<p>As earlier answers indicate, <a href="https://astronomy.stackexchange.com/questions/37161/will-jupiter-eventually-stop-shrinking">Jupiter will slowly shrink until it is some 10-20% smaller</a> with <a href="https://astronomy.stackexchange.com/questions/40254/life-cycle-of-a-gas-planet">elements slowly settling depending on density and solubility</a>.</p>
<p>One can calculate a rough Kelvin timescale for the ratio between binding energy and the blackbody power of the surface to estimate how quickly it cools down (this number will be nudged by the above considerations a bit, so it is an order of magnitude estimate):
<span class="math-container">$$\tau_{Kelvin}=\frac{3GM^2}{20\pi\sigma R^3 T^4}.$$</span>
For Jupiter this timescale is 54 billion years.</p>
<p>As the universe cools eventually it becomes a ball of layered solid degenerate matter, with a frozen hydrogen crust. This will take longer than <span class="math-container">$\tau_{Kelvin}$</span> due to various mild heating processes like crystallization heating, tidal heating from the moons, possibly dark matter annihilation, and other low-energy processes that keep objects warmer than the CMB.</p>

CC BY-SA 4.0
2021-02-20T21:53:28.453Z
A degenerate object does not cool on a KH timescale. Not even as an order of magnitude estimate.
ProfRob
CC BY-SA 4.0
2021-02-20T22:07:16.470Z
Hmm. Working that out though (the ratio of thermal energy to current luminosity), I get a 20 billion year timescale, but I think that is coincidence.
ProfRob
CC BY-SA 4.0
2021-02-20T22:52:33.380Z
It is a coincidence. The thermal energy is an order of magnitude smaller than the binding energy and the blackbody flux is about 5 times the actual intrinsic luminosity, probably because the planet is not a blackbody and also receives twice as much radiation from the Sun as its intrinsic luminosity.
ProfRob
CC BY-SA 4.0
2021-02-21T01:03:51.697Z
@ProfRob - Interesting. Could we add the calculations to the answer to describe the longer-term evolution? It feels like this is a pocket version of the Mestel cooling of white dwarfs.
Anders Sandberg
CC BY-SA 4.0
2021-02-21T08:20:33.097Z
It will be but I don't know how to correctly estimate the luminosity of Jupiter in terms of its internal temperature and the fact that it receives a very large heat input from the Sun changes things (presumably slowing it down).
ProfRob
CC BY-SA 4.0
2021-02-21T12:05:53.623Z
@ProfRob - On the timescales where it is properly degenerate the sun will no longer give a heat input.
Anders Sandberg
CC BY-SA 4.0
2021-02-22T00:07:11.433Z
It's degenerate now. Metallic hydrogen does not exist in non-degenerate conditions.
ProfRob
CC BY-SA 4.0
2021-02-19T09:16:07.157Z
2021-02-19T09:16:07.157Z
Anders Sandberg
<p>I heard Jupiter is dying like getting smaller. For example, from Guillot et al. 2004 <a href="https://lasp.colorado.edu/home/mop/files/2015/08/jupiter_ch3-1.pdf" rel="nofollow noreferrer">3: The Interior of Jupiter</a> (also <a href="https://authors.library.caltech.edu/39188/" rel="nofollow noreferrer">here</a>):</p>
<blockquote>
<p>(Jupiter)... is still contracting at the rate of ~3 cm per year while its interior cools by ~1 K per million year.</p>
</blockquote>
<p>When will it completely die, how much smaller will it be then, and what will it look like?</p>

CC BY-SA 4.0
2021-02-18T23:25:01.390Z
"I heard.." Where did you hear this?
James K
CC BY-SA 4.0
2021-02-18T23:54:38.183Z
Tomorrow. Because as God of all Gods he looks with dismay at the blasphemous people. [Citation needed].
planetmaker
CC BY-SA 4.0
2021-02-19T00:03:16.840Z
"*I heard that...*" questions are often closed when they don't include a reference to the source from where it was heard, like a book or a video or a website. There is a Wikipedia article for [Jupiter](https://en.wikipedia.org/wiki/Jupiter), perhaps you can find something in there to both support something like this, and from which you can ask a more specific question?
uhoh
CC BY-SA 4.0
2021-02-19T00:11:37.650Z
**update:** I couldn't find anything in Wikipedia, so I've added a supporting reference for your premise. I think this is an interesting question!
uhoh
CC BY-SA 4.0
2021-02-19T00:20:00.080Z
Jupiter is still sucking in comets and asteroids and such.  I guess it must be ejecting matter faster than it's absorbing it.  Losses to solar radiation almost certainly have to increase as the Sun goes Red Giant, but perhaps they will lessen to almost nothing when it becomes a white dwarf?
Connor Garcia
CC BY-SA 4.0
2021-02-19T00:42:39.023Z
Hard to provide an answer. It will continue to shrink at an ever decreasing rate.  I guess there is an asymptotic cold radius that it will reach infinitely far into the future. It is about 10-20% smaller than it is now.
ProfRob
<planet><jupiter><planetary-science>
What will a future cold and "dead" Jupiter look like?
click on my posts please
# What will a future cold and "dead" Jupiter look like?

