<p><strong>Density, Pressure, and Temperature</strong><br/>
For all of the entries in the table below (with the exception of Neptune's temperature) I have read the corresponding values off of figures in from the references.  Given the modeling uncertainties I don't think there's much value in going beyond 1 or 2 significant figures.</p>
<p>For Neptune's temperature I used equation 5 from <a href="https://www.researchgate.net/publication/231059682_Interior_Models_of_Uranus_and_Neptune" rel="nofollow noreferrer">Interior models of Uranus and Neptune</a>:
<span class="math-container">$$T = C\rho^\gamma$$</span>
where <span class="math-container">$T$</span> is temperature, <span class="math-container">$\rho$</span> is density, and <span class="math-container">$C$</span> and <span class="math-container">$\gamma$</span> are model constants.  Using the question specified density of 1 g/cm<sup>2</sup> and the model defined value of <span class="math-container">$\gamma=0.5$</span> we can solve for <span class="math-container">$C$</span> given a known pressure / temperature pair and then compute the corresponding temperature at the desire pressure.</p>
<p>For Neptune, the paper assumes, for the 1-bar pressure level a density of <span class="math-container">$\rho = 4.38\times 10^{-4} g/cm^{-3}$</span> and a temperature <span class="math-container">$T=75K$</span>.  Substituting into the model and solving for <span class="math-container">$C$</span> (I'm ignoring units for now as they get goofy with this model):
<span class="math-container">$$75 = C\sqrt{4.38\times 10^{-4}}$$</span>
<span class="math-container">$$C\approx3584$$</span></p>
<p>Now using this for a density of <span class="math-container">$\rho = 1 g/cm^{-3}$</span>:
<span class="math-container">$$T=3584\sqrt{1}=3584$$</span>
I will round this number to two significant figures in the table (3600 K).</p>
<div class="s-table-container">
<table class="s-table">
<thead>
<tr>
<th style="text-align: left;">Planet</th>
<th style="text-align: right;">1 g/cm<sup>2</sup> Depth (km)</th>
<th style="text-align: right;">Pressure<sup>*</sup> (MBar)</th>
<th style="text-align: right;">Temperature<sup>*</sup> (K)</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align: left;">Jupiter</td>
<td style="text-align: right;">15,500</td>
<td style="text-align: right;">2</td>
<td style="text-align: right;">6,500</td>
</tr>
<tr>
<td style="text-align: left;">Saturn</td>
<td style="text-align: right;">23,900</td>
<td style="text-align: right;">2</td>
<td style="text-align: right;">5,000</td>
</tr>
<tr>
<td style="text-align: left;">Uranus</td>
<td style="text-align: right;">6,100</td>
<td style="text-align: right;">0.5</td>
<td style="text-align: right;">4,800</td>
</tr>
<tr>
<td style="text-align: left;">Neptune</td>
<td style="text-align: right;">4,700</td>
<td style="text-align: right;">0.4</td>
<td style="text-align: right;">3,600</td>
</tr>
</tbody>
</table>
</div>
<p>*-At the 1 g/cm<sup>2</sup> depth</p>
<p><strong>Density Profiles</strong><br/>
To address the question about the density in the lower atmosphere I am including plots from the references here.</p>
<p><em>Jupiter</em> (Figure from <a href="https://arxiv.org/abs/1307.3094" rel="nofollow noreferrer">Structures of the planets Jupiter and Saturn</a>)<br/>
<a href="https://i.sstatic.net/Y0k6Km.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/Y0k6Km.png" alt="Jupiter Density Profile" /></a><br/></p>
<p><em>Saturn</em> (Figure from <a href="https://arxiv.org/abs/1307.3094" rel="nofollow noreferrer">Structures of the planets Jupiter and Saturn</a>)<br/>
<a href="https://i.sstatic.net/qMKclm.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/qMKclm.png" alt="Saturn Density Profile" /></a><br/></p>
<p><em>Uranus and Neptune</em> (Figure from <a href="https://www.researchgate.net/publication/231059682_Interior_Models_of_Uranus_and_Neptune" rel="nofollow noreferrer">Interior models of Uranus and Neptune</a>)<br/>
<a href="https://i.sstatic.net/fwBQhm.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/fwBQhm.png" alt="Uranus and Neptune Density Profiles" /></a><br/></p>
<p><strong>References</strong><br/></p>
<ul>
<li>Kerley, Gerald I. &quot;<a href="https://arxiv.org/abs/1307.3094" rel="nofollow noreferrer">Structures of the planets Jupiter and Saturn</a>.&quot; arXiv preprint arXiv:1307.3094 (2013).</li>
<li>Helled, Ravit, John D. Anderson, Morris Podolak, and Gerald Schubert. &quot;<a href="https://www.researchgate.net/publication/231059682_Interior_Models_of_Uranus_and_Neptune" rel="nofollow noreferrer">Interior models of Uranus and Neptune</a>.&quot; The Astrophysical Journal 726, no. 1 (2010): 15.</li>
<li>Nettelmann, Nadine, K. Wang, Jonathan J. Fortney, Sebastien Hamel, S. Yellamilli, M. Bethkenhagen, and R. Redmer. &quot;<a href="https://www.osti.gov/pages/servlets/purl/1497277" rel="nofollow noreferrer">Uranus evolution models with simple thermal boundary layers</a>.&quot; Icarus 275 (2016): 107-116.</li>
</ul>

