<p>Below are some strengths of some radio sources. Let's choose 1000 Jy and 100 MHz bandwidth, a modest 1000 m^2 single dish and 8 hour observation.</p>
<p><span class="math-container">$$1000 \times 10^{-26} \ \text{W} \text{m}^{-2} \text{Hz}^{-1} \times 1000 \ \text{m}^2 \times 10^8 \ \text{Hz} = 10^{-12} \text{W}$$</span></p>
<p>and</p>
<p><span class="math-container">$$10^{-12} \text{W} \times 28800 \text{sec} = 3 \times 10^{-8} \text{J}$$</span></p>
<p>1000 of those 30 m dishes for ten years:</p>
<p><span class="math-container">$$3 \times 10^{-8} \text{J} \times 1000 \times 10 \times 365 \times 24/8 = 0.3 \ \text{Joules!}$$</span></p>
<p><strong>On the surface the quoted sentence seems to be borderline.</strong></p>
<p>Of course astronomers would not point every radio telescope dish at the strongest sources continuously for a decade.</p>
<p>Had they been instead spending most of the time listening to weak sources (which is exactly what is going to eat up most of the observing time by necessity) then</p>
<h3>it's very possible that when considering the energy collected from the <em>actual observed targets up until 1980</em> that this number is correct!</h3>
<p>It may be true that the total received power over the full field of view of all telescopes including the CMB could be a lot larger, I'm going to cut Dr. Sagan some slack and suggest that by &quot;received&quot; he meant &quot;listened to&quot;.</p>
<p>I will defer to other answers with the estimate of a few millijoules for the snowflake.</p>
<hr />
<h3>Brightest of the brightest</h3>
<p>This is from <a href="https://reeve.com/Documents/Articles%20Papers/Reeve_CelestialRadioSources.pdf" rel="noreferrer">Important Celestial Radio Sources Whitham D. Reeve</a></p>
<p><strong>Here are the top sources in the list that also appear in the map, the list itself is much longer</strong></p>
<div class="s-table-container">
<table class="s-table">
<thead>
<tr>
<th>Object Name</th>
<th>RA (hh mm ss)</th>
<th>Dec (dd mm ss)</th>
<th>Epoch</th>
<th>Flux Density (Jy)</th>
<th>Frequency (MHz)</th>
<th>Other Name</th>
</tr>
</thead>
<tbody>
<tr>
<td>3C 461</td>
<td>23 23 24</td>
<td>58 48 54</td>
<td>2000</td>
<td>2477</td>
<td>1,420</td>
<td>SNR-Cassiopeia A</td>
</tr>
<tr>
<td>CTA 59</td>
<td>13 22 28</td>
<td>-42 46 00</td>
<td>1950</td>
<td>2010</td>
<td>960</td>
<td>Cent A NGC5128</td>
</tr>
<tr>
<td>CTB 42</td>
<td>17 42 09</td>
<td>-28 50 00</td>
<td>1950</td>
<td>1800</td>
<td>960</td>
<td>Sag A Galactic Nuccleus</td>
</tr>
<tr>
<td>3C 405</td>
<td>19 59 28</td>
<td>40 44 02</td>
<td>2000</td>
<td>1495</td>
<td>1,420</td>
<td>D</td>
</tr>
<tr>
<td>3C 144</td>
<td>05 34 32</td>
<td>22 00 52</td>
<td>2000</td>
<td>875</td>
<td>1,420</td>
<td>SNR-Crab Nebula</td>
</tr>
<tr>
<td>3C 400</td>
<td>19 23 42</td>
<td>14 30 33</td>
<td>2000</td>
<td>576</td>
<td>1,420</td>
<td></td>
</tr>
<tr>
<td>3C 145</td>
<td>05 35 17</td>
<td>-05 23 28</td>
<td>2000</td>
<td>520</td>
<td>1,420</td>
<td>Emission Nebula-OrionA</td>
</tr>
<tr>
<td>3C 274</td>
<td>12 30 49</td>
<td>12 23 28</td>
<td>2000</td>
<td>198</td>
<td>1,420</td>
<td>Elliptical Galaxy-M87</td>
</tr>
<tr>
<td>3C 392</td>
<td>18 56 06</td>
<td>01 18 00</td>
<td>2000</td>
<td>171</td>
<td>1,420</td>
<td>SNR</td>
</tr>
<tr>
<td>NRAO 5690</td>
<td>18 35 00</td>
<td>-07 20 00</td>
<td>2000</td>
<td>90</td>
<td>1,420</td>
<td></td>
</tr>
<tr>
<td>3C 390.2</td>
<td>18 47 58</td>
<td>-01 56 43</td>
