<p>Such tunnels might be possible for objects up to a few hundred kilometres in size.  Larger objects could be tunnelled if the tunnels are lined with high strength materials.</p>
<p>Assuming the centre of the object is cool enough not to melt the tunnel lining, then the tunnel will be limited by the <a href="https://en.wikipedia.org/wiki/Compressive_strength" rel="nofollow noreferrer">compressive strength</a>, <span class="math-container">$\sigma_c$</span>, of the tunnel walls.
Experience from deep mines tells us that <a href="https://doi.org/10.1007/s00603-019-01799-4" rel="nofollow noreferrer" title="Deep Mining: A Rock Engineering Challenge., Wagner, H.  Rock Mech Rock Eng 52, 1417–1446 (2019).">the maximum pressure a tunnel can sustain</a> is something like <span class="math-container">$P_{max}\sim 0.4\,\sigma_c$</span>.</p>
<p>To get a crude estimate, let's assume the objects are spherical and have uniform density throughout. (Note: This will likely overestimate the maximum tunnelable size, since larger objects often have a dense core. For example, assuming a uniform density Earth underestimates its central pressure <a href="https://physics.stackexchange.com/q/458751/145491">by a factor of two</a>.)</p>
<p>The gravitational <a href="https://physics.stackexchange.com/q/458751/145491">pressure at the centre</a> of a sphere with uniform density <span class="math-container">$\rho$</span> and radius <span class="math-container">$R$</span> is</p>
<p><span class="math-container">$$P=\frac{2}{3}\pi G\rho^2R^2$$</span></p>
<p>so a reasonable guess for the maximum radius of an object that could be tunnelled through is</p>
<p><span class="math-container">$$R_{max}\sim \frac{1}{\rho}\sqrt{\frac{3P_{max}}{2 \pi G}}\sim\frac{1}{\rho}\sqrt{\frac{\sigma_c}{2 \pi G}}$$</span></p>
<p>Here are some example estimates of the maximum tunnelable radius for some different simple object compositions.
Also shown is the maximum radius if the tunnels are lined with a <a href="https://precision-ceramics.com/materials/properties/compressive-strength/" rel="nofollow noreferrer">hard ceramic</a> such as alumina (<span class="math-container">$\sigma_c \sim 3000\,\mathrm{MPa}$</span>).</p>
<div class="s-table-container">
<table class="s-table">
<thead>
<tr>
<th style="text-align: left;">Object       <br> </th>
<th style="text-align: center;">Density<br> </th>
<th style="text-align: center;"><span class="math-container">$\mathbf{R_{max}}$</span><br>(unlined)</th>
<th style="text-align: center;"><span class="math-container">$\mathbf{R_{max}}$</span><br> (lined)</th>
<th style="text-align: left;">Notes<br> </th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align: left;"></td>
<td style="text-align: center;">(<span class="math-container">$\mathrm{g/cm^3}$</span>)</td>
<td style="text-align: center;">(<span class="math-container">$\mathrm{km}$</span>)</td>
<td style="text-align: center;">(<span class="math-container">$\mathrm{km}$</span>)</td>
<td style="text-align: left;"></td>
</tr>
<tr>
<td style="text-align: left;">Pure ice object</td>
<td style="text-align: center;">1</td>
<td style="text-align: center;">350</td>
<td style="text-align: center;">2700</td>
<td style="text-align: left;">The compressive strength of <a href="https://doi.org/10.1016/j.icarus.2020.113940" rel="nofollow noreferrer" title="A study of the compressive mechanical properties of defect-free, porous and sintered water-ice at low and high strain rates, Ryan S. Potter, et al., Icarus, Volume 351, 2020, 113940, ISSN 0019-1035"><strong>high density ice</strong></a>  at a temperature of 173K (<a href="https://phys.org/news/2015-08-asteroid-belt.html" rel="nofollow noreferrer">typical of the outer asteroid belt</a>) is <span class="math-container">$\sim$</span> 50 MPa.</td>
</tr>
<tr>
<td style="text-align: left;">Realistic icy object (e.g. similar to <a href="https://en.wikipedia.org/wiki/Ceres_(dwarf_planet)" rel="nofollow noreferrer">Ceres</a>)</td>
<td style="text-align: center;">2.2</td>
<td style="text-align: center;">160</td>
<td style="text-align: center;">1200</td>
<td style="text-align: left;">Ceres actual radius is <span class="math-container">$\sim$</span> 470 km, and it appears to be <a href="https://eos.org/articles/new-findings-suggest-dwarf-planet-ceres-is-geologically-active" rel="nofollow noreferrer">geologically active</a>, which might make even lined tunnelling difficult.</td>
</tr>
<tr>
<td style="text-align: left;">Iron-Nickel asteroid (e.g. <a href="https://en.wikipedia.org/wiki/4_Vesta" rel="nofollow noreferrer">Vesta</a> core)</td>
<td style="text-align: center;">8</td>
<td style="text-align: center;">120</td>
<td style="text-align: center;">330</td>
<td style="text-align: left;">Assumed similar to iron-nickel meteorites that have compressive strengths as high as <a href="https://doi.org/10.1016/j.pss.2018.11.003" rel="nofollow noreferrer" title="The physical properties of meteorites, D. Ostrowski, K. Bryson, Planetary and Space Science, Volume 165, 2019, Pages 148-178, ISSN 0032-0633.">400 MPa</a></td>
</tr>
<tr>
<td style="text-align: left;">Hard rock asteroid</td>
<td style="text-align: center;">3.5</td>
<td style="text-align: center;">170</td>
<td style="text-align: center;">760</td>
<td style="text-align: left;">Assumed <span class="math-container">$\sigma_c \sim$</span> 150 MPa (<a href="https://doi.org/10.1007/s00603-019-01799-4" rel="nofollow noreferrer" title="Deep Mining: A Rock Engineering Challenge., Wagner, H.  Rock Mech Rock Eng 52, 1417–1446 (2019).">typical of hard rock</a>)</td>
</tr>
</tbody>
</table>
</div>
<p>Notes:</p>
<ul>
<li>Many smaller asteroids are <a href="https://en.wikipedia.org/wiki/Rubble_pile" rel="nofollow noreferrer">rubble piles</a>. Tunnelling through them would be like digging through sand, so a lining would be essential.  Even larger objects may not be completely consolidated.</li>
<li>The above maximum (unlined) tunnelable sizes are comparable to the <a href="https://astronomy.stackexchange.com/q/2092/47727">minimum sizes for celestial objects to naturally become spherical</a>.  This is unsurprising since if gravitational forces are strong enough to make an object round, they are also strong enough to collapse any central voids. The largest tunnelable object might be one that is initially hot and malleable when formed, but then cools down to higher compressive strength solid.</li>
</ul>

