<p>One way to find distance to a collection of stars is to hope for an <a href="http://en.wikipedia.org/wiki/RR_Lyrae" rel="noreferrer">RRLyrae</a>
 in the bunch. Since RRLyrae are <a href="http://en.wikipedia.org/wiki/Standard_candle#Standard_candles" rel="noreferrer">standard candles</a>, you can use the inverse square law to extract the distance.</p>

<p><img src="https://i.sstatic.net/369Q6.jpg" alt="rrlyraePeriod"></p>

CC BY-SA 3.0
2013-11-13T20:08:18.250Z
What do you do if there is no RRLyrae?
axwcode
CC BY-SA 3.0
2013-11-13T21:17:03.360Z
What do you do when you don't have RRLyrae and you're beyond the distance parallax can be used? Hope for some other type of variable star or supernovae in order to use as a standard candle, I'd say. Beyond that I'm not entirely sure. Anything too local will not be expanding with the universe in a predictable enough way in order to relate its redshift to distance. All stars we hope to see are unfortunately local (in our own Milky Way galaxy; save for supernovae).
astromax
CC BY-SA 3.0
2013-11-20T21:27:14.553Z
This is definitely not a typical method of measuring distances to stars. RR lyrae are red giants and are extremely rare comparing to main sequence stars. What one normally does instead is estimating the absolute magnitude and extinction towards the star, which are in their turn determined by the means of multi-band photometry or spectroscopy. This way one knows the luminosity of the star and hence can derive the distance. In a sense, a star "becomes" a standard candle, once its spectrum is studied (even if by means of photometry).
Alexey Bobrick
CC BY-SA 3.0
2013-11-21T03:49:12.953Z
Hmm - not sure why a correct answer was down-voted. You could have simply said that there are more common techniques. What would have been even better is to come up with an answer of your own.
astromax
CC BY-SA 3.0
2013-11-21T04:16:32.893Z
@Alexey Bobrick Also, I was careful to say "One way..".  Please provide a detailed answer to the question.
astromax
CC BY-SA 3.0
2013-11-21T14:20:46.327Z
@astromax, sorry for downvoting your answer, I don't mean any bad. However, I stress it, it is not a correct answer to the question, and is almost irrelevant. Standard technique is as I outlined before, and parallax comes as a second most common method. What you are talking about here is more suitable for determining the distances to galaxies and stellar clusters.
Alexey Bobrick
CC BY-SA 3.0
2013-11-21T15:05:04.960Z
@AlexeyBobrick I still disagree, the question is how to find the distance to the "stars" - plural. I interpreted that as an opportunity to talk about all methods of distance determination to populations of stars. I think my answer is actually highly relevant, and regardless if it's the most common technique. It's hard to argue against standard candles. If he wanted the most common technique he would have said so. He does ask for the distance to Proxima Centauri, but my answer is in response to the first part of the question. I'm sorry, but I think you're in the wrong here.
astromax
CC BY-SA 3.0
2013-11-21T15:07:10.517Z
I personally reserve downvoting for incorrect answers - not relevant answers which are incomplete or not necessarily the best answer.
astromax
CC BY-SA 3.0
2013-11-21T15:09:50.103Z
This is the last comment I'm going to make - you seem to have a problem with my additional answer in the comments below, where I mention to, "Hope for some other type of variable star or supernovae in order to use as a standard candle, I'd say. Beyond that I'm not entirely sure." This is where I would say - come up with your own answer to this question rather than spending time on this one! I bet you'd do a fine job.
astromax
CC BY-SA 3.0
2013-11-21T16:04:23.290Z
@astromax, my vision, is that in this question the person who asks doesn't have enough expertise to judge the answers, whereas none of the existing answers are relevant to the question. Hence downvote to 1-4 level, which I think is appropriate to reasonable but irrelevant answers. In a perfect scenario I would be happy to see one more answer which gives a short summary of possible techniques (there are not that many indeed) with a bit of emphasis on two standard ones (parallax and magnitudes), which were actually the ones asked for, if you take a look at the question.
Alexey Bobrick
CC BY-SA 3.0
2013-11-24T20:06:14.060Z
@AlexeyBobrick I'm sorry - I don't really understand anything you just said. I'm calling you out here - I think you should create a answer describing the "method" you have outlined above.
astromax
CC BY-SA 3.0
2013-11-24T20:11:00.547Z
@astromax, I don't really feel like answering a basic question with an accepted answer at the moment, but can forward you the link with the two methods I was talking about: http://en.wikipedia.org/wiki/Spectroscopic_parallax . Otherwise, I suggest we can talk in a chat and you can expand your answer to make it complete.
Alexey Bobrick
CC BY-SA 3.0
2013-11-13T12:58:54.983Z
2013-11-13T12:58:54.983Z
astromax
<p>For close objects, the parallax method works perfectly. Though for higher distances, the Standard candles, as mentioned before, are used. The brightness of RR Lyrae, Supernovae type Ia, could be calculated, therefore, with the amount of light we get from these objects, we can estimate the distance. For even farther objects, the redshift method is used to calculate the distance, where a given line transition with a given frequency (iron emission for instance) is measured, and the shift in frequency, caused by the expansion of the universe (a phenomenon described mathematically) gives us a hint for the distance of the object.</p>

