<p>There have been direct measurements, but they are quite delicate -- this is all the interferometry and so on.</p>

<p>The simplest way though is based on spectroscopy, brightness and parallax. The argument goes a follows:</p>

<ol>
<li><p>The spectrum (how much light of each colour it gives off) is not hard to observe -- you basically just need a prism.</p></li>
<li><p>The spectrum of most stars basically looks like whats called a "black body spectrum" -- the light given off by a hot body with no special properties. This can be both observed on Earth and predicted from basic physics (and they agree)</p></li>
<li><p>From the position of the peak of the black body spectrum we can tell the temperature of the star</p></li>
<li><p>The total light emitted per unit area from a black body depends only on its temperature, so we can calculate the total light emitted per unit area by the star.</p></li>
<li><p>For the nearer stars we can measure their distance fairly directly by observing how their apparent position moves against that of other stars as the Earth moves around the Sun</p></li>
<li><p>Knowing the distance, the brightness per unit area, and the amount of light actually hitting our telescope, we can work out what the area (and so size) of the star must be (this is just geometry)</p></li>
</ol>

CC BY-SA 4.0
2020-05-17T05:00:21.153Z
Ok ok very interesting, that clears up a lot of things I have been wondering regarding this. Just one more point I may need a bit more of explaining about, is point two, is a "black body spectrum" something that exists in other things on earth based on their color, and we are comparing the color given off by the stars to the colors given off by other things on earth, or is it something different?
B''H Bi'ezras -- Boruch Hashem
CC BY-SA 4.0
2020-05-17T06:06:01.057Z
A traditional light bulb is also a black body radiator. Many things are - with more or less big deviations, including you yourself.
planetmaker
CC BY-SA 4.0
2020-05-17T06:46:17.390Z
@bluejayke Most hot objects give off radiation with something close to a black body spectrum -- a piece of red hot charcoal, for instance.
Steve Linton
CC BY-SA 4.0
2020-05-17T08:14:56.200Z
@SteveLinton OK cool I'm just trying to understand it, so we are comparing the stars color appearance to that of other object that we observe, to get the heat, is that right?
B''H Bi'ezras -- Boruch Hashem
CC BY-SA 4.0
2020-05-17T08:47:48.987Z
@bluejayke. essentially yes, although the process (and the physics behind it) is a lot more precise than your phrasing suggests.
Steve Linton
CC BY-SA 4.0
2020-05-17T08:49:32.043Z
@SteveLinton OK it may be more precise, but the basic idea is that we are using the same pool of information available to us on earth, and applying it to the stars, correct? Besides for getting into the details of *how* exactly it works, is there anything else specifically, regarding this point, that is necessary to know, to understand the basic idea behind it?
B''H Bi'ezras -- Boruch Hashem
CC BY-SA 4.0
2023-03-31T06:16:29.250Z
This isn't really how it's done. The effective temperature of a star is defined in terms of its radius, not the other way around, because stars are not black bodies. You can fit the spectral energy distribution using models at different effective temperatures, but they aren't black body spectra and you aren't using Wien's law. There is also the "infra red flux method" that is related, and does sometimes assume you are looking at the tail of a blackbody spectrum.
ProfRob
CC BY-SA 4.0
2020-05-16T20:22:22.683Z
2020-05-16T20:22:22.683Z
Steve Linton
<p>Title pretty much says it all.</p>
<p>Basically, what exact variables are used, and what steps need to be taken, in the calculation of the size of a star? Preferably, some example data for how a the size of a star was recently calculated, from an official government / astronomy website, would be preferred, but not necessary.</p>

CC BY-SA 4.0
2020-05-16T00:37:16.800Z
Probably you'll need to learn about [Astronomical Interferometry](https://en.wikipedia.org/wiki/Astronomical_interferometer) to get an idea for what's involved.  You'll find links on that page to articles going into more detail.  The first paper on this subject (about 1920) is linked to there and it's probably a good place to start from.  Techniques have been continually developed and improved, which means they're also more complex.  Feel free to search for modern paper on e.g. Arxiv.org (a respected preprint website fort some science papers).
StephenG - Help Ukraine
CC BY-SA 4.0
2020-05-16T00:47:29.890Z
Can you clarify whether  you asking about observational measurements of the size of stars or theoretical predictions for sizes of stars ? Depending on how accurate you want it, there is a mass-radius $Radius \sim Mass^{0.7}$ but the 0.7 power does change for high and low mass stars ([more details](http://personal.psu.edu/rbc3/A534/lec18.pdf)). It depends how accurate you want the answer and over what range of masses, age and metallicity you want it to apply to
astrosnapper
CC BY-SA 4.0
2020-05-16T00:58:45.683Z
@astrosnapper hi, preferably more observational measurement, but really both are good too
B''H Bi'ezras -- Boruch Hashem
CC BY-SA 4.0
2020-05-16T13:40:41.387Z
Does this answer your question? [Device used to measure stellar radii](https://astronomy.stackexchange.com/questions/23566/device-used-to-measure-stellar-radii)
StephenG - Help Ukraine
CC BY-SA 4.0
2023-03-31T13:55:19.487Z
Are invision and entire book to answer this question@B''HBi'ezras--BoruchHashem
Starship
<star><the-sun><observational-astronomy><galaxy><size>
What are the necessary steps required for calculating the size of a star?
B''H Bi'ezras -- Boruch Hashem
# What are the necessary steps required for calculating the size of a star?

