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Needle gauge not relevant[edit]

The example given involving the needle type speedometer is not a clear, helpful, or accurate example of parallax. — Preceding unsigned comment added by (talk) 04:24, 24 September 2011 (UTC)

Error in Formula Derivation[edit]

Following is incorrect:

x radians = xo . 180 / pi = x" . 180 . 3600 / pi

Should be changed to:

x radians = xo . pi / 180 = x" . pi / (180 . 3600)

--AndyBryson (talk) 10:36, 1 July 2009 (UTC)

Needs a picture[edit]

This is a good description of parallax. But it's a difficult thing to explain and I think a picture would help.

The article should be expanded in relatioship with cameras.

I have a question at talk:Single-lens reflex camera. --KQ

Mention added! - MV

The animated example makes the reading of the text difficult. The apparent back and forth motion creates a sort of motion sickness effect. Jef McKenzie (talk) 14:04, 26 April 2012 (UTC)

Secular parallax[edit]

Is this another type of parallax of just another name for a certain type already listed in the article?Tmchk | Talk 01:05, 20 May 2007 (UTC)

Secular parallax is based upon the motion of the Sun, rather than the Earth. It provides a longer baseline because the Sun is moving along a galactic orbit, whereas the Earth only circles the Sun. So yes, I think it should be included under the more general topic of statistical parallax. Here is a reference that discusses it.—RJH (talk) 18:00, 20 October 2008 (UTC)


you described it rather akwardly I think. The simple definition I have learned describes it I feel more simply. Parallax is the apparent movement of one object relative to another due to the movement of the observer.(o.k don't have permisson to copywrite this but hey its a leaving cert definition and is used by thousands of students every year) Show diagrams of the simple pen experiment where you hold two pens out in front of you, one above the other. The bottom one slightly further away from your face than the top. move your head and you will see parallax. But you know this already right?

OK, I added your simple definition (reworded). A drawing would be good, but I am no good at drawing - MV

What about diurnal parallax of solar system bodies?

Example Diagram[edit]

I agree that the page needed a clear, concise diagram with similar explaination - I threw something together in (don't laugh) Microsoft Word... Should be good enough until a real artist decides to make something reasonable.

The previous "informal introduction" was far too wordy and very unclear, even to someone who knows precisely what parallax is. Hopefully this should rectify the situation.

Someone improve my formatting (and image) if you like :)



added reference for Zizek Drabauer 04:39, 12 July 2007 (UTC)drabauer

Stellar parallax[edit]

The problem with the argument against heliocentrism was not that a huge size of the universe didn't occur to anyone; it's that the size was incredible. Aristarchus himself explained that the size of the sphere of fixed stars was effectively infinite compared even to the Earth's orbit. Archimedes rejected that, mainly on a quibble with the language Aristarchus used. Tycho understood the argument but thought he had good reasons to believe that the universe couldn't be as big as the lack of parallax implied. --Dandrake 00:25, Jun 11, 2005 (UTC)

I'm old![edit]

1 quibble: recent research puts age of the universe @13.8GY, doesn't it? Trekphiler 07:23, 29 December 2005 (UTC)

Confusing wording[edit]

What does "The parallax in arc seconds" mean? I think the equals sign is substituting for the word "equals"? This wording needs to be clarified. --AySz88^-^ 21:55, 9 February 2006 (UTC)

confusing symbol choice[edit]

In an article so heavily dependent on trig and geometery, is it really very clever to denote the parallax angle by π (as opposed to its more usual use as the ratio of circumference to diameter)? This forces the reader to decide whether the error in distance is proportional to the error in angle divided by the angle squared, or by a constant approximately equal to 9. And yes, of course one can see the derivation quickly... but nothing is gained by this momentary confusion, and someone not clear on the concept (i.e., the sort of person likely to be looking it up) is less likely to be confident in the derivation.

Unfortunately astronomers have been using π to denote parallax for well over a century. While it would possibly reduce some amount of momentary confusion, I think consistancy with other sources trumps in this case. --anon 7sept2006

Stellar parallax[edit]

To what range can parallax methods reliably determine the distance to a star? Is it any more than 6000 light years? If it is, than this is an excellent method for proving the universe is older than what biblethumpers declare. Wouter Lievens 12:09, 14 June 2006 (UTC)

It's about 1000 parsecs, and that comes to 3300 light years.Magmir 02:40, 23 February 2007 (UTC)
It wouldn't help anyways. I asked one about this, and he claimed the light from the stars was already set in motion. In other words, the light from a 10,000 lya (light years away) star would have been created at 6,000 lya to appear to be 4000 ly further away. -- trlkly 09:33, 28 November 2007 (UTC)
It should be possible to measure stellar parallax from Mars with one of the existing telescopes already there, or to design a telescope to be placed on Mars for that purpose. Target stars would be selected for existence of very distant background stars in the field containing the target. It might not be an expensive project, and could add some precision to terrestrial measures of the same targets. -- SyntheticET (talk) 06:20, 30 July 2015 (UTC)


Science Buddies at has many resources and ideas for science fair projects that involves ideas on this website including parallax.


