# Talk:Angular diameter

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## Visual vs Actual Diameters

First paragraph ended with: "For a spherical object at a large distance, the visual and actual diameters are the same." This statement is not correct given the definition of visual diameter earlier in the same paragraph. The difference between the actual and visual diameters of a sphere is directly proportional to the difference between the actual distance to the sphere and the distance to the projection plane. The magnitudes of these distances do not affect the difference between the actual and visual diameter so long as the ratio between actual distance and distance to projection plane is constant.

I should add that, while I removed that statement, I've noticed that the paragraph is still even more deeply flawed. It says essentially that angular diameter is visual diameter, and (emphasis mine) "The visual diameter is the diameter of the perspective projection of the object on a plane through its centre that is perpendicular to the viewing direction." True perspective projection is most accurately represented by the surface of a sphere. This is why we use angular measurements for apparent size in the first place, like how we use angular measurements to divide the Earth by longitude and latitude. Angular measurements do not project evenly along a plane. This further compromises the correctness of the statement I removed: "For a spherical object at a large distance, the visual and actual diameters are the same." If visual diameter is measured in angular units, and actual diamter is measured in units of length, the two values become entirely incomparable.

## Categorization

Not necessarily. Angular diameter is a geometric concept that applies to perspective, and not solely to astronomy — Preceding unsigned comment added by Octachoron (talkcontribs) 02:55, 8 June 2014 (UTC)

## Sun diameter inaccurate?

The angular diameter of the Sun is quoted as 30'
Elsewhere, the entry for the Sun gives mean distance and diameter figures which would correspond to about 32'
This discrepancy should be resolved.
86.141.38.201 13:02, 18 April 2007 (UTC)Peter

You are correct - I shall adjust. Jim77742 11:43, 9 September 2007 (UTC)

Me have question. I did the simple trig and I get theta = 2arctan(d/2D). Obviously, due to small angle approximation, it's close enough, but... I haven't found much (conclusive) evidence in either direction, however. Anyone mind checking? Jeff 01:26, 3 July 2007 (UTC)

You are correct - I shall adjust. Jim77742 11:43, 9 September 2007 (UTC)

Sorry chaps, the correct formula for the angular diameter of a sphere is theta = 2arcsin(d/2D) and not the one currently shown. River6rat 13:49, 2 October 2007 (UTC)

Check this:

   * Betelgeuse: 0.049″ – 0.060″
* Alpha Centauri A: ca. 0.007″
* Sirius: ca. 0.007″


What's "ca" mean? Answer: Ca is an abbreviated version of "circa"; a latin word meaning around or about. See circa

And these paragraphs:

This meaning the angular diameter of the Sun is ca. 250,000 that of Sirius (it has twice the diameter and the distance is 500,000 times as much; the Sun is 10,000,000,000 times as bright, corresponding to an angular diameter ratio of 100,000, so Sirius is roughly 6 times as bright per unit solid angle).
The angular diameter of the Sun is also ca. 250,000 that of Alpha Centauri A (it has the same diameter and the distance is 250,000 times as much; the Sun is 40,000,000,000 times as bright, corresponding to an angular diameter ratio of 200,000, so Alpha Centauri A is a little brighter per unit solid angle).
The angular diameter of the Sun is about the same as that of the Moon (the diameter is 400 times as large and the distance also; the Sun is 200,000-500,000 times as bright as the full Moon (figures vary), corresponding to an angular diameter ratio of 450-700, so a celestial body with a diameter of 2.5-4" and the same brightness per unit solid angle would have the same brightness as the full Moon).

How is this really relevant? I find it confusing and not very useful. I would like to remove them. But I'd prefer comment before I do.Jim77742 11:43, 9 September 2007 (UTC)

"For a disk-shaped object at a large distance, the visual and actual diameters are the same." This does not make sense as a disk shaped object like a galaxy will have an extremely small apparent diameter (a grain of sand held at arm's length) and a huge actual diameter (~100,000 ly). 9:23, 1Jul10. —Preceding unsigned comment added by 75.124.68.99 (talk)

## Angular Diameter of planets from Earth

Should this be appended to say that it is the angular diameter as viewed from Earth when the various bodies are closest to the Earth in their orbits? Otherwise this can be minorly misleading. Jacotto (talk) 02:39, 4 April 2008 (UTC)

It is not for when objects are closest to Earth. Look at Venus (closest) and Jupiter (largest) for two great examples. They are given as a range. Planets that are very far from the Earth simply do not vary enough to bother with a range. Only a professional telescope under the best of circumstances will resolve Ceres or Pluto as a small sphere. -- Kheider (talk) 03:27, 4 April 2008 (UTC)
Thanks for the clarification. Jacotto (talk) 16:27, 4 April 2008 (UTC)

## Formulas

When formulas are used, should there either be explanations (or examples) of each mathematical term? Or else, links to Wiki math pages that explain them? Not all of us are math wizards -- so terms such as "arctan" and "arcsin" are lost on us.

