<p>The <a href="https://cneos.jpl.nasa.gov/ca/" rel="nofollow noreferrer">Near-Earth close approches website</a> shows close approaches to the Earth by near-Earth objects (NEOs). The table showing all close encounters indicates the <a href="https://en.wikipedia.org/wiki/Absolute_magnitude#Solar_System_bodies_(H)" rel="nofollow noreferrer">absolute magnitude</a>. </p>

<p>The data can be exported to a CSV file to estimate the apparent magnitude for each object, using the following equation.</p>

<p><span class="math-container">$$
m = H + 5 \log_{10} \bigg( \frac{d_{BS}d_{BO}}{d_0^2} \bigg) - q(\alpha)
$$</span>
where <span class="math-container">$H$</span> is the absolute magnitude, <span class="math-container">$m$</span> is the apparent magnitude, d_{*} are the distances between the objects and <span class="math-container">$a(\alpha)$</span> is the reflected light. <span class="math-container">$q(\alpha)$</span> is a number between 0 and 1.</p>

<p>I only want to know what happens when the object is closest to the Earth, so I use the approximation that the distance from the Sun to the NEO is 1AU. </p>

<p><span class="math-container">$q(\alpha)$</span> is complicated to compute, so I just compute <span class="math-container">$m$</span> using <span class="math-container">$q=0$</span> and <span class="math-container">$q=1$</span>. This leads to </p>

<p>min value <span class="math-container">$ = H + 5 \log (d_{BO}) - 1 &lt; m &lt; H + 5 \log (d_{BO}) = $</span> max value</p>

<p>with <span class="math-container">$d_{BO}$</span> the distance between the Earth and the NEO expressed in astronomical units (AU). </p>

<p>The server is unhappy when I try to get the entire database, so I limited my export to the objects that come reasonably close to Earth (d&lt;0.05 AU), with no time limit.</p>

<p>Among these 24588 objects, 4 have a maximal magnitude less than 6, and 16 have a minimal magnitude less than 6. So between 1900 and 2200, no more than 16 NEOs are visible by the naked eye.</p>

<p>In particular, 99942 Apophis (2004 MN4) has an apparent magnitude between 1.7 and 2.7 based on these estimates. Its close approach date is April 13 2029. </p>

<p><a href="https://i.sstatic.net/VrM6q.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/VrM6q.png" alt="enter image description here"></a></p>

<p>But this doesn't say anything on NEOs from before 1900 or after 2200. </p>

CC BY-SA 4.0
2020-05-07T09:39:45.767Z
This seems pretty definitive, can always accept a new answer once one does. Thanks!
uhoh
CC BY-SA 4.0
2020-05-07T11:14:57.867Z
The magnitude on the table is the [solar-system-body absolute magnitude](https://en.wikipedia.org/wiki/Absolute_magnitude#Solar_System_bodies_(H)), not the visual magnitude at closest approach. Absolute Magnitude 10.4  (433 Eros) at 1 AU fully-illuminated reference distance, is about 6.3  visual if you shrink the ideal reference distance to 0.15 AU (distance of the 1975 approach.)
notovny
CC BY-SA 4.0
2020-05-07T15:17:10.730Z
@notovny Thank you for that explanation. I fixed my answer accordingly :)
usernumber
CC BY-SA 4.0
2020-05-07T16:27:49.653Z
ha! *This still* seems pretty definitive, but more appealing now :-) Okay in the 2027 to 2030 timeframe there are about four objects to "keep an eye out" for. This is great news!
uhoh
CC BY-SA 4.0
2022-01-18T21:32:37.267Z
I'd like to recalculate that and get at text capture (rather than a screenshot) but I can't figure out how you obtained that particular selection. fyi I've quoted you [here](https://astronomy.stackexchange.com/questions/48214/will-3-600ft-asteroid-be-visible-at-my-location-tonight#comment105230_48214).
uhoh
CC BY-SA 4.0
2022-01-19T08:28:25.427Z
@uhoh What did you do to try to reproduce this selection?
usernumber
CC BY-SA 4.0
2022-01-19T08:47:49.073Z
I've tried a bunch of things, I always end up with tens of thousands of results but your screen capture has only 16 entries. https://i.sstatic.net/xWTlt.png
uhoh
CC BY-SA 4.0
2022-01-22T00:21:40.953Z
@uhoh Oh, I think I get it. Because you're only using the website interface. I downloaded the data from the website, did the computations described in my answer and selected the objects with appropriate $m$.
usernumber
CC BY-SA 4.0
2022-01-22T00:23:53.460Z
Oh, now I understand, thanks!
uhoh
CC BY-SA 4.0
2022-01-23T12:56:32.157Z
@uhoh It's also important to note that H alone doesn't indicate if an object if visible to the unaided eye. Objects have to be bright AND near to be visible ;)
usernumber
CC BY-SA 4.0
2022-01-23T15:08:15.853Z
@usernumber like [this](https://astronomy.stackexchange.com/a/29973/7982) or [this](https://space.stackexchange.com/a/36742/12102) or [this](https://astronomy.stackexchange.com/a/28778/7982) or [this](https://astronomy.stackexchange.com/a/29973/7982)?
uhoh
CC BY-SA 4.0
2024-07-23T00:56:07.677Z
I've just asked [Where should I go in April 2029 for the best chance of naked-eye observing of 99942 Apophis (2004 MN4)?](https://astronomy.stackexchange.com/q/58149/7982)
uhoh
CC BY-SA 4.0
2020-05-07T08:17:20.350Z
2020-05-07T15:29:51.457Z
2020-05-07T15:29:51.457Z
usernumber
<p>The question <a href="https://astronomy.stackexchange.com/q/35962/7982">Can we see asteroid 1998 OR2 with unaided eye?</a> got me thinking. Space.com's <a href="https://www.space.com/12097-vesta-asteroid-facts-solar-system.html" rel="nofollow noreferrer">Vesta: Facts About the Brightest Asteroid</a> says:</p>