This is where I first met the word parallax: In an old CRT oscilloscop, the electron beam (cathode ray) draws a pattern on the phosphor inside the glass, which the operator reads along a grid pattern drawn on the outside of the glass. If the operator moves his head, a parallax reading error might occur. The same kind of reading error can occur in moving needle instruments (analog voltmeters, ampèremeters), which is why precision instruments had a mirror in the scale. When the needle covers its own mirror image, the operator's head is straight above the scale, without any parallax. --LA2 23:33, 26 January 2007 (UTC)

Definition of parallax mistaken[edit]

The current definition of parallax is mistaken and misleading in respect of the italicised terms below:

"Parallax, or more accurately motion parallax, is the change of angular position of two stationary points relative to each other as seen by an observer, caused by the motion of an observer. Simply put, it is the shift of an object against a background caused by a change in observer position. If there is no parallax between two objects then they occupy the same position. The term derives from the Greek παραλλαγή (parallagé), meaning "alteration"."

There can also be parallax when the observer does not move but rather the viewed objects move. The classic case in astronomy is the observed daily parallax of the Moon, Sun and planets against the stars that arises when observed from the surface of the Earth. These would be the same when observed from the same observer location on the Earth's surface whether or not it is they and the fixed stars or the Earth that rotates daily. --Logicus (talk) 19:51, 24 December 2007 (UTC)

Diagram of daily lunar parallax

--Logicus (talk) 14:23, 10 May 2008 (UTC)

This diagram illustrates the historically crucial fact that, contrary to the mistaken standard definition of ‘parallax’ as an apparent displacement of an object due to a locomotion or change of position of the observer, in fact a fixed observer can also perceive parallax purely due to the motion of the objects themselves or even just to the observer’s oblique or eccentric viewpoint without any motion of the observer nor of the objects observed. Indeed even in secondary school physics pupils are taught to avoid scientific instrument needle reading errors due to parallax caused by an oblique viewpoint of the dial and needle. The diagram shows for the case of geocentric-geostatic cosmology how the fact that a fixed observer on the Earth’s surface at the equator is displaced from the Earth’s centre by an Earth radius entails that at moonrise in the East the Moon would appear below a given fixed star, whereas at moonset in the West it would appear to have moved ahead of it, and when overhead it would appear in line with it. But for a hypothetical observer at the centre of the Earth they would always appear in alignment. The parallax of the Moon, Sun or of any planet or comet is the angle subtended at that body by the Earth’s equatorial radius. (The parallax is exaggerated here by the lunar and stellar distances being drawn radically under scale for expository purpose.) It seems a daily Lunar parallax apparent to a fixed observer on the surface of a supposedly central and non-rotating Earth was first recorded in the 2nd century BC by Hipparchus in his book On Sizes and Distances.

Because greater distance implies less parallax, calculations of planetary and cometary daily parallax and thus of their relative distances played crucial roles in ‘the astronomical revolution’. For the conclusion that Martian parallax at opposition is greater than Solar parallax, and thus that Mars is sometimes nearer the Earth than the Sun is, refuted the Ptolemaic geocentric solid orbs model because the Martian orb would have had to interpenetrate the Solar orb. In the Ptolemaic model depicted in Copernicus’s ‘ De Revolutionibus’, Mars is never nearer the Earth than the Sun is, but in the semi-heliocentric Tychonic model it is nearer when at opposition. Tycho mistakenly thought his observations showed that Mars had greater parallax at opposition than the Sun’s, which he took on faith to be 3’ without ever measuring it himself. And the calculation that comet parallax is less than Lunar parallax, whereby comets are superlunary and so must pass through various planets’ celestial orbs, refuted solid orbs more generally. Modern values for the maximum daily parallaxes of the Moon, Mars and Sun are respectively almost 1 degree (i.e. approximately two Moon diameters), some 23 arcseconds and some 9 arcseconds. Thus the Moon, for example, is apparently displaced by almost 2 degrees from moonrise to moonset.

