<p>Just to reiterate my comment. The approach is correct but the accuracy is spurious - the number of significant figures is not warranted by the quality of the distance information (the date of observation is much more precise).</p>
<p>The most recent distance determinations to the Crab (note it will not have moved far in 1000 years<span class="math-container">$^\dagger$</span>) are from <a href="https://arxiv.org/abs/2306.01617" rel="nofollow noreferrer">Lin et al. 2023</a>. They quote a parallax from radio observations (<span class="math-container">$0.53 \pm 0.06$</span> mas) and from Gaia DR3 (<span class="math-container">$0.51 \pm 0.08$</span> mas).</p>
<p>Assuming these are independent and also assuming negligible <a href="https://en.wikipedia.org/wiki/Lutz%E2%80%93Kelker_bias" rel="nofollow noreferrer">Lutz Kelker bias</a>, we can take a weighted mean of <span class="math-container">$0.52 \pm 0.05$</span> mas - i.e. precise to 10%.</p>
<p>The distance is then approximately <span class="math-container">$1920 \pm 190$</span> pc or <span class="math-container">$6270 \pm 630$</span> light years.</p>
<p>Thus your actual time of explosion is only good to <span class="math-container">$\pm 630$</span> years or so and the result should probably be quoted as <span class="math-container">$7200 \pm 600$</span> years ago - i.e. only known to two significant figures.</p>
<p><span class="math-container">$^\dagger$</span> The tangential velocity on the sky relative to the Solar System is about 120 km/s (depending on the distance - <a href="https://iopscience.iop.org/article/10.1086/529026" rel="nofollow noreferrer">Kaplan et al. 2008</a>). The line of sight velocity is uncertain but could be of similar magnitude. If we assume a net velocity away from the Sun of 200 km/s, this would change the distance by less than 1 light year in 1000 years.</p>

CC BY-SA 4.0
2023-11-07T17:09:47.637Z
Also, the distance changes over time, since we're on a planet that is orbiting around a star, which is in one of the spiral arms (Orion-Cygnus arm) of a galaxy that is orbiting around its own supermassive object, while the objects that make up that nebula are in a (arguably) different arm (Perseus) of the same galaxy. Basically all sorts of objects and groups of objects are rotating, orbiting, and moving relative to each other, and its not trivial to try to accurately backtrace all those movements in time.
T.E.D.
CC BY-SA 4.0
2023-11-07T17:19:30.127Z
@T.E.D. As I pointed out in my answer, the distance has not changed significantly in the 1000 years since the event. I've added the details.
ProfRob
CC BY-SA 4.0
2023-11-04T18:27:22.633Z
2023-11-07T17:19:36.900Z
2023-11-07T17:19:36.900Z
ProfRob
<p>The distance to the crab nebula is uncertain.  It is probably between
4900 and 8100 light years away, (with a best guess of 6500 light years). It is sometimes surprising that astronomers can measure some things so accurately, but don't have any accurate knowledge about how far away many of the astronomical objects that they observe are.</p>
<p>This means that the explosion occurred between about 7000 BC and and 3800 BC.</p>
<p>The <em>supernova</em> (the transient light visible on Earth) occurred in 1054, as was well documented by Chinese astronomers.</p>

CC BY-SA 4.0
2023-11-04T18:00:33.503Z
2023-11-04T18:00:33.503Z
James K
<p>You are absolutely right. The convention is that we date astronomical events by when we see them - which is verifiable, useful and absolutely certain.</p>
<ol>
<li><p>It wouldn’t be useful to know what year BC it exploded. We would have to add 6500 if we wanted to look (for example) in historical archives to see what had been observed and said about it.</p>
</li>
<li><p>We don’t <em>know</em> how far away the Crab Nebula is. Nobody has yet walked there with a tape measure. 6500 ly is our best estimate today. It will change, either because of refined observations or deductions or simply because of committee politics. Every time that happened one would have to go back and rewrite all the 5446 BC books. But 1054 is 1054 is 1054 and no one will ever change that.</p>
</li>
</ol>

