<blockquote>
<p><a href="https://astronomy.stackexchange.com/questions/58958/if-the-celestial-sphere-was-shrunk-down-so-it-stuck-against-the-surface-of-the-e/58960#comment136568_58958">...a star would be about 2 feet wide on earth... And that's probably not even right.</a></p>
</blockquote>
<p><em><strong>You are right!</strong></em> For the nearby and large stars where we can (relatively easily) measure their diameters and even make fuzzy images of their surfaces, they would be of order feet across if projected on to Earth's surface.</p>
<hr />
<p>Let's do a particularly interesting (<a href="https://astronomy.stackexchange.com/search?q=user%3A7982+betelgeuse+is%3Aquestion">to me</a> at least) example: <a href="https://en.wikipedia.org/wiki/Betelgeuse" rel="nofollow noreferrer">Betelgeuse</a></p>
<p>From <a href="https://en.wikipedia.org/wiki/Betelgeuse#Table_of_angular_diameter_estimates" rel="nofollow noreferrer">all the measured values for Betelgeuse's angular diameter in this table</a> let's choose θ = 42 mas because <a href="https://en.wikipedia.org/wiki/42_(number)" rel="nofollow noreferrer">42 is an interesting number</a>.</p>
<p>Divide that by 1000 to convert milliarcseconds to arcseconds, then divide that 3600 to convert to degrees, and get 0.01167×10<sup>-5</sup>°.</p>
<p>Multiply that by /180 to convert degrees to radians, and get 2.03621×10<sup>-7</sup> radians.</p>
<p>We can now use the <a href="https://en.wikipedia.org/wiki/Small-angle_approximation" rel="nofollow noreferrer">small angle approximation</a> and simply multiply the radius of the Earth (let's choose the equatorial radius) 6378137 meters by 2.03621×10<sup>-7</sup> <strong>and get 1.3 meters diameter, or <em>four feet!</em></strong></p>
<hr />
<p><a href="https://en.wiktionary.org/wiki/your_mileage_may_vary#Phrase" rel="nofollow noreferrer">Your mileage may vary</a> - almost all visible stars would be smaller, but there will probably be a few stars larger than that. See for example Wikipedia's:</p>
<ul>
<li><a href="https://en.wikipedia.org/wiki/List_of_largest_stars#Largest_stars_by_apparent_size" rel="nofollow noreferrer">Largest stars by apparent size</a></li>
<li><a href="https://en.wikipedia.org/wiki/List_of_stars_with_resolved_images" rel="nofollow noreferrer">List of stars with resolved images</a></li>
</ul>
<p><a href="https://i.sstatic.net/DdKKZAG4.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/DdKKZAG4.jpg" alt="Press Release: ESO Telescope Sees Surface of Dim Betelgeuse 14 February 2020 https://www.eso.org/public/news/eso2003/" /></a></p>
<p>Source: <a href="https://www.eso.org/public/news/eso2003/" rel="nofollow noreferrer">Press Release: ESO Telescope Sees Surface of Dim Betelgeuse 14 February 2020</a></p>