CC BY-SA 3.0
2013-11-20T15:50:10.057Z
2013-11-20T15:50:10.057Z
guest
<p>The currently accepted answer is not relevant for finding the distance to a star like Proxima Centauri.</p>

<p>Here's how parallax works. You measure the position of a star in a field of stars that are (presumably) much further way. You do this twice, separated by 6 months. You then calculate the angle that the star has moved against its background stars. This angle forms part of a large triangle, with a base that is equal to the <em>diameter</em> of the Earth's orbit around the Sun. Trigonometry then tells you what the distance is as a multiple of the distance from the Earth to the Sun. [In practice you perform many measurements with any separation in time and combine them all.]</p>

<p>The "parallax angle" is actually <em>half</em> this angular displacement, and a star is said to be 1 parsec away if the parallax angle is 1 second of arc. So 1pc is 1 AU/$\tan (\theta) = 3.08\times10^{16}$ m. The larger the parallax, the closer the star.</p>

<p>The Gaia satellite is currently mapping the entire sky and will estimate tiny parallaxes 
with precisions of $10^{-5}$ to $10^{-4}$ arcseconds (depending on target brightness) for about a billion stars.</p>

<p><em>Parallax - as illustrated at <a href="http://www.bbc.co.uk/schools/gcsebitesize/science/21c/earth_universe/earth_stars_galaxiesrev4.shtml" rel="noreferrer">http://www.bbc.co.uk/schools/gcsebitesize/science/21c/earth_universe/earth_stars_galaxiesrev4.shtml</a></em></p>

<p><img src="https://i.sstatic.net/mr5ad.gif" alt="Parallax, taken from the BBC &quot;bitesize website&quot;"></p>

<p>Now in reality, it is a bit more difficult than this because stars also have a "proper motion" across the sky due to their motion in our Galaxy relative to the Sun. This means you have to do more than two measurements to separate out this component of motion on the sky. In the case of Proxima Centauri the motion against the background stars due to proper motion is larger than the parallax. But the two components can clearly be seen and separated (see below). It is (half) the amplitude of the curved motion in the picture below that corresponds to the parallax. The proper motion is just the constant linear trend with respect to the background stars.</p>

<p><em>HST images of the path of Proxima Centauri against background stars. The green curve shows the measured and predicted path of the star against the background field over the next few years.</em></p>

<p><img src="https://i.sstatic.net/GFQkp.jpg" alt="HST images of Proxima Centauri"></p>

<p>Parallax measurements work best for nearby stars, because the parallax angle is larger. For more distant stars or those without a parallax measurement, there are a battery of techniques. For isolated stars, the most common is to attempt to establish what type of star it is, either from its colour(s) or preferably from a spectrum that can reveal its temperature and gravity. From this one can estimate what the absolute luminosity of the object is and then from its observed brightness one can calculate the distance. This is known as a <em>photometric parallax</em> or <em>spectroscopic parallax</em>.</p>

CC BY-SA 3.0
2014-12-13T22:29:43.960Z
2015-04-05T10:53:34.603Z
2015-04-05T10:53:34.603Z
ProfRob
<p>I was just watching a lecture from Carl Sagan. He talked about figuring out the distance to the stars; it got me interested in learning more about the subject.</p>