The diagram provides a corrective pedagogical alternative to the somewhat misleading and confusing diagram of daily parallax in Kuhn’s 1957 ‘The Copernican Revolution’ [See Fig 39, p207 1959 Vintage Books edition] that misrepresents this parallax as due to the transportation or to different locations of the observer rather than to their displacement from the centre of the Earth, and also mistakenly claims “The large size of the moon and its rapid orbital motion disguise the parallactic effect.” It was crucially Kuhn’s inattention to observations and his neglect of analysing the logical role of crucial observations and observational conclusions in the heliocentric revolution, such as daily parallax, the phases of Venus and stellar aberration, combined with the traditional failure of ‘ignoring the elephant in the room’ initiated by Galileo in his 1632 ’Dialogue on the two chief world systems’, which utterly failed to compare or even mention the most scientifically and culturally relevant geocentric model of the day, namely the Tychonic geo-heliocentric third world system favoured by the Church, with the heliocentric model, and further combined with the traditional failure of historians to reliably date and quantify the majority conversion in the scientific community from geocentrism in its post-Ptolemaic geo-heliocentric models that became dominant in the 17th century after the 1610 telescopic confirmation of the phases of Venus, to pure heliocentrism in the 18th century after the discovery of stellar aberration, that led him to invalidly conclude this ‘scientific revolution’ was empirically irrational. This in turn induced his subsequent Wittgensteinian-Koyrean irrationalist general theory of scientific revolutions as incommensurable ‘paradigm‘ changes rather than empirically rational progress, published in his 1962 ‘The Structure of Scientific Revolutions’, with its non-logical sociopsycho-babble approach to the history of scientific discovery.

In conclusion, the standard definition of parallax typically to be found in dictionaries, encyclopedias and in science and history of science textbooks, which (mal)defines it as a function or consequence of motion, and in particular only of the motion of the observer, is thus at least twofold mistakenly restrictive, for there can also be (i) a parallax of moving objects for a static observer, such as assumed in Ptolemy’s lunar parallax observations, and also (ii) static parallax when there is no motion at all, neither of the observer nor of the observed, such as when it is caused purely by an eccentric or oblique viewpoint in a mistaken scientific instrument dial reading, as taught in secondary school elementary experimental physics, or even in primary school numeracy teaching of accurate clock reading. And of course most people are also basically intuitively familiar with static parallax from sport, where the very purpose of a linesman is to eliminate static parallax due to an oblique or eccentric viewpoint of other spectators in estimating the instantaneous location of a ball or person, for example, in relation to some line, such as the line in a goalmouth, for example, in the most notorious of all soccer parallax disputes, namely “Was it in ref. ?”. Thus we must distinguish between motion parallax caused by a motion either of the observer or of the observed, and static parallax not due to any motion at all, neither of the observer nor of the observed, but rather just to the observer’s oblique or eccentric but static viewpoint.

However, defining the general notion of parallax involved in both motion and static parallax seems difficult, but at least to essentially involve the notion of obliquity or eccentricity of viewpoint, or at least of the deviation of one line of sight from another, rather than that of motion.

I invite Wikipedians to attempt an adequate general definition of parallax here with this analysis in mind, and whilst I try to come up with one.

--Logicus (talk) 14:39, 11 May 2008 (UTC)

Edited and expanded 12 May --Logicus (talk) 18:12, 12 May 2008 (UTC)

Further edited and expanded 14 May--Logicus (talk) 18:15, 14 May 2008 (UTC)

Be bold and change the page rather than talking about it. As long as you cite reliable sources, the change will stick. However, this article is primarily about the modern scientific concept of parallax and thus the modern definition seems to be the relevant one, although a history section might be an interesting addition to the article. ASHill (talk | contribs) 15:15, 11 May 2008 (UTC)
Thanks ASHill, but still developing. You are surely miss the main point in claiming the current definition is ‘the modern scientific one’. For it is simply wrong, whether modern, ancient or antedeluvian, as my text explains, even for schoolgirl physics. —Preceding unsigned comment added by Logicus (talkcontribs) 18:16, 12 May 2008 (UTC)
Then you missed my point. If there's a change to be made, make it! I've gathered that you think a change should me made to the definition, and I'm encouraging you to change it with the warning that it should be a modern, scientific definition and it must be properly sourced. If you want to put your actual proposed text here on the talk page before implementing it, that would be fine. Frankly, I'm not going to carefully read a verbose explanation of a suggested revision (without the actual proposed new text) on the talk page, so I haven't read your comments well enough to know if your proposed definition is the modern scientific one. ASHill (talk | contribs) 18:30, 12 May 2008 (UTC)
Contrary to what ASHill claims, there is no requirement that the definition be "the modern scientific one", whatever that means, but merely to be correct. Logicus —Preceding unsigned comment added by (talk) 18:16, 15 May 2008 (UTC)

The SOED Definition best ?:The principal definition of 'parallax' of the 1968 Shorter Oxford English Dictionary, namely

“Mutual inclination of two lines meeting in an angle.”

seems a plausible candidate for a general definition if adapted as follows:

‘The inclination of two lines of sight meeting in an angle.’