CC BY-SA 4.0
2024-11-20T01:49:14.747Z
2024-11-20T01:54:29.637Z
2024-11-20T01:54:29.637Z
uhoh
<p>We can make some sense of the question by asking what <strong>range</strong> of size would <strong>naked eye</strong> stars have if the celestial sphere were collapsed onto the surface of the Earth.</p>
<p>The naked eye star with the largest angular diameter as seen from Earth is the Sun. Let's ignore that and move to the second largest, which is R Dor (<span class="math-container">$V=4.8$</span>), with an angular diameter of <span class="math-container">$51$</span> milli-arcseconds.</p>
<p>Using simple trigonometry, something that subtends 51 milli arcseconds (<span class="math-container">$\theta = 2.47 \times 10^{-7}$</span> radians), will have a projected diameter of <span class="math-container">$R\theta$</span> on the Earth's surface, where <span class="math-container">$R=6370$</span>,km.</p>
<p>Thus the <strong>maximum</strong> diameter of a star would be 1.57 m.</p>
<p>Every other star will be projected to a size smaller than this that depends on its absolute diameter divided by its distance. A star similar to the Sun, will have an angular diameter of 9 milliarcsec at a distance of 1 pc; 0.9 milli arcsec at 10 pc; 0.09 milli arcsec at 100 pc and so on.</p>
<p>Thus stars could be projected to <strong>any</strong> smaller diameter than this just depending on how far away they are.</p>
<p>You coud perhaps focus the question by asking how small the smallest naked eye star could be? We can estimate that by noting that the Sun would have an apparent magnitude of 6.5 (about the faintest you can see) at a distance of around 23 pc. At this distance it would have an angular diameter of 0.4 milli arcsec, which would project to a diameter of <strong>1.2 cm.</strong> The answer would be <em>slightly</em> different for a star of a different spectral type.</p>
<p><strong>Thus the answer is between about 1 centimetre and 1.6 metres.</strong></p>
<p>An alternative way to consider the question would be that, when viewed through the Earth's atmosphere, all stellar images are blurred to an angular diameter of about 1 arcsecond (at best). This would mean that <strong>all stars are projected to a diameter of at least 31 metres.</strong></p>

CC BY-SA 4.0
2024-11-20T08:45:16.527Z
2024-11-20T08:55:35.423Z
2024-11-20T08:55:35.423Z
ProfRob
<p>Assume a celestial globe the size of Earth: how big would the &quot;points&quot; or footprints be which indicate the individual stars?</p>
<p>One can assume a typical naked-eye visible star, e.g. an angular diameter of 2 mas (milli arc seconds).</p>

CC BY-SA 4.0
2024-11-20T18:00:15.390Z
**Comments have been [moved to chat](https://chat.stackexchange.com/rooms/156313/discussion-on-question-by-miss-understands-if-the-celestial-sphere-was-shrunk-do); please do not continue the discussion here.** Before posting a comment below this one, please review the [purposes of comments](/help/privileges/comment). Comments that do not request clarification or suggest improvements usually belong as an [answer](/help/how-to-answer), on [meta], or in [chat]. Comments continuing discussion may be removed.
Connor Garcia
CC BY-SA 4.0
2024-11-22T22:49:10.923Z
There is an xkcd about this https://www.xkcd.com/1276/  A "Typical naked eye star" would be about 15 cm across.  For comparison the sun is the size of London, and the Sag A* black hole is about 1 mm.
James K
<space-geometry>
If the Celestial Sphere was shrunk down so it stuck against the surface of the earth, how wide would a star be?
Miss Understands
# If the Celestial Sphere was shrunk down so it stuck against the surface of the earth, how wide would a star be?

(Asked by: username_0 on 2024-11-19)

Assume a celestial globe the size of Earth: how big would the "points" or footprints be which indicate the individual stars?

One can assume a typical naked-eye visible star, e.g. an angular diameter of 2 mas (milli arc seconds).

**Tags:** space-geometry
> **Comments:**
> **username_1**: **Comments have been [moved to chat](https://chat.stackexchange.com/rooms/156313/discussion-on-question-by-miss-understands-if-the-celestial-sphere-was-shrunk-do); please do not continue the discussion here.** Before posting a comment below this one, please review the [purposes of comments](/help/privileges/comment). Comments that do not request clarification or suggest improvements usually belong as an [answer](/help/how-to-answer), on [meta], or in [chat]. Comments continuing discussion may be removed.  
> **username_2**: There is an xkcd about this https://www.xkcd.com/1276/  A "Typical naked eye star" would be about 15 cm across.  For comparison the sun is the size of London, and the Sag A* black hole is about 1 mm.  