<blockquote>
  <p>Vesta is the second most massive body in the asteroid belt, surpassed only by Ceres, which is classified as a dwarf planet. The brightest asteroid in the sky, <strong>Vesta is occasionally visible from Earth with the naked eye.</strong> It is the first of the four largest asteroids (Ceres, Vesta, Pallas and Hygiea) to be visited by a spacecraft. The Dawn mission orbited Vesta in 2011, providing new insights into this rocky world.</p>
</blockquote>

<p>The brightness of an object seen from Earth is proportional to (among other things) <span class="math-container">$1/r^2$</span> so an object which occasionally passes very close to Earth will occasionally be far brighter than normal; an object normally of order 200 million km away that comes to within 200 thousand km will be a million times brighter, and at 2.5 magnitudes per power of ten that means that for a brief time it could be 15 magnitudes brighter than average.</p>

<p><strong>Questions:</strong></p>

<ol>
<li>Has a near earth object in heliocentric orbit ever been bright enough to be visible to the unaided eye?</li>
<li>Are there any predictions of events in the foreseeable future when this will happen? </li>
</ol>

<p>Please exclude comets which are themselves invisible and it's the giant clouds of dust and gas they produce that we see and planets (and dwarf planets) who's heliocentric orbits make them regularly visible.</p>

<p>The following may provide some helpful definitions:</p>

<ul>
<li><a href="https://astronomy.stackexchange.com/q/35142/7982">Is there a distinction between NEOs and near-Earth asteroids? Is there a difference?</a></li>
<li><a href="https://astronomy.stackexchange.com/q/18117/7982">What (actually) defines an Aten-class near-earth asteroid?</a></li>
<li><a href="https://astronomy.stackexchange.com/q/32388/7982">Has Hubble ever been used to try to image a near Earth asteroid?</a></li>
<li><a href="https://astronomy.stackexchange.com/q/28028/7982">Is the passage of three asteroids near Earth today just coincidental?</a></li>
<li><a href="https://space.meta.stackexchange.com/q/1459/12102">https://space.meta.stackexchange.com/q/1459/12102</a></li>
</ul>

CC BY-SA 4.0
2020-04-29T04:32:49.410Z
Also see [How big will Apophis appear?](/q/14671)
Mike G
<solar-system><amateur-observing><asteroids><near-earth-object>
Has a near earth object in heliocentric orbit ever been bright enough to be visible to the unaided eye?
uhoh
# Has a near earth object in heliocentric orbit ever been bright enough to be visible to the unaided eye?

(Asked by: username_0 on 2020-04-29)

The question [Can we see asteroid 1998 OR2 with unaided eye?](https://astronomy.stackexchange.com/q/35962/7982) got me thinking. Space.com's [Vesta: Facts About the Brightest Asteroid](https://www.space.com/12097-vesta-asteroid-facts-solar-system.html) says:

> Vesta is the second most massive body in the asteroid belt, surpassed only by Ceres, which is classified as a dwarf planet. The brightest asteroid in the sky, **Vesta is occasionally visible from Earth with the naked eye.** It is the first of the four largest asteroids (Ceres, Vesta, Pallas and Hygiea) to be visited by a spacecraft. The Dawn mission orbited Vesta in 2011, providing new insights into this rocky world.

The brightness of an object seen from Earth is proportional to (among other things) $1/r^2$ so an object which occasionally passes very close to Earth will occasionally be far brighter than normal; an object normally of order 200 million km away that comes to within 200 thousand km will be a million times brighter, and at 2.5 magnitudes per power of ten that means that for a brief time it could be 15 magnitudes brighter than average.

**Questions:**

1. Has a near earth object in heliocentric orbit ever been bright enough to be visible to the unaided eye?
2. Are there any predictions of events in the foreseeable future when this will happen?

Please exclude comets which are themselves invisible and it's the giant clouds of dust and gas they produce that we see and planets (and dwarf planets) who's heliocentric orbits make them regularly visible.