CC BY-SA 4.0
2023-11-05T01:16:54.503Z
Until somebody invents a planetary-scale stardrive, that is. :)  The astronomers would **really** hate that!
Loren Pechtel
CC BY-SA 4.0
2023-11-06T10:36:50.473Z
 And I would walk 500 light-years, and I would walk 500 more, just to be the man who walked who walked 1000 light years just to measure the distance to your nebula 
Sebastian Lenartowicz
CC BY-SA 4.0
2023-11-06T17:18:02.960Z
This is an honest question that's confused me about this sort of thing ever since I learned details on relativity: Isn't there a third problem in that since the actual supernova itself is spacelike-separated from every moment on Earth before its light got here, describing it as having happened at a particular time in the past is meaningless anyway? In the right reference frame, can't it be said to have happened a millisecond before its light arrived, or one billion years before? Maybe that's just my mind being overly pedantic, but it's honestly something that's bugged me for a while for this.
Idran
CC BY-SA 4.0
2023-11-06T18:47:17.290Z
@JustinHilyard: the absolute majority of astronomical objects do not move relative to us at speeds where time dilation would be significant. For stars in the Milky way and nearby galaxies, I don't think there is any issue talking about simultaneity.
Martin Argerami
CC BY-SA 4.0
2023-11-06T19:26:59.880Z
Fair point, @Justin. But as Martin says, the relativistic effects are negligible within the galaxy. OTOH, for a sufficiently distant observer, even small relative velocities can change the order of space-like separated events, https://en.wikipedia.org/wiki/Rietdijk%E2%80%93Putnam_argument#Andromeda_paradox
PM 2Ring
CC BY-SA 4.0
2023-11-06T19:49:48.187Z
That clears things up greatly for me; thanks Martin and PM
Idran
CC BY-SA 4.0
2023-11-04T15:22:08.330Z
2023-11-06T17:14:22.677Z
2023-11-06T17:14:22.677Z
Martin Kochanski
<p>I am watching <a href="https://youtu.be/xubOa8xR2lw?si=rzPV1OWzzhRg3GHY&amp;t=412" rel="noreferrer">a youtube video</a> that says that, there is plenty of historic records that shows that the star, that turned into the Crab nebula, blew up in 1054. According to the video, it is located 6500 light years away.</p>
<p>The video author gives up calculating when it happen but that <em>should</em> be super easy.</p>
<p>1054 is 969 years ago.</p>
<p>One light year, is the distance light travels in a year.</p>
<pre><code>969 + 6500 = 7469
</code></pre>
<p>7469 years ago was in the year 5446 BC. Is that correct, or am I missing something?</p>
<h2>EDIT</h2>
<p>I wrote year 1057 instead of 1054! Sorry about that and thanks @PM-2ring</p>

CC BY-SA 4.0
2023-11-04T15:20:48.563Z
That would be correct although with spurious precision on the distance - call it 7500 years ago.
ProfRob
<light><distances><nebula>
Distance of the Crab nebula and the speed of light
dotnetCarpenter
# Distance of the Crab nebula and the speed of light

(Asked by: username_0 on 2023-11-04)

I am watching a youtube video that says that, there is plenty of historic records that shows that the star, that turned into the Crab nebula, blew up in 1054. According to the video, it is located 6500 light years away.
The video author gives up calculating when it happen but that should be super easy.
1054 is 969 years ago.
One light year, is the distance light travels in a year.
969 + 6500 = 7469

7469 years ago was in the year 5446 BC. Is that correct, or am I missing something?
EDIT
I wrote year 1057 instead of 1054! Sorry about that and thanks @PM-2ring

**Tags:** light, distances, nebula

> **Comments:**
> **username_1**: That would be correct although with spurious precision on the distance - call it 7500 years ago.  

---

## 3 answers

### Answer by username_4 on 2023-11-04. Score: 29 | Accepted answer

You are absolutely right. The convention is that we date astronomical events by when we see them - which is verifiable, useful and absolutely certain.

1. It wouldn’t be useful to know what year BC it exploded. We would have to add 6500 if we wanted to look (for example) in historical archives to see what had been observed and said about it.
2. We don’t *know* how far away the Crab Nebula is. Nobody has yet walked there with a tape measure. 6500 ly is our best estimate today. It will change, either because of refined observations or deductions or simply because of committee politics. Every time that happened one would have to go back and rewrite all the 5446 BC books. But 1054 is 1054 is 1054 and no one will ever change that.