CC BY-SA 4.0
2023-04-17T18:39:19.673Z
2023-04-24T01:20:24.497Z
2023-04-24T01:20:24.497Z
David Bailey
<p>Old science fiction had lots of stories that involved people exploring the center of Earth, like for example <a href="https://en.wikipedia.org/wiki/Journey_to_the_Center_of_the_Earth" rel="nofollow noreferrer">Journey to the Center of the Earth</a>, by <a href="https://en.wikipedia.org/wiki/Jules_Verne" rel="nofollow noreferrer">Jules Verne</a>. As Earth sciences advanced, this sort of story fell out of favor, and today even sounds somewhat ludicrous, as now is well understood pressure and temperature increase fast as one descends into Earth, so it's unfeasible to dig and hold open large cavities anywhere near the core, much less survive for any period of time there. So, despite the fact Earth radius is close to 6400km, the deepest mine in the planet, <a href="https://en.wikipedia.org/wiki/Mponeng_Gold_Mine" rel="nofollow noreferrer">Mponeng Gold Mine</a>, goes only 4km under ground level, or 0.0625% of the distance required to reach the center of Earth. I don't know how deeper could it go, and if the limiting factor precluding greater depths is heat removal due to high temperatures or tunnel collapse due to overburden pressure, but I don't believe it can go much beyond current depth.</p>
<p>But if our planet is too large for this scenario, making it infeasible here, surely there is a lower threshold for mass and size making it actually possible. So I'd like to know, what's the maximum size for a planet/dwarf planet/asteroid, where would be possible in principle to dig tunnels all the way down to the core, or perhaps even to build some sort of &quot;corescrapper&quot;, an underground multi-floor building going from surface to the core? By tunnels I mean tunnels that people could actually pass through, using technology similar to what is used in current mines here on Earth. So just being drillable, like in a oil well, to the core, doesn't count.</p>
<p>If necessary, the putative celestial body can be assumed to have rocky composition, perhaps with a metallic core, and age similar to the current age of the solar system.</p>