Of course it needs expanding in its application to the various different kinds of parallax, but this seems to be the general notion common them all.--Logicus (talk) 16:05, 16 May 2008 (UTC)

Change to page[edit]

Thank you for actually providing an edit to discuss. However, the new opening sentences ("Most generally parallax is the inclination of two lines of sight meeting in an angle, caused either by the motion of the observer or else of the objects observed. Motion parallax, is the change of angular position of two observations of a single object relative to each other as seen by an observer, caused by the motion of the observer.") are inconsistent with the Oxford English Dictionary definition: "Difference or change in the apparent position or direction of an object as seen from two different points."

I'm reverting to the previous version; please make sure any changes to the definition are properly cited. ASHill (talk | contribs) 15:31, 27 June 2008 (UTC)

Logicus comments: In fact the proposed edit to discuss was provided on 16 May, namely an improving edit of the proposed SOED definition, but you failed to make any objection, nor did anybody else, so I implemented it.
Why should the SOED and OED definitions be consistent ? If they are, the question is then which one is valid.
If you bother to read my discussion you will hopefully understand why the OED definition you state is untenable, as is the previous version you have restored.
The OED definition fails the 'same observation point' parallax test i.e. parallax can be observed from the same point, e.g. clock reading parallax.
And the previous definition fails the 'static observer' parallax test, not caused by any motion of the observer.
Given these counterexamples to those definitions, I therefore restore my edit given the invalidity of your objections.
I plan including a discussion of static observer parallax in the article, which currently only discusses mobile observer parallax, hopefully including the above diagram of lunar parallax for a fixed observer on a geostatic Earth I have designed to illustrate it, and which refutes the definition of parallax you propose.

--Logicus (talk) 17:06, 28 June 2008 (UTC)

I now see I should not have added "caused either by the motion of the observer or else of the objects observed" to my proposed definition, since it is refuted by clock reading parallax, for example. --Logicus (talk) 17:14, 28 June 2008 (UTC)
We can't assert that the "OED definition... is untenable"; Wikipedia can only include work that appears in reliable sources elsewhere. Please find a citation for your new proposed definition and include the citation in the article. If no citation is added, the new definition appears to be original research, and is therefore not suitable for Wikipedia. (See WP:OR for the original research policy.) I will not revert for the time being.
I suggest that a new "History" or "Etymology" section on differing definitions of the word might be interesting (provided it's sourced!), based on your comments above.
(This article is certainly inadequately sourced—I'll try to improve that in the future—but a substantially new definition needs to be the consensus definition in the field. If The OED can't even agree between multiple editions, there's clearly no consensus for the new definition.) ASHill (talk | contribs) 17:44, 28 June 2008 (UTC)
Logicus on Ashill's comments: Thank you for your imperious observations, lectures on Wikipedia rules and your advice. However, in the first instance, before we go into any intellectually more complicated matters, and before you start criticising and possibly editing or deleting my proposed definition of parallax, may I respectfully suggest you first resolve the problem that the OED citation sourced in footnote 1 to justify the article's current definition given of 'motion parallax' blatantly fails to justify that definition given, at least since the former makes no mention whatever of parallax being caused by any motion of the observer, unlike the latter, which states "...caused by the motion of the observer."
Also further note that more generally the definition given in the main text is extensively different from that given by the OED as reported in the justificatory footnote, as follows.
Wikipedia definition:
"Motion parallax is the change of angular position of two observations of a single object relative to each other as seen by an observer, caused by the motion of the observer."
VERSUS OED definition cited
“(Astron.) Apparent displacement, or difference in the apparent position, of an object, caused by actual change (or difference) of position of the point of observation; spec. the angular amount of such displacement or difference of position, being the angle contained between the two straight lines drawn to the object from the two different points of view, and constituting a measure of the distance of the object.”
I have therefore flagged the article's definition of 'motion parallax' as essentially unsourced, its current source cited being an apparent bogus citation since as you can hopefully now see when the two definitions are put alongside each other, it is radically different.
Specifically note that the definition I give is only a most minor edit of the SOED definition, and only for the purpose of its clarification, such that I regard my proposed definition as sourced, and certainly far better sourced than the Wikipedia one you advocate.
The 1968 SOED definition was "Mutual inclination of two lines meeting in an angle.” and my proposed minor edit was ‘The inclination of two lines of sight meeting in an angle.’, surely a pedagogical improvement and far less Wiki OR, if any, than your definition re the OED one ?
I should also add that no dictionary I know of, including the OED, defines the compound term 'motion parallax'. This notion seems to be a purely Wikipedia invention.
Most generally, in case you had not noticed, it should be pointed out that very few Wikipedia articles provide any justifying source for their beginning definitions, and if you propose their deletion in the absence of justifying sources, then you will probably have to delete the definitions of most articles.
You must also bear in mind that many dictionary definitions are mistaken simply because dictionaries are not written by very logically competent people trained in constructing counterexamples and definitions that avoid obvious counterexamples. Arguably standards have declined somewhat since Dr Johnson's day (-: Many dictionary definitions of parallax are a good case in point, mistakenly restricting it as they do to parallax caused by motion of the observer, and it may well be that the majority of dictionaries commit this elementary error. But in the earliest known discussion of parallax in science, in Ptolemy's Almagest in which daily parallax features significantly, lunar parallax is not caused by any motion of the observer, but rather by the motion of the objects observed, as I hope my Wiki Commons diagram Lunparallax.png well illustrates. And some other examples of parallax are not caused by any motion at all e.g. clock-hands parallax. (You can perhaps say it is caused by a divergence of the line of sight from the required or 'correct' line of sight, with parallax being the angular measure of that divergence.) Certainly note that the most familiarly cited practical example of parallax, that produced by monocular viewing of one's own finger held out at armslength against some background by each eye in turn, is not caused by any motion of the observer nor of the observed, but rather just by two different lines of sight.
I suggest Wikipedia should not reproduce such elementary errors, but rather should provide reliable definitions based on wide reviews of the literature that also use pedagogical good sense to discriminate against patently mistaken definitions, even if they are not in the minority. As I hope I have done in this case, this may even be achieved by very minor edits of some published definition(s).
I suggest you should now leave my definition alone, but rather direct your efforts to sorting out the current muddle of the 'unsourced' definition of 'motion parallax' you seem to advocate and trying to clarify the OED definition of parallax. Then once you have devoted sufficient attention and logical thought to the problems of defining parallax, may I hazard you may come to agree that my proposal, being a minor clarifying edit of the SOED definition, is the best possible effort in all the circumstances ?

