first establish that this is not a fringe theory, and that is best done elsewhere at the pages suggested. siafu (talk) 21:18, 11 March 2011 (UTC)[reply]

For the record, I'm not a cosmologist, but I am an expert on astrodynamics, which is also a relevant field here. AFAIK, this theory is not being actively discussed by anyone in the field. siafu (talk) 19:49, 12 March 2011 (UTC)[reply]

,

Do not include For the reasons given by siafu. There is no evidence that this is not a fringe theory, in fact a quick Google shows that it is a fringe theory. Martin Hogbin (talk) 14:50, 12 March 2011 (UTC)[reply]

Pompous verdict - how would you like the evidence to look like? Did you look for this Google score? For the record, neither am I a professional cosmologist, but I have during the past few years, taken on all theoretical graduate courses in astrophysics given at the University of Stockholm. As siafu stated, expertise has no say om WP. I have read most of Masreliez papers and found his model to be far from fringe. / Kurtan (talk) 22:16, 17 March 2011 (UTC)[reply]

It's not very productive to call your fellow editors pompous. I also don't think that a google score provides any evidence of fringe v. non-fringe (the Time Cube handily defeats the number of hits for scale expanding cosmos, after all). So we can't go by that, and we can't go by your expertise, either. Really, this is very simple: find papers that cite this new theory in the appropriate journals that also don't reject it in the process. siafu (talk) 03:16, 18 March 2011 (UTC)[reply]

My comment has nothing to do with a 'google score', whatever that is. I Googled the subject and read the links. They clearly show this to be a fringe theory. Martin Hogbin (talk) 11:41, 17 July 2011 (UTC)[reply]

weak do not include. I'd like to hear from an expert or two, but failing that, this smells of fringery and should not be included without clear evidence of notability William M. Connolley (talk) 16:23, 12 March 2011 (UTC)[reply]
Include as EST/SEC is just providing a formula for Kolesnik's observational findings, which are not at stake here. Masreliez's model is a full cosmology and his velocity hampering drag effect can explain other issues that the Big Bang does not. It is controversial but new physics, where it is needed and rather proto-science than fringe science. You can compare it with the so popular empiric MOND ad hoc formula. Mariguld (talk) 00:55, 16 March 2011 (UTC)[reply]

This may be true, but it's really not for us to decide. The best route to inclusion would be to prove that this theory is taken seriously in the scientific community. In particular, the fields of cosmology/astrophysics and astrodynamics. siafu (talk) 02:21, 16 March 2011 (UTC)[reply]

And this is clearly not the case. The theory is clearly fringe, to say the least. Martin Hogbin (talk) 09:04, 16 March 2011 (UTC)[reply]

Include as Kolesnik's empiric findings call for an explanation most likely invoking new physics, just as i.a. the Pioneer anomaly and Galaxy rotation problem do. ;) Mr Gearloose (talk) 17:23, 16 March 2011 (UTC)[reply]

Wikipedia is intended to contain accepted physics, as published in reputable peer reviewed journals, not new physics. Martin Hogbin (talk) 18:00, 16 March 2011 (UTC)[reply]

New physics is explicitly the sort of thing that wikipedia is not meant to include. Wikipedia is an encyclopedia, not a journal of cutting-edge research. See WP:OR. siafu (talk) 21:02, 16 March 2011 (UTC)[reply]

Several attempts have from time to time been undertaken to analyze and predict such gravitational deviations from ordinary satellite orbits

This seems unnecessarily mysterious. I think what it is trying to say it that the mutual gravitational attractions of the various planets produce not-quite-elliptical orbits of individual planets. But the phrase "ordinary satellite orbits" doesn't help, because ordinary satellites suffer from this too William M. Connolley (talk) 08:25, 17 July 2011 (UTC)[reply]

This article is not about secular variations

It is about perturbations and the French VSOP. Secular variations are non-periodic changes in the elements that result from an averaging of perturbations as the bodies occupy every possible configuration over very long periods. No mention of that here. Does anyone know what the intent of this article was? Tfr000 (talk) 19:46, 8 March 2012 (UTC)[reply]

The originator of this article chose to use a direct English translation of the French "Variations Séculaires des Orbites Planétaires" = "Secular variations of the planetary orbits" (although "the" is superfluous). But neither full name is ever used in English, only the initials VSOP (never SVPO). It is a classical derivation of Newton's theory of gravity (up to 20,000 terms) including a few hundred correction terms for Einstein's theory of relativity needed to find the position of any planet on the celestial sphere at any time within a few thousand years of the present. Or per [3], "VSOP87 contains the newtonian perturbations of the eight planets between themselves, the perturbations of the Moon on the Earth-Moon barycenter and on all the planets and the relativistic perturbations expressed in isotropic coordinates." For a time this article contained an alternative relativity theory. Although this article should be moved to VSOP, by which it is known in English, that is a disambiguation page to several unrelated uses. So a parenthetical term is needed — I recommend moving this article to VSOP (planets). Other possibilities might be VSOP (orbits) or VSOP (planetary orbits) or VSOP (planetary positions) or VSOP (IMCCE). "Variations séculaires des orbites planétaires" currently redirects here, but that term is a not standard in English. — Joe Kress (talk) 02:15, 9 March 2012 (UTC)[reply]

Yes, I'm familiar with the VSOP. And we should probably have a page about it, since we have one about the JPL DE series. So yes, I agree, renaming this to VSOP (planets) or VSOP (astronomy) or something similar is probably a good idea, and then just mentioning the "Secular variations of the planetary orbits" as the English translation down in the article would probably be good enough. We should probably Wikilink it to Institut_de_mécanique_céleste_et_de_calcul_des_éphémérides, although that article is still a stub. Need to check "what links here", I think some of them are expecting a discussion of secular perturbations, which of course this is not. Tfr000 (talk) 18:19, 10 March 2012 (UTC)[reply]