<p>As far as I know, the Inverse square law and parallax can be used. Can anyone expand on these? Specifically with regards to what I could do to measure the distance from Earth to Proxima  Centauri.</p>

CC BY-SA 3.0
2013-11-13T12:56:01.223Z
In order for you to use the inverse square law you must know the distance first (unless you use what's known as a standard candle).
astromax
CC BY-SA 3.0
2013-11-21T14:23:58.840Z
As I have outlined in the comments below, the accepted answer here is barely relevant to standard techniques of determining distance to stars in astronomy. Relevant info can be found instead, e.g. in this reference: http://en.wikipedia.org/wiki/Spectroscopic_parallax
Alexey Bobrick
CC BY-SA 3.0
2015-04-05T19:43:43.117Z
@barrycarter It's almost that simple, but not quite - see below.
ProfRob
<star><distances>
Calculate Distance To Stars
axwcode
# Calculate Distance To Stars

(Asked by: username_0 on 2013-11-13)

I was just watching a lecture from Carl Sagan. He talked about figuring out the distance to the stars; it got me interested in learning more about the subject.

As far as I know, the Inverse square law and parallax can be used. Can anyone expand on these? Specifically with regards to what I could do to measure the distance from Earth to Proxima Centauri.

**Tags:** star, distances

> **Comments:**
> **username_1**: In order for you to use the inverse square law you must know the distance first (unless you use what's known as a standard candle).  
> **username_2**: As I have outlined in the comments below, the accepted answer here is barely relevant to standard techniques of determining distance to stars in astronomy. Relevant info can be found instead, e.g. in this reference: http://en.wikipedia.org/wiki/Spectroscopic_parallax  
> **username_3**: @barrycarter It's almost that simple, but not quite - see below.  

---

## 3 answers

### Answer by username_3 on 2014-12-13. Score: 10 | Accepted answer

The currently accepted answer is not relevant for finding the distance to a star like Proxima Centauri.

Here's how parallax works. You measure the position of a star in a field of stars that are (presumably) much further way. You do this twice, separated by 6 months. You then calculate the angle that the star has moved against its background stars. This angle forms part of a large triangle, with a base that is equal to the *diameter* of the Earth's orbit around the Sun. Trigonometry then tells you what the distance is as a multiple of the distance from the Earth to the Sun. [In practice you perform many measurements with any separation in time and combine them all.]

The "parallax angle" is actually *half* this angular displacement, and a star is said to be 1 parsec away if the parallax angle is 1 second of arc. So 1pc is 1 AU/$\tan (\theta) = 3.08\times10^{16}$ m. The larger the parallax, the closer the star.

The Gaia satellite is currently mapping the entire sky and will estimate tiny parallaxes
with precisions of $10^{-5}$ to $10^{-4}$ arcseconds (depending on target brightness) for about a billion stars.

*Parallax - as illustrated at <http://www.bbc.co.uk/schools/gcsebitesize/science/21c/earth_universe/earth_stars_galaxiesrev4.shtml>*

![Parallax, taken from the BBC "bitesize website"](https://i.sstatic.net/mr5ad.gif)

Now in reality, it is a bit more difficult than this because stars also have a "proper motion" across the sky due to their motion in our Galaxy relative to the Sun. This means you have to do more than two measurements to separate out this component of motion on the sky. In the case of Proxima Centauri the motion against the background stars due to proper motion is larger than the parallax. But the two components can clearly be seen and separated (see below). It is (half) the amplitude of the curved motion in the picture below that corresponds to the parallax. The proper motion is just the constant linear trend with respect to the background stars.

*HST images of the path of Proxima Centauri against background stars. The green curve shows the measured and predicted path of the star against the background field over the next few years.*

![HST images of Proxima Centauri](https://i.sstatic.net/GFQkp.jpg)

Parallax measurements work best for nearby stars, because the parallax angle is larger. For more distant stars or those without a parallax measurement, there are a battery of techniques. For isolated stars, the most common is to attempt to establish what type of star it is, either from its colour(s) or preferably from a spectrum that can reveal its temperature and gravity. From this one can estimate what the absolute luminosity of the object is and then from its observed brightness one can calculate the distance. This is known as a *photometric parallax* or *spectroscopic parallax*.