--Logicus (talk) 17:49, 1 July 2008 (UTC)

(outdent) I too have been bothered by the term "motion parallax", which I don't see in many sources. I'd be happy to remove that term, but it does distinguish the two definitions that are currently in the article. I agree that most Wikipedia articles do not cite their opening definition, but that is only because the basic definition is rarely controversial. If there is a controversy, it should be settled by references, not assertions.

I disagree that the definition that cites the OED definition is inconsistent with the OED definition; I think the article's definition (which I didn't write) is actually a very nice, concise version that has essentially the same meaning. My problem with the SOED definition is that it is inconsistent with the 1989 2nd edition and in progress 3rd edition of the OED and the other sources I find, so I think it's not a commonly accepted definition

Again, claiming that most dictionary definitions of parallax have "elementary errors" without a source[1] constitutes original research, so I do not agree with the current definition. I'm going to ask for third opinions at WikiProject Astronomy; is there another place you think might be a good place to ask for outside opinion? ASHill (talk | contribs) 18:20, 1 July 2008 (UTC)

  1. ^ You do cite the OED source for your definition, but no reliable source that supports your claim that other dictionary definitions are invalid.
Logicus to ASHill:You seem to entirely overlook my main point that the Wiki definition of 'motion parallax' you like is not justified by the OED source cited, which does not say parallax is caused by motion, inter alia. -- (talk) 18:15, 2 July 2008 (UTC)
Good lord. I said above: "I disagree that the definition that cites the OED definition is inconsistent with the OED definition; I think the article's definition (which I didn't write) is actually a very nice, concise version that has essentially the same meaning." The OED definition says "caused by actual change (or difference) of position of the point of observation"; i. e. motion. ASHill (talk | contribs) 18:37, 2 July 2008 (UTC)
Logicus: Ye Gods ! NO, "change or difference of position" is not motion, simply because the second disjunct of the logical connective 'or' is 'difference of position', which is not necessarily due to motion.
Given you think the article's definition of 'motion parallax' has essentialy the same meaning as the OED definition of parallax it quotes, I have come to the conclusion you are either dyslexic or American (-: or possibly even both, and so could possibly accept that the following proposed definition
'Parallax is an apparent displacement or difference of orientation of an object viewed along two different lines of sight, and is measured by the angle or semi-angle of inclination between those two lines.'
also has essentially the same meaning as the following OED definition you favour:
“(Astron.) Apparent displacement, or difference in the apparent position, of an object, caused by actual change (or difference) of position of the point of observation; spec. the angular amount of such displacement or difference of position, being the angle contained between the two straight lines drawn to the object from the two different points of view, and constituting a measure of the distance of the object.”
I commend you do so, whereby we can have done with this silly controversy.
As for your third opinions from WikiAstronomy, remember parallax is by no means an exclusively astronomical notion, such as that taught in school physics for correct instrument reading, for example. --Logicus (talk) 18:16, 3 July 2008 (UTC)
I've incorporated the proposed definition, along with a rewrite/streamlining of the rest of the lead. (With the rewrite, I put the meaning of parallax as referring to the angle itself in the astronomical context.) I hope this version is OK.
I interpreted "motion" as a slightly informal shorthand for "change of position", but the new wording avoids that difference altogether.
Re 3rd opinion: I suggested the astronomy project because it was the best place I could think of; your concern is why I asked if there's another group you'd suggest to ask for a 3rd opinion. However, I'm OK with this revision and don't think we need outside opinions on this silly thing anymore. ASHill (talk | contribs) 19:33, 3 July 2008 (UTC)
Logicus: Since you seemed to agree with my above proposed definition of 3 July, I hope you will accept it replacing the significantly different one you then inserted without agreement, and also without my having to explain why the latter is wrong, unlike the one I proposed. --Logicus (talk) 16:33, 8 July 2008 (UTC)
Logicus to ASHill: Do you think the best place for my diagram of Ptolemaic lunar parallax not due to a change of position of the observer would be in the section on lunar parallax, along with some brief explanation ?--Logicus (talk) 16:39, 8 July 2008 (UTC)

