<p>I agree with your naked eye figures, but the sensitivity of JWST has been over-estimated - it could &quot;see&quot; the Sun at 4 million light years.</p>
<p>The Sun has an absolute visual magnitude of about 4.75. This means, that ignoring extinction, it will have an apparent magnitude of 6 at a distance modulus of <span class="math-container">$6-4.75 = 1.25$</span>.</p>
<p>Distance modulus is <span class="math-container">$5\log_{10}d - 5$</span>, where <span class="math-container">$d$</span> is the distance in parsecs. A distance modulus of 1.25 implies <span class="math-container">$d=17.8$</span> parsecs, or 58 light years, so it sounds like you are more-or-less correct.</p>
<p>However, extending that argument to an apparent magnitude of 34, whilst numerically correct (I get 23 million light years) is likely to overestimate how far away the Sun could be seen by JWST. Firstly, the extinction to an object at <span class="math-container">$\sim$</span> 20 million light years is unlikely to be negligible and could be quite large depending on which direction you look. Secondly, it's one thing giving a theoretical magnitude limit and another to pick out a source from all the other faint objects crowding the sky at those limits. Thirdly, a paper by <a href="https://www.aanda.org/articles/aa/abs/2020/08/aa37450-20/aa37450-20.html" rel="nofollow noreferrer">Kauffmann et al. (2020)</a> suggests that an apparent magnitude limit of 31 is more likely in JWST deep surveys (using the <a href="https://en.m.wikipedia.org/wiki/AB_magnitude" rel="nofollow noreferrer">AB magnitude system</a>). However, JWST is most sensitive in the near infrared at about 2 microns. The Sun's absolute magnitude on the AB system through the JWST NIRCAM F277W filter is <a href="http://mips.as.arizona.edu/%7Ecnaw/sun.html" rel="nofollow noreferrer">about 5.5</a>. This means JWST could pick out the Sun at a distance of only 4 million light years (assuming no extinction; probably ok in the infrared).</p>
<p>This limit is quite consistent in some of the other, bluer filters. For example the JWST limit is likely to be about 30 in the F090W filter (just into the near infrared), but the Sun's absolute AB magnitude would be 4.5 in this filter, giving the same limiting distance.</p>

CC BY-SA 4.0
2022-12-27T00:30:23.337Z
2022-12-27T09:23:57.093Z
2022-12-27T09:23:57.093Z
ProfRob
<p>Images from various space probes show we see sun from far away.... Voyager 1 took an image of the sun on February 14, 1990 at a distance of just about 6 billion kilometers. 40x further than the Earth. <a href="https://i.sstatic.net/EFQbF.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/EFQbF.jpg" alt="enter image description here" /></a></p>

CC BY-SA 4.0
2022-12-31T04:48:32.907Z
Is the exposure from Voyager 1 equivalent to the unaided eye? (That is the question in the original post.) Is it more sensitive or less sensitive than the unaided eye? Once you add that information to your answer, can you then calculate the answer to the original post: how far can you be from the Sun and see it with the naked eye? It should be much farther than 6 billion km.
JohnHoltz
CC BY-SA 4.0
2022-12-30T05:46:01.567Z
2022-12-30T05:46:01.567Z
LazyReader
<p>How far away can we see the Sun with the naked eye?</p>
<p>How far with an amateur telescope? And with the James Webb telescope?</p>
<p>In my own calculations the Sun would appear magnitude 6 at 56 ly, magnitude 8 (extreme naked eye limit) at 140 ly.</p>
<p>Wikipedia says that the limit magnitude for JWST is about 34 so at a distance of 22 million light years. Are my calculations right?</p>

<observational-astronomy><star><the-sun><apparent-magnitude><naked-eye>
A what distance could we see the Sun?
HugoF
# A what distance could we see the Sun?

(Asked by: username_0 on 2022-12-15)

How far away can we see the Sun with the naked eye?

How far with an amateur telescope? And with the James Webb telescope?

In my own calculations the Sun would appear magnitude 6 at 56 ly, magnitude 8 (extreme naked eye limit) at 140 ly.

Wikipedia says that the limit magnitude for JWST is about 34 so at a distance of 22 million light years. Are my calculations right?

**Tags:** observational-astronomy, star, the-sun, apparent-magnitude, naked-eye

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## 2 answers

### Answer by username_1 on 2022-12-27. Score: 7

I agree with your naked eye figures, but the sensitivity of JWST has been over-estimated - it could "see" the Sun at 4 million light years.

The Sun has an absolute visual magnitude of about 4.75. This means, that ignoring extinction, it will have an apparent magnitude of 6 at a distance modulus of $6-4.75 = 1.25$.

Distance modulus is $5\log\_{10}d - 5$, where $d$ is the distance in parsecs. A distance modulus of 1.25 implies $d=17.8$ parsecs, or 58 light years, so it sounds like you are more-or-less correct.

However, extending that argument to an apparent magnitude of 34, whilst numerically correct (I get 23 million light years) is likely to overestimate how far away the Sun could be seen by JWST. Firstly, the extinction to an object at $\sim$ 20 million light years is unlikely to be negligible and could be quite large depending on which direction you look. Secondly, it's one thing giving a theoretical magnitude limit and another to pick out a source from all the other faint objects crowding the sky at those limits. Thirdly, a paper by [Kauffmann et al. (2020)](https://www.aanda.org/articles/aa/abs/2020/08/aa37450-20/aa37450-20.html) suggests that an apparent magnitude limit of 31 is more likely in JWST deep surveys (using the [AB magnitude system](https://en.m.wikipedia.org/wiki/AB_magnitude)). However, JWST is most sensitive in the near infrared at about 2 microns. The Sun's absolute magnitude on the AB system through the JWST NIRCAM F277W filter is [about 5.5](http://mips.as.arizona.edu/%7Ecnaw/sun.html). This means JWST could pick out the Sun at a distance of only 4 million light years (assuming no extinction; probably ok in the infrared).

This limit is quite consistent in some of the other, bluer filters. For example the JWST limit is likely to be about 30 in the F090W filter (just into the near infrared), but the Sun's absolute AB magnitude would be 4.5 in this filter, giving the same limiting distance.


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### Answer by username_2 on 2022-12-30. Score: 0

Images from various space probes show we see sun from far away.... Voyager 1 took an image of the sun on February 14, 1990 at a distance of just about 6 billion kilometers. 40x further than the Earth. [![enter image description here](https://i.sstatic.net/EFQbF.jpg)](https://i.sstatic.net/EFQbF.jpg)

> **Comments:**
> **username_3**: Is the exposure from Voyager 1 equivalent to the unaided eye? (That is the question in the original post.) Is it more sensitive or less sensitive than the unaided eye? Once you add that information to your answer, can you then calculate the answer to the original post: how far can you be from the Sun and see it with the naked eye? It should be much farther than 6 billion km.  

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