---

### Answer by username_1 on 2013-11-13. Score: 5

One way to find distance to a collection of stars is to hope for an [RRLyrae](http://en.wikipedia.org/wiki/RR_Lyrae)
in the bunch. Since RRLyrae are [standard candles](http://en.wikipedia.org/wiki/Standard_candle#Standard_candles), you can use the inverse square law to extract the distance.

![rrlyraePeriod](https://i.sstatic.net/369Q6.jpg)

> **Comments:**
> **username_0**: What do you do if there is no RRLyrae?  
> **username_1**: What do you do when you don't have RRLyrae and you're beyond the distance parallax can be used? Hope for some other type of variable star or supernovae in order to use as a standard candle, I'd say. Beyond that I'm not entirely sure. Anything too local will not be expanding with the universe in a predictable enough way in order to relate its redshift to distance. All stars we hope to see are unfortunately local (in our own Milky Way galaxy; save for supernovae).  
> **username_2**: This is definitely not a typical method of measuring distances to stars. RR lyrae are red giants and are extremely rare comparing to main sequence stars. What one normally does instead is estimating the absolute magnitude and extinction towards the star, which are in their turn determined by the means of multi-band photometry or spectroscopy. This way one knows the luminosity of the star and hence can derive the distance. In a sense, a star "becomes" a standard candle, once its spectrum is studied (even if by means of photometry).  
> **username_1**: Hmm - not sure why a correct answer was down-voted. You could have simply said that there are more common techniques. What would have been even better is to come up with an answer of your own.  
> **username_1**: @username_2 Also, I was careful to say "One way..".  Please provide a detailed answer to the question.  
> **username_2**: @username_1, sorry for downvoting your answer, I don't mean any bad. However, I stress it, it is not a correct answer to the question, and is almost irrelevant. Standard technique is as I outlined before, and parallax comes as a second most common method. What you are talking about here is more suitable for determining the distances to galaxies and stellar clusters.  
> **username_1**: @username_2 I still disagree, the question is how to find the distance to the "stars" - plural. I interpreted that as an opportunity to talk about all methods of distance determination to populations of stars. I think my answer is actually highly relevant, and regardless if it's the most common technique. It's hard to argue against standard candles. If he wanted the most common technique he would have said so. He does ask for the distance to Proxima Centauri, but my answer is in response to the first part of the question. I'm sorry, but I think you're in the wrong here.  
> **username_1**: I personally reserve downvoting for incorrect answers - not relevant answers which are incomplete or not necessarily the best answer.  
> **username_1**: This is the last comment I'm going to make - you seem to have a problem with my additional answer in the comments below, where I mention to, "Hope for some other type of variable star or supernovae in order to use as a standard candle, I'd say. Beyond that I'm not entirely sure." This is where I would say - come up with your own answer to this question rather than spending time on this one! I bet you'd do a fine job.  
> **username_2**: @username_1, my vision, is that in this question the person who asks doesn't have enough expertise to judge the answers, whereas none of the existing answers are relevant to the question. Hence downvote to 1-4 level, which I think is appropriate to reasonable but irrelevant answers. In a perfect scenario I would be happy to see one more answer which gives a short summary of possible techniques (there are not that many indeed) with a bit of emphasis on two standard ones (parallax and magnitudes), which were actually the ones asked for, if you take a look at the question.  
> **username_1**: @username_2 I'm sorry - I don't really understand anything you just said. I'm calling you out here - I think you should create a answer describing the "method" you have outlined above.  
> **username_2**: @username_1, I don't really feel like answering a basic question with an accepted answer at the moment, but can forward you the link with the two methods I was talking about: http://en.wikipedia.org/wiki/Spectroscopic_parallax . Otherwise, I suggest we can talk in a chat and you can expand your answer to make it complete.  

---

### Answer by username_4 on 2013-11-20. Score: 3

For close objects, the parallax method works perfectly. Though for higher distances, the Standard candles, as mentioned before, are used. The brightness of RR Lyrae, Supernovae type Ia, could be calculated, therefore, with the amount of light we get from these objects, we can estimate the distance. For even farther objects, the redshift method is used to calculate the distance, where a given line transition with a given frequency (iron emission for instance) is measured, and the shift in frequency, caused by the expansion of the universe (a phenomenon described mathematically) gives us a hint for the distance of the object.


---