> **Comments:**
> **username_5**: Until somebody invents a planetary-scale stardrive, that is. :)  The astronomers would **really** hate that!  
> **username_6**:  And I would walk 500 light-years, and I would walk 500 more, just to be the man who walked who walked 1000 light years just to measure the distance to your nebula   
> **username_7**: This is an honest question that's confused me about this sort of thing ever since I learned details on relativity: Isn't there a third problem in that since the actual supernova itself is spacelike-separated from every moment on Earth before its light got here, describing it as having happened at a particular time in the past is meaningless anyway? In the right reference frame, can't it be said to have happened a millisecond before its light arrived, or one billion years before? Maybe that's just my mind being overly pedantic, but it's honestly something that's bugged me for a while for this.  
> **username_8**: @JustinHilyard: the absolute majority of astronomical objects do not move relative to us at speeds where time dilation would be significant. For stars in the Milky way and nearby galaxies, I don't think there is any issue talking about simultaneity.  
> **username_9**: Fair point, @Justin. But as Martin says, the relativistic effects are negligible within the galaxy. OTOH, for a sufficiently distant observer, even small relative velocities can change the order of space-like separated events, https://en.wikipedia.org/wiki/Rietdijk%E2%80%93Putnam_argument#Andromeda_paradox  
> **username_7**: That clears things up greatly for me; thanks Martin and PM  

---

### Answer by username_1 on 2023-11-04. Score: 20

Just to reiterate my comment. The approach is correct but the accuracy is spurious - the number of significant figures is not warranted by the quality of the distance information (the date of observation is much more precise).

The most recent distance determinations to the Crab (note it will not have moved far in 1000 years$^\dagger$) are from [Lin et al. 2023](https://arxiv.org/abs/2306.01617). They quote a parallax from radio observations ($0.53 \pm 0.06$ mas) and from Gaia DR3 ($0.51 \pm 0.08$ mas).

Assuming these are independent and also assuming negligible [Lutz Kelker bias](https://en.wikipedia.org/wiki/Lutz%E2%80%93Kelker_bias), we can take a weighted mean of $0.52 \pm 0.05$ mas - i.e. precise to 10%.

The distance is then approximately $1920 \pm 190$ pc or $6270 \pm 630$ light years.

Thus your actual time of explosion is only good to $\pm 630$ years or so and the result should probably be quoted as $7200 \pm 600$ years ago - i.e. only known to two significant figures.

$^\dagger$ The tangential velocity on the sky relative to the Solar System is about 120 km/s (depending on the distance - [Kaplan et al. 2008](https://iopscience.iop.org/article/10.1086/529026)). The line of sight velocity is uncertain but could be of similar magnitude. If we assume a net velocity away from the Sun of 200 km/s, this would change the distance by less than 1 light year in 1000 years.

> **Comments:**
> **username_2**: Also, the distance changes over time, since we're on a planet that is orbiting around a star, which is in one of the spiral arms (Orion-Cygnus arm) of a galaxy that is orbiting around its own supermassive object, while the objects that make up that nebula are in a (arguably) different arm (Perseus) of the same galaxy. Basically all sorts of objects and groups of objects are rotating, orbiting, and moving relative to each other, and its not trivial to try to accurately backtrace all those movements in time.  
> **username_1**: @username_2 As I pointed out in my answer, the distance has not changed significantly in the 1000 years since the event. I've added the details.  

---

### Answer by username_3 on 2023-11-04. Score: 9

The distance to the crab nebula is uncertain. It is probably between
4900 and 8100 light years away, (with a best guess of 6500 light years). It is sometimes surprising that astronomers can measure some things so accurately, but don't have any accurate knowledge about how far away many of the astronomical objects that they observe are.

This means that the explosion occurred between about 7000 BC and and 3800 BC.

The *supernova* (the transient light visible on Earth) occurred in 1054, as was well documented by Chinese astronomers.


---

