<p>The mass of the sun is just a unit of convenience in a astronomy. The sun's mass and luminosity, in particular, are relatively easy for us to measure precisely, and when we're talking about stars, provide a convenient scale where the numbers won't be too "astronomical" (be too high a power of $10$ to picture easily). You could derive the Chandrasekhar limit in grams, kilograms, or slugs from the relevant physics, if you wanted. The relevant equation (<A HREF="https://en.wikipedia.org/wiki/Chandrasekhar_limit" rel="noreferrer">from the Wikipedia article</A>) is:
$$M_{\mathrm{limit}} = \frac{\omega_3^0 \sqrt{3\pi}}{2} \left(\frac{\hbar c}{G}\right)^{3/2} \frac{1}{(\mu_e m_\mathrm{H})^2},$$
where $\mu_e$ is the average molecular weight per electron (stellar composition dependent), $m_\mathrm{H}$ is the mass of hydrogen, and $\omega_3^0$ is a numerical constant that is approximately $2.018236\ldots$.</p>

<p>It should be noted that the Chandrasekhar limit is a limit on the mass of the final white dwarf, not of the object that will produce the white dwarf.</p>

CC BY-SA 3.0
2017-09-18T21:43:45.613Z
The conversion factor for the mass of the Sun to kilograms is 1 solar mass equals 1.9885 × 10^30 kg. Thus, 1.4 solar masses equals 2.7846 x 10^30 kg.
ohwilleke
CC BY-SA 3.0
2017-09-19T06:29:02.253Z
+1 The first sentence, "The mass of the sun is just a unit of convenience in a astronomy." summarises it very nicely. Our Solar System is often used as a reference - Sun, Earth, Jupiter, distance from Sun to Earth (1 au) etc.
Mick
CC BY-SA 3.0
2017-09-19T07:42:20.290Z
Obligatory request for someone to workout the Chandrasekhar limit in slugs.
SGR
CC BY-SA 3.0
2017-09-19T08:04:05.820Z
@SGR It's just a unit conversion; https://www.wolframalpha.com/input/?i=Chandrasekhar+limit+in+slugs
Taemyr
CC BY-SA 3.0
2017-09-19T08:11:43.107Z
@Taemyr The internet is a wonderful thing. For anyone interested: 1.9×10^29 slugs
SGR
CC BY-SA 3.0
2017-09-19T10:46:14.903Z
That would make a slug 14.65kg
r_ahlskog
CC BY-SA 3.0
2017-09-19T11:49:01.087Z
Yes, it's using [this Imperial Slug](https://en.wikipedia.org/wiki/Slug_(mass)) rather than [this invertebrate slug](https://en.wikipedia.org/wiki/Slug)
Useless
CC BY-SA 3.0
2017-09-19T11:51:25.697Z
@Useless you ninja'd me, tho' I was going to suggest banana slugs because they taste better
Carl Witthoft
CC BY-SA 3.0
2017-09-19T11:52:57.607Z
Wolfram Alpha is surprisingly bad at explaining what it thinks a unit means!
Useless
CC BY-SA 3.0
2017-09-19T20:39:20.117Z
@Mick The au wasn't originally a unit of convenience. It sits at the base of the [cosmological distance ladder](https://en.wikipedia.org/wiki/Cosmic_distance_ladder) and, before radar ranging had really nailed down the size of the solar system, was a significant source of correlated uncertainties in measurements. By making the au a unit, you isolate that source of error, and prevent underestimation of your uncertainty. For more, see: https://astronomy.stackexchange.com/questions/20466/why-dont-astronomers-use-meters-to-measure-astronomical-distances/20469#20469
Sean Lake
CC BY-SA 3.0
2017-09-19T20:46:27.427Z
As far as I know, though, the mass of the sun has always been a unit of convenience, since all that's required to measure it is Kepler's laws, plus Newton's law of gravitation, and $G$. So it would initially have been fixed by the radius of the Earth (via $g$ and the Earth's radius to get $GM_{\mathrm{Earth}}$), it would have been pretty well nailed down as soon as Cavendish measured $G$ directly. The unit of luminosity that sits at the base of measurements in astronomy, though, is usually the that of Vega, not the sun. https://www.astro.umd.edu/~ssm/ASTR620/mags.html
Sean Lake
CC BY-SA 3.0
2017-09-19T20:48:06.107Z
Why, Vega? Ask Ptolemy: https://en.wikipedia.org/wiki/Apparent_magnitude
Sean Lake
CC BY-SA 3.0
2017-09-18T17:43:57.473Z
2017-09-18T19:55:19.987Z
2017-09-18T19:55:19.987Z
Sean Lake
<p>In 1931, <a href="https://en.wikipedia.org/wiki/Subrahmanyan_Chandrasekhar" rel="noreferrer">Chandrasekhar</a> was able to show that there is a certain critical mass (<a href="https://en.wikipedia.org/wiki/Chandrasekhar_limit" rel="noreferrer">Chandrasekhar's limit</a>) beyond which a white dwarf cannot exist, since the electronic fluid at that point cannot support its weight no matter how compressed it is. </p>

<p>The core of such a star will simply collapse inward. </p>

<p>The critical mass, Chandrasekhar showed, is 1.4 times that of the Sun.</p>

<p>When I first heard this, I was totally confused. Sun is a star too. The Sun will eventually enter the Red Giant Phase, and then it will eventually become a white-dwarf.</p>

<p>How and why did Chandrasekar express his limit relative to Sun?</p>

CC BY-SA 3.0
2017-09-18T18:35:10.763Z
@JamesK - thank you. corrected my description.
Senthil Kumaran
CC BY-SA 3.0
2017-09-18T20:29:26.990Z
Note that the red giant phase of the sun will not increase its mass, only its radius.
Derrell Durrett
CC BY-SA 4.0
2021-10-18T09:20:18.580Z
Point of fact:  In 1931 Chandrasekhar did not know what white dwarfs were made of and said the limiting mass was 0.91 solar masses. https://ui.adsabs.harvard.edu/abs/1931ApJ....74...81C/abstract
ProfRob
<the-sun>
Why is Chandrasekar Limit expressed relative to Sun?
Senthil Kumaran
# Why is Chandrasekar Limit expressed relative to Sun?