The Scale of the Universe -- Why?[edit]

Maybe this has been discussed, or maybe someone has a clear idea, but: why is this section here? As written it describes three methods of distance estimation, none of which is based on parallax. It also discusses the end goal, estimating the size of the universe, which again has nothing to do with the topic in question.

I don't believe this section belongs. If no one can give a good justification, I am going to delete it. atakdoug (talk) 19:59, 7 January 2008 (UTC)

I agree, and the material is all covered in cosmic distance ladder anyway. I added a bit to the intro mentioning that parallax is the basis of the distance ladder. Ashill (talk) 09:24, 15 January 2008 (UTC)
And I deleted the section, which I forgot to mention. Ashill (talk) 09:26, 15 January 2008 (UTC)


The current equation seemed very lacking. Surely a formula to work out the error given the perpendicular distance and parallel distance, or the angle from perpendicular, combined with the distance from the observed object and frame of reference, would be very desirably and helpful? It would certainly have helped me. Larklight (talk) 10:13, 30 January 2008 (UTC)


"In astronomy, parallax is the only direct method by which distances to objects (typically stars) beyond the Solar System can be measured" - what about SN1987a? (talk) 01:14, 14 August 2008 (UTC)JohnS

There's no direct measurement. Any "direct" measurement of the distance to SN 1987A requires an estimate of the intrinsic luminosity of the object. With parallax, once you know the distance from the Earth to the Sun, you can measure distance purely geometrically, without assumptions about something about the nature of the object. —Alex (ASHill | talk | contribs) 01:30, 14 August 2008 (UTC)

Statistical parallax[edit]

I was wondering whether this article could discuss statistical parallax, or if it should be on a separate page? (See part D of this, for example.) Thank you.—RJH (talk) 23:23, 18 October 2008 (UTC)

Parallax caused by outer planets[edit]

When planets move around the sun, the sun itself also moves (but of course slower and in a smaller ellipse), and Jupiter causes the Sun's position to change by about 1.5 million km within 6 years. Earth orbits Sun in a close orbit compared to Jupiter, so it can be expected to follow this movement of the Sun (in addition to orbiting it). This should produce an additional parallax of about 7 milliarcseconds at α Centauri - this should be measurable e. g. with Hipparcos. Does this additional parallax have a special name? Maybe the article should mention it. Icek (talk) 22:32, 20 November 2008 (UTC)


This section only mentioned naval artillery. However, the same holds for field artillery. Here, too, fire control must correct for the exact gun positions. I changed the section accordingly. (I am not an military engineer myself, but I presume that, given the exact coordinates of both the target and each individual gun, it must be quite simple for the fire control software to calculate the aiming parameters for each separate gun, thus automatically correcting for parallax.) HHahn (Talk) 16:34, 10 February 2010 (UTC)