(Asked by: username_0 on 2020-05-16)

Title pretty much says it all.

Basically, what exact variables are used, and what steps need to be taken, in the calculation of the size of a star? Preferably, some example data for how a the size of a star was recently calculated, from an official government / astronomy website, would be preferred, but not necessary.

**Tags:** star, the-sun, observational-astronomy, galaxy, size

> **Comments:**
> **username_1**: Probably you'll need to learn about [Astronomical Interferometry](https://en.wikipedia.org/wiki/Astronomical_interferometer) to get an idea for what's involved.  You'll find links on that page to articles going into more detail.  The first paper on this subject (about 1920) is linked to there and it's probably a good place to start from.  Techniques have been continually developed and improved, which means they're also more complex.  Feel free to search for modern paper on e.g. Arxiv.org (a respected preprint website fort some science papers).  
> **username_2**: Can you clarify whether  you asking about observational measurements of the size of stars or theoretical predictions for sizes of stars ? Depending on how accurate you want it, there is a mass-radius $Radius \sim Mass^{0.7}$ but the 0.7 power does change for high and low mass stars ([more details](http://personal.psu.edu/rbc3/A534/lec18.pdf)). It depends how accurate you want the answer and over what range of masses, age and metallicity you want it to apply to  
> **username_0**: @username_2 hi, preferably more observational measurement, but really both are good too  
> **username_1**: Does this answer your question? [Device used to measure stellar radii](https://astronomy.stackexchange.com/questions/23566/device-used-to-measure-stellar-radii)  
> **username_3**: Are invision and entire book to answer this question@username_0  

---

## 1 answers

### Answer by username_4 on 2020-05-16. Score: 4

There have been direct measurements, but they are quite delicate -- this is all the interferometry and so on.

The simplest way though is based on spectroscopy, brightness and parallax. The argument goes a follows:

1. The spectrum (how much light of each colour it gives off) is not hard to observe -- you basically just need a prism.
2. The spectrum of most stars basically looks like whats called a "black body spectrum" -- the light given off by a hot body with no special properties. This can be both observed on Earth and predicted from basic physics (and they agree)
3. From the position of the peak of the black body spectrum we can tell the temperature of the star
4. The total light emitted per unit area from a black body depends only on its temperature, so we can calculate the total light emitted per unit area by the star.
5. For the nearer stars we can measure their distance fairly directly by observing how their apparent position moves against that of other stars as the Earth moves around the Sun
6. Knowing the distance, the brightness per unit area, and the amount of light actually hitting our telescope, we can work out what the area (and so size) of the star must be (this is just geometry)

> **Comments:**
> **username_0**: Ok ok very interesting, that clears up a lot of things I have been wondering regarding this. Just one more point I may need a bit more of explaining about, is point two, is a "black body spectrum" something that exists in other things on earth based on their color, and we are comparing the color given off by the stars to the colors given off by other things on earth, or is it something different?  
> **username_5**: A traditional light bulb is also a black body radiator. Many things are - with more or less big deviations, including you yourself.  
> **username_4**: @bluejayke Most hot objects give off radiation with something close to a black body spectrum -- a piece of red hot charcoal, for instance.  
> **username_0**: @username_4 OK cool I'm just trying to understand it, so we are comparing the stars color appearance to that of other object that we observe, to get the heat, is that right?  
> **username_4**: @bluejayke. essentially yes, although the process (and the physics behind it) is a lot more precise than your phrasing suggests.  
> **username_0**: @username_4 OK it may be more precise, but the basic idea is that we are using the same pool of information available to us on earth, and applying it to the stars, correct? Besides for getting into the details of *how* exactly it works, is there anything else specifically, regarding this point, that is necessary to know, to understand the basic idea behind it?  
> **username_6**: This isn't really how it's done. The effective temperature of a star is defined in terms of its radius, not the other way around, because stars are not black bodies. You can fit the spectral energy distribution using models at different effective temperatures, but they aren't black body spectra and you aren't using Wien's law. There is also the "infra red flux method" that is related, and does sometimes assume you are looking at the tail of a blackbody spectrum.  

---