Thanks —Preceding unsigned comment added by 75.45.95.166 (talk) 15:51, 2 August 2008 (UTC)

If you enter "arctan" or "arcsin" in the search box and hit Go, you're immediately transported to an explanation. In general it is not practical to explain all maths notation used; some people may not even know what a square root is, or exponentiation. And if you're not a "math wizard", then most likely the explanation at Inverse trigonometric functions won't do much for you; however, you can use that for all practical purposes these formulas are equal to δ = d / D. To get degrees instead of radians, multiply by 180o/π ≈ 57.3o.  --Lambiam 23:04, 10 August 2008 (UTC)

Isn't 2*arctan(d/2D) the same as arctan(d/D)? 83.26.53.183 (talk) 16:45, 29 March 2014 (UTC)

## Atmosphere lens effect

The Sun appears to be wider when close to the horizon, please explain why and how much. — Preceding unsigned comment added by 201.141.5.237 (talk) 06:09, 26 January 2014 (UTC)

No, the Sun isn't wider when it's closer to the horizon. It's flattened top to bottom by refraction. Refraction is greater closer to the horizon so the lower limb of the Sun is lifted more than the upper limb causing that flattening. There is also a perceptual illusion when the Sun or especially the Moon is close to the horizon, known as the "Moon Illusion", which makes astronomical objects look larger near the horizon, but this is entirely in our heads. There is no magnification by the atmosphere. In fact, the Sun and Moon are actually slightly smaller (when measured objectively) when they are on the horizon, due to both the flattening from refraction and the slightly greater distance. 70.192.19.6 (talk) 18:51, 6 April 2014 (UTC)

## Apparent Size

So the apparent size of an object is related arccotangentially to the distance from the object? —Preceding unsigned comment added by 67.232.193.190 (talk) 02:28, 7 December 2008 (UTC)

The caption for Figure 2 entitled "angular diameter" is more than a little strange. Comparison to a "football" is meaningless without giving the distance to the football. Also, Pluto's orbital radius averages about 40 AU. But a tennis ball is NOT 40 times smaller in diameter than a football. It doesn't matter whether "football" refers to a soccer ball or a "pigskin" viewed from the end. The figure is helpful enough without the nonsensical statements in the caption. — Preceding unsigned comment added by 140.208.1.244 (talkcontribs) 20:34, 9 March 2009 (UTC)

## Football and tennis ball

The caption of the second diagram reads as follows:

Angular diameter : The sun appears the size of a football when seen from Earth. But when it is seen from Pluto (The dwarf planet - plutoid) its size will be like a tennis ball.

This is meaningless unless some indication is given of the distance at which the ball is held. I haven't checked—it's raining today, and I don't have a football anyway—but I'm pretty sure that the angular diameter of a football held at arm's length (whose arm?) is larger than that of the sun.

DES (talk) 14:16, 4 August 2009 (UTC)

## Merge discussion

The following discussion is closed. Please do not modify it. Subsequent comments should be made in a new section. A summary of the conclusions reached follows.
The result was no consensus to merge Djr32 (talk) 16:59, 22 August 2010 (UTC)

These three articles overlap greatly. Surely one robust article is better than bits across three articles? Casliber (talk · contribs) 20:51, 13 August 2010 (UTC)

### Support

1. Casliber (talk · contribs) 20:51, 13 August 2010 (UTC)
2. Sadalsuud (talk) 01:33, 14 August 2010 (UTC)

### Oppose

1. While the other two may be be roughly the same, Angular diameter distance is different (albeit related). Unlike the others, it has to do with cosmology. JRSpriggs (talk) 23:37, 13 August 2010 (UTC)
2. Angular distance = separation between two objects. Angular diameter = size of a single object. Trying to merge the two is going to lead to more confusion, not less. To give a specific example, the concept of angular diameter isn't very helpful when talking about two objects at vastly different distances. Djr32 (talk) 11:58, 14 August 2010 (UTC)
3. Per the above though they are the same conclusions I came to when I read the articles before coming here. Also, Angular distance seems to be more about math while the others are more astronomical subjects. All three articles are short and stubby and perhaps not sustainable on their own, but don't think the proposed merge is the right one. Distance measures (cosmology) lists several distance measures, two of which have a decent amount of material, so perhaps Angular diameter distance could be expanded along these lines. Angular distance as a mathematical concept seems very similar to Great-circle distance so perhaps there could be a merge in that direction.--RDBury (talk) 14:42, 14 August 2010 (UTC)

### Discussion

Yes. JRSpriggs (talk) 00:11, 14 August 2010 (UTC)
• I believe the three should be merged as it would provide for a much richer understanding of the fundamental issues, while clearly pointing out the differences. Having the three articles separated the way they are only engenders confusion. Too much is left up to the imagination of the reader. A second reason for merging all three is that this topic is central to many of the Starbox distinctions, hence every single star article that is written, not to mention the many other astronomical articles. So as an editor of such articles you inevitably want to point to one article that will clarify the issues for the reader and you can't! All you can do is leave the reader hanging somewhere in the stratosphere. That's not useful. One article, I believe, will solve that problem. Another possibility would be to create a new article entitled "Angular solutions" and point to the three articles in question. An introductory discussion of parallax could also come under such a heading. Just an idea. --Sadalsuud (talk) 01:53, 14 August 2010 (UTC)

The above discussion is closed. Please do not modify it. Subsequent comments should be made in a new section.

## Wrong formula

"For a spherical object whose actual diameter equals ${\displaystyle d_{\mbox{act}},}$ and where ${\displaystyle D}$ is the distance to the centre of the sphere, the angular diameter can be found by the formula: ${\displaystyle \delta =\arcsin \left({\tfrac {d_{\mbox{act}}}{D}}\,\right)}$" — Really? No, ${\displaystyle \delta =2\arcsin \left({\tfrac {d_{\mbox{act}}}{2D}}\,\right);}$ just draw the right triangle. Boris Tsirelson (talk) 18:53, 5 September 2014 (UTC)

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