In the meantime, several people have modified this paragraph, mainly by adding statements on rangefinders, shooting sights, etc. Someone then split this up into different paragraphs, which is fine, as the sighting problem for one personal firearm is quite different from (and smaller than!) the multi-gun artillery problem described in this paragraph.
However, unfortunately my previous addtion of field artillery has been dropped somehow. In actual fact, the parallax problem may be even bigger in field artillery than in naval artillery, as field guns may be positioned wider apart that those on a warship, where the distance is usually limited by the ship's size.
On the other hand, I presume that in modern systems the fire control computer knows the exact coordinates of each gun, as well as those of the target. So it can calculate the targeting parameters for each single gun based on these coordinates (together with the wind parameters etc.). This way, the actual parallax problem is complete solved within the fire control computer.
I therefore changed the paragraph title to "Artillery" and added field artillery in the text.
HHahn (Talk) 11:32, 22 August 2011 (UTC)


This section is entitled Parallax compensation for firearm and archery sights, but doesn't mention archery. —Preceding unsigned comment added by (talk) 21:10, 28 September 2010 (UTC)

sin or tan ?[edit]

Is this correct?

Shouldn't it be:

This is probably a matter of defiition. And don't forget that when the angles involved are very small, both sin (φ) and tan (φ) converge to the same value.
HHahn (Talk) 10:09, 17 July 2010 (UTC) (corrected HHahn (Talk) 10:13, 17 July 2010 (UTC))

Annual parallax[edit]

This statement is false: "Annual parallax is defined as the difference in position of a star as seen from the Earth and Sun". When a star near the ecliptic is occulted by the Sun (a syzygy), there is no difference in position between geocentric and heliocentric observations. A slightly less incorrect statement would be "the difference in position of a star as seen from the Earth and the solar system barycenter during astronomical quadrature". Unlike observations made from the sun, Earth based observations are strongly effected by stellar aberration. Only the "absolute parallax" is significantly effected by aberration. Absolute parallax is the change in angle measured relative to a non-rotating frame of reference. "Relative parallax" is the change in angle relative to adjacent points of reference.

Also, annual parallax is not "the angle subtended at a star by the mean radius of the Earth's orbit around the Sun". That is actually the "unit of parallax angle". Quoted parallax angles are not the actual measured parallax, but what the parallax would have been if it had been measured with a baseline of 1 au. The Sun is offset an average of about 456 kilometers from the Sun/earth/moon barycenter. This means the Earth's heliocentric orbit is not 2 au across, it is 2*(au-456 km) across. As mentioned by Icek above, the Sun/Earth/Moon barycenter is orbiting the solar system barycenter with a period of about 12 years, this adds an additional parallax which must be accounted for when calculating the star's distance.

Confusing Sentence[edit]

The following is the first sentence of the As a metaphor section. I think it should be revised, does anybody agree?

"In a philosophic/geometric sense: An apparent change in the direction of an object, caused by a change in observational position that provides a new line of sight." — Preceding unsigned comment added by (talk) 14:26, 5 August 2011 (UTC)

Parallax in optical sights[edit]

The section "Parallax compensation for firearm and archery sights" starts out just plain wrong. "the distance between the sighting mechanism and the weapon's bore" is "Sight Height". I am not seeing any reference that it is referred to as "parallax". "Parallax is the apparent movement of the target relative to the reticle when moving your head up and down," (or left and right for that matter) per this document (page 16). "parallax compensation" does not correct for Sight Height, it corrects for miss matches in planes of focus at different distances, i.e. it is a correction in the sight to keep it aligned in relationship to itself (its optical axis). Fountains of Bryn Mawr (talk) 13:31, 23 August 2011 (UTC)

Little mistake in the section "Dynamic Paralax"[edit]

Proper motion is not measured in arc seconds -a unit of length-. The correct units are arc seconds per year. JuancitoxTw (talk) 16:53, 29 February 2012 (UTC)

Use in animation[edit]

Is there any scope for the use of parallax in animation? For example, the 1988 film Akira has an opening scene in which parallax is exploited to produce the effect of panning by moving different layers of background across each other at different speeds. — Sasuke Sarutobi (talk) 13:36, 7 January 2014 (UTC)

Sounds like a good idea for an addition to the article. Its actually not Parallax, its a simulation of it called "multiplane"[1], made using a Multiplane camera. In modern computer graphics and phone interfaces, etc these simulations are called Parallax scrolling[2]. I removed an overlong (redundant) section on it a while ago[3] since it was out of place but I can see a section on all aspects of "simulation" it in a section title like "Simulated parallax", maybe right above the "As a metaphor" section. Fountains of Bryn Mawr (talk) 15:28, 7 January 2014 (UTC)

Use of parallax in measures within the solar system[edit]