<td>2000</td>
<td>80</td>
<td>1,420</td>
<td></td>
</tr>
<tr>
<td>3C 403.2</td>
<td>19 54 12</td>
<td>32 54 00</td>
<td>2000</td>
<td>75</td>
<td>1,420</td>
<td></td>
</tr>
<tr>
<td>3C 147.1</td>
<td>05 41 43</td>
<td>-01 54 17</td>
<td>2000</td>
<td>65</td>
<td>1,420</td>
<td>Emission Nebula-OrionB</td>
</tr>
<tr>
<td>3C 353</td>
<td>17 20 28</td>
<td>-00 58 47</td>
<td>2000</td>
<td>57</td>
<td>1,420</td>
<td>D Galaxy</td>
</tr>
<tr>
<td>NRAO 6210</td>
<td>20 01 42</td>
<td>33 17 00</td>
<td>2000</td>
<td>55</td>
<td>1,420</td>
<td></td>
</tr>
<tr>
<td>3C 387</td>
<td>18 41 00</td>
<td>-05 16 00</td>
<td>2000</td>
<td>51</td>
<td>1,420</td>
<td></td>
</tr>
<tr>
<td>3C 123</td>
<td>04 37 04</td>
<td>29 40 14</td>
<td>2000</td>
<td>47</td>
<td>1,420</td>
<td>Galaxy</td>
</tr>
<tr>
<td>NRAO 5980</td>
<td>19 10 19</td>
<td>09 04 07</td>
<td>2000</td>
<td>47</td>
<td>1,420</td>
<td></td>
</tr>
<tr>
<td>3C 273</td>
<td>12 29 07</td>
<td>02 03 09</td>
<td>2000</td>
<td>46</td>
<td>1,420</td>
<td>Quasar</td>
</tr>
<tr>
<td>NRAO 6500</td>
<td>21 12 21</td>
<td>52 28 58</td>
<td>2000</td>
<td>46</td>
<td>1,420</td>
<td></td>
</tr>
<tr>
<td>3C 348</td>
<td>16 51 08</td>
<td>04 59 34</td>
<td>2000 45</td>
<td>1,420</td>
<td>D</td>
<td>Galaxy</td>
</tr>
<tr>
<td>3C 10</td>
<td>00 25 13</td>
<td>64 08 42</td>
<td>2000</td>
<td>44</td>
<td>1,420</td>
<td>SNR-Tycho's Supernova</td>
</tr>
<tr>
<td>3C 218</td>
<td>09 18 06</td>
<td>-12 05 44</td>
<td>2000</td>
<td>43</td>
<td>1,420</td>
<td>D Galaxy</td>
</tr>
<tr>
<td>3C 139.1</td>
<td>05 22 25</td>
<td>33 29 55</td>
<td>2000</td>
<td>40</td>
<td>1,420</td>
<td>Emission Nebula</td>
</tr>
</tbody>
</table>
</div>
<p><a href="https://i.sstatic.net/TpYE5.jpg" rel="noreferrer"><img src="https://i.sstatic.net/TpYE5.jpg" alt="This Celestial Radio Map is a composite of four individual quadrant maps from the referenced source (see upper-left corner)" /></a></p>
<blockquote>
<p>This Celestial Radio Map is a composite of four individual quadrant maps from the referenced source (see upper-left corner). Annotations show the approximate locations of sources with flux density ≥ 40 Jy. The S-shaped region where the contour lines are close together is the region around the Milky Way galactic equator. The contour lines represent lines of constant noise temperature as measured at 408 MHz. However, note that the flux density annotations are mostly at 1420 MHz with exceptions noted in the table. The ecliptic is indicated by a dashed line. The ecliptic is the path the Sun follows in the sky over a period of one year as viewed on Earth.</p>
</blockquote>
<hr />
<ul>
<li><a href="https://www.mpifr-bonn.mpg.de/1041051/Porcas_Intro_Radio.pdf" rel="noreferrer">https://www.mpifr-bonn.mpg.de/1041051/Porcas_Intro_Radio.pdf</a></li>
<li><a href="https://reeve.com/Documents/Articles%20Papers/Reeve_CelestialRadioSources.pdf" rel="noreferrer">https://reeve.com/Documents/Articles%20Papers/Reeve_CelestialRadioSources.pdf</a></li>
<li><a href="https://web.archive.org/web/20130516042600/http://astro.u-strasbg.fr/%7Ekoppen/10GHz/basics.html" rel="noreferrer">Fundamentals of Radio Astronomy; Joachim Köppen Strasbourg 2010</a></li>
</ul>
<p><a href="https://i.sstatic.net/YGzXo.gif" rel="noreferrer"><img src="https://i.sstatic.net/YGzXo.gif" alt="typical flux vs frequency for various astronomical sources: Fundamentals of Radio Astronomy; Joachim Köppen Strasbourg 2010" /></a></p>