CC BY-SA 4.0
2022-07-22T00:19:45.273Z
This would probably be more of an earth science question than an astronomy one.
Fred
CC BY-SA 4.0
2022-07-22T00:28:09.043Z
With reference to your question, if the celestial body has a hot core or even a hot mantle, no tunnel will be able to get anywhere near the core because of high temperature. If the body has a cold core & mantle then the limiting factor with be geomechanical stresses. Overburden pressure may not be the only geomechanical stresses; at depth sometimes the horizontal stresses can be higher than the vertical stresses. The other factor will be the cost of developing the tunnels.
Fred
CC BY-SA 4.0
2022-07-22T01:33:00.070Z
Please check the sister site Earth science.SE or SpaceEx.SE
Nilay Ghosh
CC BY-SA 4.0
2022-07-22T09:09:28.400Z
I don't think [Earthscience.se]  would accept this, as its not about the Earth.  It is on topic at [space.se] but it could also fit here.  It might well go un-answered, simply because "nobody knows".
James K
CC BY-SA 4.0
2022-07-22T10:44:37.030Z
Different but related: [How deep could a lunar mine go?](https://space.stackexchange.com/q/23445/12102)
uhoh
CC BY-SA 4.0
2022-07-23T10:03:02.270Z
@JamesK: this is definitely a planetary sciences question & despite its name SE Earth Science does accept some planetary science questions, but as you state it can can also fit in with SE Space Exploration. SE Earth Science has a `planetary-sciences` with 133 questions associated with it. It's sometimes a case of trying one's luck on one & if it get knocked back on one site, maybe try the other.
Fred
CC BY-SA 4.0
2022-07-24T21:51:50.190Z
This is an engineering problem.
ProfRob
CC BY-SA 4.0
2022-07-25T03:27:26.860Z
Are we talking about a solar system object or an exoplanet around an 11 billion year old system?  The composition and temperature profile would need to be specified. How long has it been cooling?  Planets have different compositions, different degrees of differentiation, and so different structural strengths.   Probably you need to be discussing an asteroid sized object, not a planet.
eshaya
CC BY-SA 4.0
2022-07-25T04:01:43.557Z
@uhoh: re: How deep could a lunar mine go, I don't dispute the answers there given for the theoretical/technical. depths, based on geothermal or geomechanical criteria. In terms of engineering limitations the depths will be much less. Part of the problem will be what equipment would be available, energy availability, access method. Not having a atmosphere on the Moon presents its own problems. If the question were to asked about Mars, its weak CO2 presents other issues compared to Earth's atmosphere. This could easily be the subject of a doctoral thesis - "how long is a piece of string?".
Fred
<planet><earth><planetary-science><size><core>
What is the maximum size for a solid celestial body such that it still can be tunneled down to the core?
ksousa
# What is the maximum size for a solid celestial body such that it still can be tunneled down to the core?