A couple of recent edits have centered on removal and then restoration of this topic in the second lead paragraph. Now, I'm not greatly expert in the subject, and currently have no reliable source to offer, but neither has user David J Wilson supplied one, and the article has none either. Perhaps it's time there was one (or more), for the article's sake. At present, I recognize the diurnal parallax measures as having been in use historically, but I am under the impression that they are largely superseded these days by more direct techniques, often taken by spacecraft, and involving laser or radar reflection to produce very precise measures. I know for certain that the Apollo 11 mission left a reflector at the Sea of Tranquility, and that earth-based radar signals used it to measure distances to the moon beginning immediately (1969). Has something of that kind not also been done on any of the multiple Mars landers? And we've had flybys of all the planets. Is earth-based parallax measure really sufficient to provide useful information that is accurate enough to improve on what we know from those sources? I ask, because perhaps someone here already knows. But if answers are not readily available that way, I may go in search of something concrete myself, because (inexpert as I am), this just seems somewhat dubious (or perhaps, merely dated). Evensteven (talk) 20:05, 30 March 2014 (UTC)

Let me illustrate the point about accuracy. It is my understanding that the best parallax resolutions currently available resolve to measures on the order of milliarcseconds, and that those are not available from the surface of the earth (due to atmospheric distortions), but from spacecraft only. Yet planetary disks are themselves only on the order of tens of arcminutes wide at most. How much larger could a useful diurnal parallax be? Observation times within the solar system must be highly critical, since the apparent movement of planets and other bodies occurs at a much quicker pace. So, a measure of diurnal parallax on the order of 10 arcminutes, to within one mas, yields (generously) 7 significant digits of accuracy, 19 or 20 significant bits if one wants to go binary. Yet radar measures of lunar distance give accuracies to within hundredths of cm across distances of hundreds of thousands of km. That's pretty easily 13 significant digits. There is no possible parallax measure under 360 degrees that can be made at that level of accuracy. How then is diurnal parallax useful to present-day solar system measures? Evensteven (talk) 20:54, 30 March 2014 (UTC)

Mea culpa. You are quite right. I have now restored your edit and added a footnote about the historical use of diurnal parallax to measure distances to local celestial objects.
David Wilson (talk · cont) 12:38, 31 March 2014 (UTC)
Say, thanks for verifying this item. As you can see, I didn't really know directly, but just had snippets of different things that seemed to imply it couldn't be otherwise. I also have a nagging memory that I heard this once, but haven't been able to pin that down - not at all good enough for this purpose either. Evensteven (talk) 15:29, 31 March 2014 (UTC)

Aristarchus and the parallax?[edit]

From the article: "One way to determine the lunar parallax from one location is by using a lunar eclipse. A full shadow of the Earth on the Moon has an apparent radius of curvature equal to the difference between the apparent radii of the Earth and the Sun as seen from the Moon. This radius can be seen to be equal to 0.75 degree, from which (with the solar apparent radius 0.25 degree) we get an Earth apparent radius of 1 degree. This yields for the Earth–Moon distance 60.27 Earth radii or 384,399 kilometres (238,854 mi) This procedure was first used by Aristarchus of Samos[17] and Hipparchus, and later found its way into the work of Ptolemy.[18] "

While this seems to me like a correct exposition of Aristarchus' (and Ptolemy's) method, but I don't understand how the determination of lunar distance necessarily has anything to do with determination of parallax. The paragraph points to a Gutzwiller article I have no access to. However, here is a quote from O. Neugebauer from A History of Mathematical Astronomy, which can be found here [1] (pg. 635):

"He [Aristarchus] asserts that the moon is illuminated by the sun, that the (circular) lunar orbit has a smaller radius than the then solar orbit, and that parallax may by ignored, allowing us to identify our eye with the center E of the earth which is also the center of lunar and solar orbit."

Furthermore, I could find no quotes reinforcing the Gutzwillerian view. I'm pretty new here and don't know if I'm interpreting Neugebaeur correctly (I am in no way an astronomer by training), but I feel like mentioning Aristarchus in an article on parallax is highly misleading and should be removed. Ptolemy made the same initial point as Aristarchus, but did attempt to calculate parallax by other mechanisms. I personally think the entire paragraph and illustration should be removed.

Even the wikipedia article on Aristarchus' On The Sizes and Distances correctly shows a right triangle[2]. While the measurement of distance is relevant to parallax, they are not equivalent. If someone does not explain to me why I am mistaken within the week I will delete the paragraph. At least, I think an additional comment should be added signalling Aristarchus did not measure parallax.

LilChaki (talk) 20:56, 4 May 2016 (UTC) J.S. Chaki Fauber


There are certainly several problems with the text of the paragraph. I'm not sure I completely understand the nature of your objections, but I agree that the characterisation of the relation between the procedure described in the paragraph and that followed by Aristarchus is misleading. While I don't have any objection to the current paragraph's being removed, I also don't think it would take a huge amount of work to rectify the problems with it.
David Wilson (talk · cont) 01:13, 10 May 2016 (UTC)