CC BY-SA 4.0
2022-02-13T20:28:46.023Z
2022-02-13T20:28:46.023Z
GrapefruitIsAwesome
<p>At what depth in the atmospheres of the gas giants does the density of their atmospheres equal 1 gram per cubic centimeter? What is the pressure and temperature at these depths?  Are the radiations levels congenial to human life at these depths?</p>
<p>Wikipedia's <a href="https://en.wikipedia.org/wiki/Saturn#Physical_characteristics" rel="nofollow noreferrer">Saturn; Physical characteristics</a> says</p>
<blockquote>
<p>Finally, the lower layers [of the Saturnian atmosphere], where pressures are between 10–20 bar and temperatures are 270–330 K, contains a region of water droplets with ammonia in aqueous solution.</p>
</blockquote>
<p>What is the density of the atmosphere in the lower atmosphere?  The lower atmosphere of Neptune is 275K at 50 bar.</p>

<gas-giants><saturn><neptune><planetary-science><uranus>
Qualities of gas giant atmospheres at a density of 1 gram per cubic centimeter
user141802
# Qualities of gas giant atmospheres at a density of 1 gram per cubic centimeter

(Asked by: username_0 on 2020-10-03)

At what depth in the atmospheres of the gas giants does the density of their atmospheres equal 1 gram per cubic centimeter? What is the pressure and temperature at these depths? Are the radiations levels congenial to human life at these depths?

Wikipedia's [Saturn; Physical characteristics](https://en.wikipedia.org/wiki/Saturn#Physical_characteristics) says

> Finally, the lower layers [of the Saturnian atmosphere], where pressures are between 10–20 bar and temperatures are 270–330 K, contains a region of water droplets with ammonia in aqueous solution.

What is the density of the atmosphere in the lower atmosphere? The lower atmosphere of Neptune is 275K at 50 bar.

**Tags:** gas-giants, saturn, neptune, planetary-science, uranus

---

## 1 answers

### Answer by username_1 on 2022-02-13. Score: 2

**Density, Pressure, and Temperature**  
For all of the entries in the table below (with the exception of Neptune's temperature) I have read the corresponding values off of figures in from the references. Given the modeling uncertainties I don't think there's much value in going beyond 1 or 2 significant figures.

For Neptune's temperature I used equation 5 from [Interior models of Uranus and Neptune](https://www.researchgate.net/publication/231059682_Interior_Models_of_Uranus_and_Neptune):
$$T = C\rho^\gamma$$
where $T$ is temperature, $\rho$ is density, and $C$ and $\gamma$ are model constants. Using the question specified density of 1 g/cm2 and the model defined value of $\gamma=0.5$ we can solve for $C$ given a known pressure / temperature pair and then compute the corresponding temperature at the desire pressure.

For Neptune, the paper assumes, for the 1-bar pressure level a density of $\rho = 4.38\times 10^{-4} g/cm^{-3}$ and a temperature $T=75K$. Substituting into the model and solving for $C$ (I'm ignoring units for now as they get goofy with this model):
$$75 = C\sqrt{4.38\times 10^{-4}}$$
$$C\approx3584$$

Now using this for a density of $\rho = 1 g/cm^{-3}$:
$$T=3584\sqrt{1}=3584$$
I will round this number to two significant figures in the table (3600 K).

| Planet | 1 g/cm2 Depth (km) | Pressure\* (MBar) | Temperature\* (K) |
| --- | --- | --- | --- |
| Jupiter | 15,500 | 2 | 6,500 |
| Saturn | 23,900 | 2 | 5,000 |
| Uranus | 6,100 | 0.5 | 4,800 |
| Neptune | 4,700 | 0.4 | 3,600 |

\*-At the 1 g/cm2 depth

**Density Profiles**  
To address the question about the density in the lower atmosphere I am including plots from the references here.

*Jupiter* (Figure from [Structures of the planets Jupiter and Saturn](https://arxiv.org/abs/1307.3094))  
[![Jupiter Density Profile](https://i.sstatic.net/Y0k6Km.png)](https://i.sstatic.net/Y0k6Km.png)

*Saturn* (Figure from [Structures of the planets Jupiter and Saturn](https://arxiv.org/abs/1307.3094))  
[![Saturn Density Profile](https://i.sstatic.net/qMKclm.png)](https://i.sstatic.net/qMKclm.png)

*Uranus and Neptune* (Figure from [Interior models of Uranus and Neptune](https://www.researchgate.net/publication/231059682_Interior_Models_of_Uranus_and_Neptune))  
[![Uranus and Neptune Density Profiles](https://i.sstatic.net/fwBQhm.png)](https://i.sstatic.net/fwBQhm.png)

**References**

* Kerley, Gerald I. "[Structures of the planets Jupiter and Saturn](https://arxiv.org/abs/1307.3094)." arXiv preprint arXiv:1307.3094 (2013).
* Helled, Ravit, John D. Anderson, Morris Podolak, and Gerald Schubert. "[Interior models of Uranus and Neptune](https://www.researchgate.net/publication/231059682_Interior_Models_of_Uranus_and_Neptune)." The Astrophysical Journal 726, no. 1 (2010): 15.
* Nettelmann, Nadine, K. Wang, Jonathan J. Fortney, Sebastien Hamel, S. Yellamilli, M. Bethkenhagen, and R. Redmer. "[Uranus evolution models with simple thermal boundary layers](https://www.osti.gov/pages/servlets/purl/1497277)." Icarus 275 (2016): 107-116.


---