(Asked by: username_0 on 2022-07-21)

Old science fiction had lots of stories that involved people exploring the center of Earth, like for example [Journey to the Center of the Earth](https://en.wikipedia.org/wiki/Journey_to_the_Center_of_the_Earth), by [Jules Verne](https://en.wikipedia.org/wiki/Jules_Verne). As Earth sciences advanced, this sort of story fell out of favor, and today even sounds somewhat ludicrous, as now is well understood pressure and temperature increase fast as one descends into Earth, so it's unfeasible to dig and hold open large cavities anywhere near the core, much less survive for any period of time there. So, despite the fact Earth radius is close to 6400km, the deepest mine in the planet, [Mponeng Gold Mine](https://en.wikipedia.org/wiki/Mponeng_Gold_Mine), goes only 4km under ground level, or 0.0625% of the distance required to reach the center of Earth. I don't know how deeper could it go, and if the limiting factor precluding greater depths is heat removal due to high temperatures or tunnel collapse due to overburden pressure, but I don't believe it can go much beyond current depth.

But if our planet is too large for this scenario, making it infeasible here, surely there is a lower threshold for mass and size making it actually possible. So I'd like to know, what's the maximum size for a planet/dwarf planet/asteroid, where would be possible in principle to dig tunnels all the way down to the core, or perhaps even to build some sort of "corescrapper", an underground multi-floor building going from surface to the core? By tunnels I mean tunnels that people could actually pass through, using technology similar to what is used in current mines here on Earth. So just being drillable, like in a oil well, to the core, doesn't count.

If necessary, the putative celestial body can be assumed to have rocky composition, perhaps with a metallic core, and age similar to the current age of the solar system.

**Tags:** planet, earth, planetary-science, size, core

> **Comments:**
> **username_1**: This would probably be more of an earth science question than an astronomy one.  
> **username_1**: With reference to your question, if the celestial body has a hot core or even a hot mantle, no tunnel will be able to get anywhere near the core because of high temperature. If the body has a cold core & mantle then the limiting factor with be geomechanical stresses. Overburden pressure may not be the only geomechanical stresses; at depth sometimes the horizontal stresses can be higher than the vertical stresses. The other factor will be the cost of developing the tunnels.  
> **username_2**: Please check the sister site Earth science.SE or SpaceEx.SE  
> **username_3**: I don't think [Earthscience.se]  would accept this, as its not about the Earth.  It is on topic at [space.se] but it could also fit here.  It might well go un-answered, simply because "nobody knows".  
> **username_4**: Different but related: [How deep could a lunar mine go?](https://space.stackexchange.com/q/23445/12102)  
> **username_1**: @username_3: this is definitely a planetary sciences question & despite its name SE Earth Science does accept some planetary science questions, but as you state it can can also fit in with SE Space Exploration. SE Earth Science has a `planetary-sciences` with 133 questions associated with it. It's sometimes a case of trying one's luck on one & if it get knocked back on one site, maybe try the other.  
> **username_5**: This is an engineering problem.  
> **username_6**: Are we talking about a solar system object or an exoplanet around an 11 billion year old system?  The composition and temperature profile would need to be specified. How long has it been cooling?  Planets have different compositions, different degrees of differentiation, and so different structural strengths.   Probably you need to be discussing an asteroid sized object, not a planet.  
> **username_1**: @username_4: re: How deep could a lunar mine go, I don't dispute the answers there given for the theoretical/technical. depths, based on geothermal or geomechanical criteria. In terms of engineering limitations the depths will be much less. Part of the problem will be what equipment would be available, energy availability, access method. Not having a atmosphere on the Moon presents its own problems. If the question were to asked about Mars, its weak CO2 presents other issues compared to Earth's atmosphere. This could easily be the subject of a doctoral thesis - "how long is a piece of string?".  

---

## 1 answers

### Answer by username_7 on 2023-04-17. Score: 7 | Accepted answer

Such tunnels might be possible for objects up to a few hundred kilometres in size. Larger objects could be tunnelled if the tunnels are lined with high strength materials.

Assuming the centre of the object is cool enough not to melt the tunnel lining, then the tunnel will be limited by the [compressive strength](https://en.wikipedia.org/wiki/Compressive_strength), $\sigma\_c$, of the tunnel walls.
Experience from deep mines tells us that [the maximum pressure a tunnel can sustain](https://doi.org/10.1007/s00603-019-01799-4 "Deep Mining: A Rock Engineering Challenge., Wagner, H.  Rock Mech Rock Eng 52, 1417–1446 (2019).") is something like $P\_{max}\sim 0.4\,\sigma\_c$.