I included an explanation of VSOP for the benefit of those editors who added the alternative relativity theory, who apparently ignored the VSOP material already in the article and focused instead on the article's name, which you have already pointed out is not really appropriate for VSOP. I also included the explanation to emphasize that most of VSOP concerns Newtonian theory, not some relativity theory. — Joe Kress (talk) 08:00, 11 March 2012 (UTC)[reply]

Ok, I added the rename proposal. See directly above for the discussion so far. Tfr000 (talk) 16:36, 13 March 2012 (UTC)[reply]

I don't understand your "No mention of that here". The first half of the article seems concerned with the general concept, the second half with one particular model for calculating it. Martijn Meijering (talk) 23:04, 13 March 2012 (UTC)[reply]

Yes, I can see what you mean. Perhaps I didn't word that properly. What I meant was, "secular variations" are a very specific result of the (mathematical) methods of general perturbations. This article, by its title, seems as if it would discuss that - what the terms are and how the they are derived. And while VSOP does contain secular variations, it is an unfortunate translation, because 99% of what is in VSOP is periodic perturbations, which are not "secular". Someone coming here to see an explanation of "secular" terms, gets instead a general discussion of long-term perturbations and the VSOP theory. It is obvious that the article was intended to be about VSOP, hence the proposal to change the name. Tfr000 (talk) 13:22, 16 March 2012 (UTC)[reply]

OK, that makes sense. Does that mean that the French name VSOP is actually a misnomer? Martijn Meijering (talk) 17:30, 16 March 2012 (UTC)[reply]

Good question. Maybe in French, it doesn't mean quite the same thing as in English? My French isn't that good! Tfr000 (talk) 18:47, 16 March 2012 (UTC)[reply]

"Secular" is normally used in celestial mechanics for any change of an elliptical orbit, either in shape or orientation, with a period that is much longer than the orbital period of the planet (or Moon) in question. [C. M. Clinton, From Eudoxus to Einstein: A history of mathematical astronomy, p. 310.] Thus the 19.34-year period of the Moon's apsides is a secular variation of its elliptical orbit because it is much longer than its one month orbital period, even though much of it can be modeled sinusoidally. Similarly, the great inequality of Jupiter and Saturn (peak errors in their positions of about 15 and 30 arcminutes, respectively) has a 883-year period, much longer than their respective orbital periods of 12 and 30 years, but are modeled sinusoidally. All orbital elements are periodic even though many of their periods are tens of thousands of years long. These are also called "secular" within a few thousand years of the present. The latter are listed in section 5 of [4] as polynomials. About two-thirds of the secular acceleration of the Moon is truely secular, caused by Earth's slowing rotation (section 7 of [5]). A gradual decrease in Earth's orbital eccentricity causes most of the rest, although it is quasi-periodic over tens of thousands of years. Although "secular variations" is normal astronomical usage even for terms that are not truely secular, which do appear in VSOP, the rest of VSOP consists of 20,000 sinusoidal terms with periods near the orbital period, so its usage here is somewhat misleading. — Joe Kress (talk) 04:29, 19 March 2012 (UTC)[reply]

Ok, the article has been renamed. I cleaned up all of the Wikilinks to the old article - there were only two that seemed to want to discuss secular perturbations rather than VSOP - now fixed. Tfr000 (talk) 20:12, 22 March 2012 (UTC)[reply]

Comparing VSOP and the Ptolemaic system.

Modelling VSOP on a ubiquitous PC computer program, starting with only one element for each of the three parameters (L, B R) and then slowly incrementing the number of elements, gives a sense of irony that it is in fact nothing more than a more complex development of the ancient deferent / epicycle system used by Ptolemy. A system that despite being totally dismissed out of hand for being intellectually "wrong", was able to provide a prediction service accurate enough to match the observational resolution available (naked eye, with no reliable mechanical timekeeping). A system that, astoundingly to this author, was able to detect and measure, accurately, the lunar evection, one of the still-used perturbations of the Earth-Moon system. Summing powers of sines and cosines is certainly tantamount to circles upon (or perhaps within) circles; recursing, or perhaps simply nesting, almost endlessly. Whilst of course this is totally irrelevant to the mathematics, it perhaps behooves Wikipedia's wider terms of reference to include this as a philosophical point. 121.217.64.105 (talk) 11:24, 29 May 2014 (UTC)[reply]

VSOP2010, VSOP2013 and TOP2013

Why are VSOP2010, VSOP2013 and TOP2013 absent in article?Voproshatel (talk) 14:11, 8 September 2018 (UTC)[reply]

VSOP2000?

The VSOP/TOP2010/2013 versions have now be addressed, but what about VSOP2000? It is compared to in the VSOP2010 section and mentioned in the 2011 conference proceedings, but I can find no publication for that version and neither do the proceedings give a reference. Also, the IMCCE FTP server shows 87, 2010 and 2013, but no 2000... Does the VSOP2000 theory exist? AstroFloyd (talk) 12:54, 27 January 2019 (UTC)[reply]

OK, I found a (closed-journal) reference for VSOP2000 (and VSOP2002, which was never finished due to the death of Bretangon) on the German Wikipedia page, and added a section VSOP2000 to this page. The info is sparse, and I could not find any data. AstroFloyd (talk) 14:16, 27 January 2019 (UTC)[reply]

Requested move 24 May 2022

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

The result of the move request was: page moved. Andrewa (talk) 05:34, 31 May 2022 (UTC)[reply]

VSOP (planets) → VSOP model – Planets is a poor choice of disambiguation for this topic, since the subject is not a group of planets. –LaundryPizza03 (d c̄) 04:18, 24 May 2022 (UTC)[reply]

The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.