The following may provide some helpful definitions:

* [Is there a distinction between NEOs and near-Earth asteroids? Is there a difference?](https://astronomy.stackexchange.com/q/35142/7982)
* [What (actually) defines an Aten-class near-earth asteroid?](https://astronomy.stackexchange.com/q/18117/7982)
* [Has Hubble ever been used to try to image a near Earth asteroid?](https://astronomy.stackexchange.com/q/32388/7982)
* [Is the passage of three asteroids near Earth today just coincidental?](https://astronomy.stackexchange.com/q/28028/7982)
* <https://space.meta.stackexchange.com/q/1459/12102>

**Tags:** solar-system, amateur-observing, asteroids, near-earth-object
> **Comments:**
> **username_1**: Also see [How big will Apophis appear?](/q/14671)  

---

## 1 answers

### Answer by username_2 on 2020-05-07. Score: 5 | Accepted answer

The [Near-Earth close approches website](https://cneos.jpl.nasa.gov/ca/) shows close approaches to the Earth by near-Earth objects (NEOs). The table showing all close encounters indicates the [absolute magnitude](https://en.wikipedia.org/wiki/Absolute_magnitude#Solar_System_bodies_(H)).

The data can be exported to a CSV file to estimate the apparent magnitude for each object, using the following equation.

$$
m = H + 5 \log\_{10} \bigg( \frac{d\_{BS}d\_{BO}}{d\_0^2} \bigg) - q(\alpha)
$$
where $H$ is the absolute magnitude, $m$ is the apparent magnitude, d\_{\*} are the distances between the objects and $a(\alpha)$ is the reflected light. $q(\alpha)$ is a number between 0 and 1.

I only want to know what happens when the object is closest to the Earth, so I use the approximation that the distance from the Sun to the NEO is 1AU.

$q(\alpha)$ is complicated to compute, so I just compute $m$ using $q=0$ and $q=1$. This leads to

min value $ = H + 5 \log (d\_{BO}) - 1 < m < H + 5 \log (d\_{BO}) = $ max value

with $d\_{BO}$ the distance between the Earth and the NEO expressed in astronomical units (AU).

The server is unhappy when I try to get the entire database, so I limited my export to the objects that come reasonably close to Earth (d<0.05 AU), with no time limit.

Among these 24588 objects, 4 have a maximal magnitude less than 6, and 16 have a minimal magnitude less than 6. So between 1900 and 2200, no more than 16 NEOs are visible by the naked eye.

In particular, 99942 Apophis (2004 MN4) has an apparent magnitude between 1.7 and 2.7 based on these estimates. Its close approach date is April 13 2029.

[![enter image description here](https://i.sstatic.net/VrM6q.png)](https://i.sstatic.net/VrM6q.png)

But this doesn't say anything on NEOs from before 1900 or after 2200.

> **Comments:**
> **username_0**: This seems pretty definitive, can always accept a new answer once one does. Thanks!  
> **username_3**: The magnitude on the table is the [solar-system-body absolute magnitude](https://en.wikipedia.org/wiki/Absolute_magnitude#Solar_System_bodies_(H)), not the visual magnitude at closest approach. Absolute Magnitude 10.4  (433 Eros) at 1 AU fully-illuminated reference distance, is about 6.3  visual if you shrink the ideal reference distance to 0.15 AU (distance of the 1975 approach.)  
> **username_2**: @notovny Thank you for that explanation. I fixed my answer accordingly :)  
> **username_0**: ha! *This still* seems pretty definitive, but more appealing now :-) Okay in the 2027 to 2030 timeframe there are about four objects to "keep an eye out" for. This is great news!  
> **username_0**: I'd like to recalculate that and get at text capture (rather than a screenshot) but I can't figure out how you obtained that particular selection. fyi I've quoted you [here](https://astronomy.stackexchange.com/questions/48214/will-3-600ft-asteroid-be-visible-at-my-location-tonight#comment105230_48214).  
> **username_2**: @uhoh What did you do to try to reproduce this selection?  
> **username_0**: I've tried a bunch of things, I always end up with tens of thousands of results but your screen capture has only 16 entries. https://i.sstatic.net/xWTlt.png  
> **username_2**: @uhoh Oh, I think I get it. Because you're only using the website interface. I downloaded the data from the website, did the computations described in my answer and selected the objects with appropriate $m$.  
> **username_0**: Oh, now I understand, thanks!  
> **username_2**: @uhoh It's also important to note that H alone doesn't indicate if an object if visible to the unaided eye. Objects have to be bright AND near to be visible ;)  
> **username_0**: @usernumber like [this](https://astronomy.stackexchange.com/a/29973/7982) or [this](https://space.stackexchange.com/a/36742/12102) or [this](https://astronomy.stackexchange.com/a/28778/7982) or [this](https://astronomy.stackexchange.com/a/29973/7982)?  
> **username_0**: I've just asked [Where should I go in April 2029 for the best chance of naked-eye observing of 99942 Apophis (2004 MN4)?](https://astronomy.stackexchange.com/q/58149/7982)  

---