To get a crude estimate, let's assume the objects are spherical and have uniform density throughout. (Note: This will likely overestimate the maximum tunnelable size, since larger objects often have a dense core. For example, assuming a uniform density Earth underestimates its central pressure [by a factor of two](https://physics.stackexchange.com/q/458751/145491).)

The gravitational [pressure at the centre](https://physics.stackexchange.com/q/458751/145491) of a sphere with uniform density $\rho$ and radius $R$ is

$$P=\frac{2}{3}\pi G\rho^2R^2$$

so a reasonable guess for the maximum radius of an object that could be tunnelled through is

$$R\_{max}\sim \frac{1}{\rho}\sqrt{\frac{3P\_{max}}{2 \pi G}}\sim\frac{1}{\rho}\sqrt{\frac{\sigma\_c}{2 \pi G}}$$

Here are some example estimates of the maximum tunnelable radius for some different simple object compositions.
Also shown is the maximum radius if the tunnels are lined with a [hard ceramic](https://precision-ceramics.com/materials/properties/compressive-strength/) such as alumina ($\sigma\_c \sim 3000\,\mathrm{MPa}$).

| Object | Density | $\mathbf{R\_{max}}$ (unlined) | $\mathbf{R\_{max}}$  (lined) | Notes |
| --- | --- | --- | --- | --- |
|  | ($\mathrm{g/cm^3}$) | ($\mathrm{km}$) | ($\mathrm{km}$) |  |
| Pure ice object | 1 | 350 | 2700 | The compressive strength of [**high density ice**](https://doi.org/10.1016/j.icarus.2020.113940 "A study of the compressive mechanical properties of defect-free, porous and sintered water-ice at low and high strain rates, Ryan S. Potter, et al., Icarus, Volume 351, 2020, 113940, ISSN 0019-1035") at a temperature of 173K ([typical of the outer asteroid belt](https://phys.org/news/2015-08-asteroid-belt.html)) is $\sim$ 50 MPa. |
| Realistic icy object (e.g. similar to [Ceres](https://en.wikipedia.org/wiki/Ceres_(dwarf_planet))) | 2.2 | 160 | 1200 | Ceres actual radius is $\sim$ 470 km, and it appears to be [geologically active](https://eos.org/articles/new-findings-suggest-dwarf-planet-ceres-is-geologically-active), which might make even lined tunnelling difficult. |
| Iron-Nickel asteroid (e.g. [Vesta](https://en.wikipedia.org/wiki/4_Vesta) core) | 8 | 120 | 330 | Assumed similar to iron-nickel meteorites that have compressive strengths as high as [400 MPa](https://doi.org/10.1016/j.pss.2018.11.003 "The physical properties of meteorites, D. Ostrowski, K. Bryson, Planetary and Space Science, Volume 165, 2019, Pages 148-178, ISSN 0032-0633.") |
| Hard rock asteroid | 3.5 | 170 | 760 | Assumed $\sigma\_c \sim$ 150 MPa ([typical of hard rock](https://doi.org/10.1007/s00603-019-01799-4 "Deep Mining: A Rock Engineering Challenge., Wagner, H.  Rock Mech Rock Eng 52, 1417–1446 (2019).")) |

Notes:

* Many smaller asteroids are [rubble piles](https://en.wikipedia.org/wiki/Rubble_pile). Tunnelling through them would be like digging through sand, so a lining would be essential. Even larger objects may not be completely consolidated.
* The above maximum (unlined) tunnelable sizes are comparable to the [minimum sizes for celestial objects to naturally become spherical](https://astronomy.stackexchange.com/q/2092/47727). This is unsurprising since if gravitational forces are strong enough to make an object round, they are also strong enough to collapse any central voids. The largest tunnelable object might be one that is initially hot and malleable when formed, but then cools down to higher compressive strength solid.


---