(Asked by: username_0 on 2021-02-18)

I heard Jupiter is dying like getting smaller. For example, from Guillot et al. 2004 [3: The Interior of Jupiter](https://lasp.colorado.edu/home/mop/files/2015/08/jupiter_ch3-1.pdf) (also [here](https://authors.library.caltech.edu/39188/)):

> (Jupiter)... is still contracting at the rate of ~3 cm per year while its interior cools by ~1 K per million year.

When will it completely die, how much smaller will it be then, and what will it look like?

**Tags:** planet, jupiter, planetary-science
> **Comments:**
> **username_1**: "I heard.." Where did you hear this?  
> **username_2**: Tomorrow. Because as God of all Gods he looks with dismay at the blasphemous people. [Citation needed].  
> **username_3**: "*I heard that...*" questions are often closed when they don't include a reference to the source from where it was heard, like a book or a video or a website. There is a Wikipedia article for [Jupiter](https://en.wikipedia.org/wiki/Jupiter), perhaps you can find something in there to both support something like this, and from which you can ask a more specific question?  
> **username_3**: **update:** I couldn't find anything in Wikipedia, so I've added a supporting reference for your premise. I think this is an interesting question!  
> **username_4**: Jupiter is still sucking in comets and asteroids and such.  I guess it must be ejecting matter faster than it's absorbing it.  Losses to solar radiation almost certainly have to increase as the Sun goes Red Giant, but perhaps they will lessen to almost nothing when it becomes a white dwarf?  
> **username_5**: Hard to provide an answer. It will continue to shrink at an ever decreasing rate.  I guess there is an asymptotic cold radius that it will reach infinitely far into the future. It is about 10-20% smaller than it is now.  

---

## 1 answers

### Answer by username_6 on 2021-02-19. Score: 1

As earlier answers indicate, [Jupiter will slowly shrink until it is some 10-20% smaller](https://astronomy.stackexchange.com/questions/37161/will-jupiter-eventually-stop-shrinking) with [elements slowly settling depending on density and solubility](https://astronomy.stackexchange.com/questions/40254/life-cycle-of-a-gas-planet).

One can calculate a rough Kelvin timescale for the ratio between binding energy and the blackbody power of the surface to estimate how quickly it cools down (this number will be nudged by the above considerations a bit, so it is an order of magnitude estimate):
$$\tau\_{Kelvin}=\frac{3GM^2}{20\pi\sigma R^3 T^4}.$$
For Jupiter this timescale is 54 billion years.

As the universe cools eventually it becomes a ball of layered solid degenerate matter, with a frozen hydrogen crust. This will take longer than $\tau\_{Kelvin}$ due to various mild heating processes like crystallization heating, tidal heating from the moons, possibly dark matter annihilation, and other low-energy processes that keep objects warmer than the CMB.

> **Comments:**
> **username_5**: A degenerate object does not cool on a KH timescale. Not even as an order of magnitude estimate.  
> **username_5**: Hmm. Working that out though (the ratio of thermal energy to current luminosity), I get a 20 billion year timescale, but I think that is coincidence.  
> **username_5**: It is a coincidence. The thermal energy is an order of magnitude smaller than the binding energy and the blackbody flux is about 5 times the actual intrinsic luminosity, probably because the planet is not a blackbody and also receives twice as much radiation from the Sun as its intrinsic luminosity.  
> **username_6**: @ProfRob - Interesting. Could we add the calculations to the answer to describe the longer-term evolution? It feels like this is a pocket version of the Mestel cooling of white dwarfs.  
> **username_5**: It will be but I don't know how to correctly estimate the luminosity of Jupiter in terms of its internal temperature and the fact that it receives a very large heat input from the Sun changes things (presumably slowing it down).  
> **username_6**: @ProfRob - On the timescales where it is properly degenerate the sun will no longer give a heat input.  
> **username_5**: It's degenerate now. Metallic hydrogen does not exist in non-degenerate conditions.  

---