CC BY-SA 4.0
2021-09-25T02:26:48.560Z
2021-09-25T02:26:48.560Z
uhoh
<p>Radio waves (approximately <span class="math-container">$\lambda=1\rm\,m$</span><sup><a href="https://en.wikipedia.org/wiki/Five-hundred-meter_Aperture_Spherical_Telescope#:%7E:text=0.10%C2%A0m%20(3.0%C2%A0GHz)%E2%80%934.3%C2%A0m%20(70%C2%A0MHz)" rel="nofollow noreferrer">[1]</a></sup>) are very weak, about <span class="math-container">$E=\frac{hc}{\lambda}=\frac{6.63\cdot10^{-34}\cdot 3\cdot 10^8}{1}\rm\,J\approx2\cdot 10^{-25}\rm\,J$</span> every photon.</p>
<p>An <span class="math-container">$1\rm\,mg=1\cdot10^{-6}\rm\,kg$</span><sup><a href="https://hypertextbook.com/facts/2001/JudyMoy.shtml" rel="nofollow noreferrer">[2]</a></sup> snowflake falling at <span class="math-container">$0.7\rm\,\frac{m}{s}$</span><sup><a href="https://www.metoffice.gov.uk/weather/learn-about/weather/types-of-weather/snow/10-facts-about-snow" rel="nofollow noreferrer">[3]</a></sup> has <span class="math-container">$$K=\frac{mv^2}{2}=\frac{1\cdot10^{-6}\cdot 0.7^2}{2}\rm\,J\approx2.5\cdot10^{-7}\rm\,J$$</span> of kinetic energy.</p>
<p>That is equivalent to <span class="math-container">$10^{18}$</span> photons' energy. I think we can say that's close to the amount of photons collected by us by the time Carl said this.</p>
<p>This shows that Carl Sagan knew his numbers.</p>
<p><em><strong>Ps.</strong> There are over 100 radio telescopes now, but this quote comes from 1980,
back then a low number of radio telescopes existed and they used weren't very powerful. That's why the number of photons are reasonable.</em></p>