(Asked by: username_0 on 2017-09-18)

In 1931, [Chandrasekhar](https://en.wikipedia.org/wiki/Subrahmanyan_Chandrasekhar) was able to show that there is a certain critical mass ([Chandrasekhar's limit](https://en.wikipedia.org/wiki/Chandrasekhar_limit)) beyond which a white dwarf cannot exist, since the electronic fluid at that point cannot support its weight no matter how compressed it is.

The core of such a star will simply collapse inward.

The critical mass, Chandrasekhar showed, is 1.4 times that of the Sun.

When I first heard this, I was totally confused. Sun is a star too. The Sun will eventually enter the Red Giant Phase, and then it will eventually become a white-dwarf.

How and why did Chandrasekar express his limit relative to Sun?

**Tags:** the-sun
> **Comments:**
> **username_0**: @JamesK - thank you. corrected my description.  
> **username_1**: Note that the red giant phase of the sun will not increase its mass, only its radius.  
> **username_2**: Point of fact:  In 1931 Chandrasekhar did not know what white dwarfs were made of and said the limiting mass was 0.91 solar masses. https://ui.adsabs.harvard.edu/abs/1931ApJ....74...81C/abstract  

---

## 1 answers

### Answer by username_3 on 2017-09-18. Score: 29 | Accepted answer

The mass of the sun is just a unit of convenience in a astronomy. The sun's mass and luminosity, in particular, are relatively easy for us to measure precisely, and when we're talking about stars, provide a convenient scale where the numbers won't be too "astronomical" (be too high a power of $10$ to picture easily). You could derive the Chandrasekhar limit in grams, kilograms, or slugs from the relevant physics, if you wanted. The relevant equation ([from the Wikipedia article](https://en.wikipedia.org/wiki/Chandrasekhar_limit)) is:
$$M\_{\mathrm{limit}} = \frac{\omega\_3^0 \sqrt{3\pi}}{2} \left(\frac{\hbar c}{G}\right)^{3/2} \frac{1}{(\mu\_e m\_\mathrm{H})^2},$$
where $\mu\_e$ is the average molecular weight per electron (stellar composition dependent), $m\_\mathrm{H}$ is the mass of hydrogen, and $\omega\_3^0$ is a numerical constant that is approximately $2.018236\ldots$.

It should be noted that the Chandrasekhar limit is a limit on the mass of the final white dwarf, not of the object that will produce the white dwarf.

> **Comments:**
> **username_4**: The conversion factor for the mass of the Sun to kilograms is 1 solar mass equals 1.9885 × 10^30 kg. Thus, 1.4 solar masses equals 2.7846 x 10^30 kg.  
> **username_5**: +1 The first sentence, "The mass of the sun is just a unit of convenience in a astronomy." summarises it very nicely. Our Solar System is often used as a reference - Sun, Earth, Jupiter, distance from Sun to Earth (1 au) etc.  
> **username_6**: Obligatory request for someone to workout the Chandrasekhar limit in slugs.  
> **username_7**: @SGR It's just a unit conversion; https://www.wolframalpha.com/input/?i=Chandrasekhar+limit+in+slugs  
> **username_6**: @Taemyr The internet is a wonderful thing. For anyone interested: 1.9×10^29 slugs  
> **username_8**: That would make a slug 14.65kg  
> **username_9**: Yes, it's using [this Imperial Slug](https://en.wikipedia.org/wiki/Slug_(mass)) rather than [this invertebrate slug](https://en.wikipedia.org/wiki/Slug)  
> **username_10**: @Useless you ninja'd me, tho' I was going to suggest banana slugs because they taste better  
> **username_9**: Wolfram Alpha is surprisingly bad at explaining what it thinks a unit means!  
> **username_3**: @Mick The au wasn't originally a unit of convenience. It sits at the base of the [cosmological distance ladder](https://en.wikipedia.org/wiki/Cosmic_distance_ladder) and, before radar ranging had really nailed down the size of the solar system, was a significant source of correlated uncertainties in measurements. By making the au a unit, you isolate that source of error, and prevent underestimation of your uncertainty. For more, see: https://astronomy.stackexchange.com/questions/20466/why-dont-astronomers-use-meters-to-measure-astronomical-distances/20469#20469  
> **username_3**: As far as I know, though, the mass of the sun has always been a unit of convenience, since all that's required to measure it is Kepler's laws, plus Newton's law of gravitation, and $G$. So it would initially have been fixed by the radius of the Earth (via $g$ and the Earth's radius to get $GM_{\mathrm{Earth}}$), it would have been pretty well nailed down as soon as Cavendish measured $G$ directly. The unit of luminosity that sits at the base of measurements in astronomy, though, is usually the that of Vega, not the sun. https://www.astro.umd.edu/~ssm/ASTR620/mags.html  
> **username_3**: Why, Vega? Ask Ptolemy: https://en.wikipedia.org/wiki/Apparent_magnitude  

---