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## 2 answers

### Answer by username_3 on 2024-11-20. Score: 2 | Accepted answer

> [...a star would be about 2 feet wide on earth... And that's probably not even right.](https://astronomy.stackexchange.com/questions/58958/if-the-celestial-sphere-was-shrunk-down-so-it-stuck-against-the-surface-of-the-e/58960#comment136568_58958)

***You are right!*** For the nearby and large stars where we can (relatively easily) measure their diameters and even make fuzzy images of their surfaces, they would be of order feet across if projected on to Earth's surface.

---

Let's do a particularly interesting ([to me](https://astronomy.stackexchange.com/search?q=user%3A7982+betelgeuse+is%3Aquestion) at least) example: [Betelgeuse](https://en.wikipedia.org/wiki/Betelgeuse)

From [all the measured values for Betelgeuse's angular diameter in this table](https://en.wikipedia.org/wiki/Betelgeuse#Table_of_angular_diameter_estimates) let's choose θ = 42 mas because [42 is an interesting number](https://en.wikipedia.org/wiki/42_(number)).

Divide that by 1000 to convert milliarcseconds to arcseconds, then divide that 3600 to convert to degrees, and get 0.01167×10-5°.

Multiply that by /180 to convert degrees to radians, and get 2.03621×10-7 radians.

We can now use the [small angle approximation](https://en.wikipedia.org/wiki/Small-angle_approximation) and simply multiply the radius of the Earth (let's choose the equatorial radius) 6378137 meters by 2.03621×10-7 **and get 1.3 meters diameter, or *four feet!***

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[Your mileage may vary](https://en.wiktionary.org/wiki/your_mileage_may_vary#Phrase) - almost all visible stars would be smaller, but there will probably be a few stars larger than that. See for example Wikipedia's:

* [Largest stars by apparent size](https://en.wikipedia.org/wiki/List_of_largest_stars#Largest_stars_by_apparent_size)
* [List of stars with resolved images](https://en.wikipedia.org/wiki/List_of_stars_with_resolved_images)

[![Press Release: ESO Telescope Sees Surface of Dim Betelgeuse 14 February 2020 https://www.eso.org/public/news/eso2003/](https://i.sstatic.net/DdKKZAG4.jpg)](https://i.sstatic.net/DdKKZAG4.jpg)

Source: [Press Release: ESO Telescope Sees Surface of Dim Betelgeuse 14 February 2020](https://www.eso.org/public/news/eso2003/)


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### Answer by username_4 on 2024-11-20. Score: 6

We can make some sense of the question by asking what **range** of size would **naked eye** stars have if the celestial sphere were collapsed onto the surface of the Earth.

The naked eye star with the largest angular diameter as seen from Earth is the Sun. Let's ignore that and move to the second largest, which is R Dor ($V=4.8$), with an angular diameter of $51$ milli-arcseconds.

Using simple trigonometry, something that subtends 51 milli arcseconds ($\theta = 2.47 \times 10^{-7}$ radians), will have a projected diameter of $R\theta$ on the Earth's surface, where $R=6370$,km.

Thus the **maximum** diameter of a star would be 1.57 m.

Every other star will be projected to a size smaller than this that depends on its absolute diameter divided by its distance. A star similar to the Sun, will have an angular diameter of 9 milliarcsec at a distance of 1 pc; 0.9 milli arcsec at 10 pc; 0.09 milli arcsec at 100 pc and so on.

Thus stars could be projected to **any** smaller diameter than this just depending on how far away they are.

You coud perhaps focus the question by asking how small the smallest naked eye star could be? We can estimate that by noting that the Sun would have an apparent magnitude of 6.5 (about the faintest you can see) at a distance of around 23 pc. At this distance it would have an angular diameter of 0.4 milli arcsec, which would project to a diameter of **1.2 cm.** The answer would be *slightly* different for a star of a different spectral type.

**Thus the answer is between about 1 centimetre and 1.6 metres.**

An alternative way to consider the question would be that, when viewed through the Earth's atmosphere, all stellar images are blurred to an angular diameter of about 1 arcsecond (at best). This would mean that **all stars are projected to a diameter of at least 31 metres.**


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