CC BY-SA 4.0
2021-09-23T17:02:14.633Z
@WalidSiddik No problem. You messed up with the grams and kilograms regarding kinetic energy.
User123
CC BY-SA 4.0
2021-09-23T18:23:55.810Z
@WalidSiddik How did you estimate the amount of photons collected?
samcarter_is_at_topanswers.xyz
CC BY-SA 4.0
2021-09-23T15:45:18.913Z
2021-09-24T05:44:49.720Z
2021-09-24T05:44:49.720Z
Was'
<p><em>“The total amount of energy from outside the solar system ever received by all the radio telescopes on the planet Earth is less than the energy of a single snowflake striking the ground.”</em></p>
<p>― Carl Sagan, <a href="https://en.wikipedia.org/wiki/Cosmos_(Sagan_book)" rel="nofollow noreferrer">Cosmos</a></p>

CC BY-SA 4.0
2021-09-23T09:43:59.763Z
Do you mean the assertion is true or he made it?
Alchimista
<observational-astronomy><radio-astronomy><radio-telescope>
Is Carl Sagan's famous "snowflake" quote correct?
ZAB
# Is Carl Sagan's famous "snowflake" quote correct?

(Asked by: username_0 on 2021-09-22)

*“The total amount of energy from outside the solar system ever received by all the radio telescopes on the planet Earth is less than the energy of a single snowflake striking the ground.”*

― Carl Sagan, [Cosmos](https://en.wikipedia.org/wiki/Cosmos_(Sagan_book))

**Tags:** observational-astronomy, radio-astronomy, radio-telescope

> **Comments:**
> **username_1**: Do you mean the assertion is true or he made it?  

---

## 2 answers

### Answer by username_2 on 2021-09-25. Score: 5

Below are some strengths of some radio sources. Let's choose 1000 Jy and 100 MHz bandwidth, a modest 1000 m^2 single dish and 8 hour observation.

$$1000 \times 10^{-26} \ \text{W} \text{m}^{-2} \text{Hz}^{-1} \times 1000 \ \text{m}^2 \times 10^8 \ \text{Hz} = 10^{-12} \text{W}$$

and

$$10^{-12} \text{W} \times 28800 \text{sec} = 3 \times 10^{-8} \text{J}$$

1000 of those 30 m dishes for ten years:

$$3 \times 10^{-8} \text{J} \times 1000 \times 10 \times 365 \times 24/8 = 0.3 \ \text{Joules!}$$

**On the surface the quoted sentence seems to be borderline.**

Of course astronomers would not point every radio telescope dish at the strongest sources continuously for a decade.

Had they been instead spending most of the time listening to weak sources (which is exactly what is going to eat up most of the observing time by necessity) then

### it's very possible that when considering the energy collected from the *actual observed targets up until 1980* that this number is correct!

It may be true that the total received power over the full field of view of all telescopes including the CMB could be a lot larger, I'm going to cut Dr. Sagan some slack and suggest that by "received" he meant "listened to".

I will defer to other answers with the estimate of a few millijoules for the snowflake.

---

### Brightest of the brightest

This is from [Important Celestial Radio Sources Whitham D. Reeve](https://reeve.com/Documents/Articles%20Papers/Reeve_CelestialRadioSources.pdf)

**Here are the top sources in the list that also appear in the map, the list itself is much longer**

| Object Name | RA (hh mm ss) | Dec (dd mm ss) | Epoch | Flux Density (Jy) | Frequency (MHz) | Other Name |
| --- | --- | --- | --- | --- | --- | --- |
| 3C 461 | 23 23 24 | 58 48 54 | 2000 | 2477 | 1,420 | SNR-Cassiopeia A |
| CTA 59 | 13 22 28 | -42 46 00 | 1950 | 2010 | 960 | Cent A NGC5128 |
| CTB 42 | 17 42 09 | -28 50 00 | 1950 | 1800 | 960 | Sag A Galactic Nuccleus |
| 3C 405 | 19 59 28 | 40 44 02 | 2000 | 1495 | 1,420 | D |
| 3C 144 | 05 34 32 | 22 00 52 | 2000 | 875 | 1,420 | SNR-Crab Nebula |
| 3C 400 | 19 23 42 | 14 30 33 | 2000 | 576 | 1,420 |  |
| 3C 145 | 05 35 17 | -05 23 28 | 2000 | 520 | 1,420 | Emission Nebula-OrionA |
| 3C 274 | 12 30 49 | 12 23 28 | 2000 | 198 | 1,420 | Elliptical Galaxy-M87 |
| 3C 392 | 18 56 06 | 01 18 00 | 2000 | 171 | 1,420 | SNR |
| NRAO 5690 | 18 35 00 | -07 20 00 | 2000 | 90 | 1,420 |  |
| 3C 390.2 | 18 47 58 | -01 56 43 | 2000 | 80 | 1,420 |  |
| 3C 403.2 | 19 54 12 | 32 54 00 | 2000 | 75 | 1,420 |  |
| 3C 147.1 | 05 41 43 | -01 54 17 | 2000 | 65 | 1,420 | Emission Nebula-OrionB |
| 3C 353 | 17 20 28 | -00 58 47 | 2000 | 57 | 1,420 | D Galaxy |
| NRAO 6210 | 20 01 42 | 33 17 00 | 2000 | 55 | 1,420 |  |
| 3C 387 | 18 41 00 | -05 16 00 | 2000 | 51 | 1,420 |  |
| 3C 123 | 04 37 04 | 29 40 14 | 2000 | 47 | 1,420 | Galaxy |
| NRAO 5980 | 19 10 19 | 09 04 07 | 2000 | 47 | 1,420 |  |
| 3C 273 | 12 29 07 | 02 03 09 | 2000 | 46 | 1,420 | Quasar |
| NRAO 6500 | 21 12 21 | 52 28 58 | 2000 | 46 | 1,420 |  |
| 3C 348 | 16 51 08 | 04 59 34 | 2000 45 | 1,420 | D | Galaxy |
| 3C 10 | 00 25 13 | 64 08 42 | 2000 | 44 | 1,420 | SNR-Tycho's Supernova |
| 3C 218 | 09 18 06 | -12 05 44 | 2000 | 43 | 1,420 | D Galaxy |
| 3C 139.1 | 05 22 25 | 33 29 55 | 2000 | 40 | 1,420 | Emission Nebula |

[![This Celestial Radio Map is a composite of four individual quadrant maps from the referenced source (see upper-left corner)](https://i.sstatic.net/TpYE5.jpg)](https://i.sstatic.net/TpYE5.jpg)

> This Celestial Radio Map is a composite of four individual quadrant maps from the referenced source (see upper-left corner). Annotations show the approximate locations of sources with flux density ≥ 40 Jy. The S-shaped region where the contour lines are close together is the region around the Milky Way galactic equator. The contour lines represent lines of constant noise temperature as measured at 408 MHz. However, note that the flux density annotations are mostly at 1420 MHz with exceptions noted in the table. The ecliptic is indicated by a dashed line. The ecliptic is the path the Sun follows in the sky over a period of one year as viewed on Earth.

---

* <https://www.mpifr-bonn.mpg.de/1041051/Porcas_Intro_Radio.pdf>
* <https://reeve.com/Documents/Articles%20Papers/Reeve_CelestialRadioSources.pdf>
* [Fundamentals of Radio Astronomy; Joachim Köppen Strasbourg 2010](https://web.archive.org/web/20130516042600/http://astro.u-strasbg.fr/%7Ekoppen/10GHz/basics.html)

[![typical flux vs frequency for various astronomical sources: Fundamentals of Radio Astronomy; Joachim Köppen Strasbourg 2010](https://i.sstatic.net/YGzXo.gif)](https://i.sstatic.net/YGzXo.gif)


---

### Answer by username_3 on 2021-09-23. Score: 4

Radio waves (approximately $\lambda=1\rm\,m$[[1]](https://en.wikipedia.org/wiki/Five-hundred-meter_Aperture_Spherical_Telescope#:%7E:text=0.10%C2%A0m%20(3.0%C2%A0GHz)%E2%80%934.3%C2%A0m%20(70%C2%A0MHz))) are very weak, about $E=\frac{hc}{\lambda}=\frac{6.63\cdot10^{-34}\cdot 3\cdot 10^8}{1}\rm\,J\approx2\cdot 10^{-25}\rm\,J$ every photon.

An $1\rm\,mg=1\cdot10^{-6}\rm\,kg$[[2]](https://hypertextbook.com/facts/2001/JudyMoy.shtml) snowflake falling at $0.7\rm\,\frac{m}{s}$[[3]](https://www.metoffice.gov.uk/weather/learn-about/weather/types-of-weather/snow/10-facts-about-snow) has $$K=\frac{mv^2}{2}=\frac{1\cdot10^{-6}\cdot 0.7^2}{2}\rm\,J\approx2.5\cdot10^{-7}\rm\,J$$ of kinetic energy.

That is equivalent to $10^{18}$ photons' energy. I think we can say that's close to the amount of photons collected by us by the time Carl said this.

This shows that Carl Sagan knew his numbers.

***Ps.** There are over 100 radio telescopes now, but this quote comes from 1980,
back then a low number of radio telescopes existed and they used weren't very powerful. That's why the number of photons are reasonable.*

> **Comments:**
> **username_4**: @WalidSiddik No problem. You messed up with the grams and kilograms regarding kinetic energy.  
> **username_5**: @WalidSiddik How did you estimate the amount of photons collected?  

---

