<p>Like the Sun, gas giant planets are <em>approximately</em> in hydrostatic equilibrium - a pressure <em>gradient</em> in their interiors balances the gravitational forces acting towards the centre.</p>
<p>However, there is a big difference between the Sun and a gas giant planet - both the Sun and planets are losing energy from their surfaces. In the Sun, this energy output is almost exclusively provided by nuclear reactions in its core - that is, the luminosity of the Sun equals the energy generation rate by nuclear reactions in its interior. This means that the Sun's interior temperature, structure and radius are stable on timescales for the nuclear energy generation rate to change (billions of years). In a gas giant planet there are no nuclear reactions and so the only source of heat is from the gas in its interior, ultimately heated by the release of gravitational potential as the planet contracts.</p>
<p>A complication is that the gas in the deep interior of a gas giant planet is so dense that it becomes electron-degenerate. This breaks the direct connection between temperature and pressure and means that as time goes on, a gas giant planet will cool-off at almost constant radius, because the electron-degenerate gas can maintain its pressure regardless of temperature.</p>
<p>Giant planets are more similar to contracting protostars - which also derive their luminosity from gravitational contraction. The difference is that a giant planet's interior becomes electron degenerate at a temperature much lower tahn required to start nuclear fusion.</p>
<p>Here is an example of a model for the time-evolution of the radii of Jupiter and Saturn (from <a href="https://iopscience.iop.org/article/10.1088/0004-637X/729/1/32" rel="noreferrer">Fortney at al. 2011</a>); the black and red curves are for different assumptions about the atmospheres and the vertical dotted line represents the present day.</p>
<p><a href="https://i.sstatic.net/tRf1o.jpg" rel="noreferrer"><img src="https://i.sstatic.net/tRf1o.jpg" alt="Radii of Jupier and Saturn" /></a></p>
<p>Thus, the answer to your question is that gas giant planets are more dynamic than (main sequence) stars. They are gradually contracting, but at a decreasing rate, in order to maintain hydrosttaic equilibrium as they lose heat from their surfaces.</p>

CC BY-SA 4.0
2022-07-21T15:35:59.147Z
The linked article is not Fortney+2011.
AtmosphericPrisonEscape
CC BY-SA 4.0
2022-07-21T16:10:08.717Z
@AtmosphericPrisonEscape fixed
ProfRob
CC BY-SA 4.0
2022-07-21T17:03:15.153Z
On a related note, stars like the Sun are in this “quasi-hydrostatic” state (slowly contracting due to energy loss at the surface) in the first part of their lives, before they reach the main sequence and core H fusion begins.  The exact amount of time varies with mass, but for 1 solar mass it’s about 100 million years.
Eric Jensen
CC BY-SA 4.0
2022-07-21T17:30:52.480Z
@EricJensen it's about 10 Myr for a 1 solar mass star. The difference between a contracting pre-main sequence star and a giant planet is that the the core of the star become hot enough to burn hydrogen *before* it become electron-degenerate.
ProfRob
CC BY-SA 4.0
2022-07-22T15:12:18.580Z
@ProfRob  Looking at stellar models ([MIST isochrones](https://waps.cfa.harvard.edu/MIST/interp_tracks.html)), at 10 Myr, the H-burning luminosity is 0.2% of the total stellar luminosity.  It surpasses 50% of total L at about 30 Myr.  So I was a bit high, but I'd argue 10 Myr is a bit low.  But you are correct that H fusion has begun at 10 Myr - earlier than I remembered.
Eric Jensen
CC BY-SA 4.0
2022-07-22T15:44:00.633Z
@EricJensen agreed. 10 Myr is more like an "ignition age". 30-50 Myr is where a 1 solar mass star transitions to being totally supported by nuclear reactions.
ProfRob
CC BY-SA 4.0
2022-07-21T14:55:40.680Z
2022-07-21T17:35:25.327Z
2022-07-21T17:35:25.327Z
ProfRob
<p>Why don't gas planets get bigger and smaller over time? Are their sizes constant? Are they in hydrostatic equilibrium like the Sun? Is there an internal force against gravity that does not allow gravity to compress the planet?</p>

CC BY-SA 4.0
2022-07-21T13:40:26.707Z
take a manual tire pump, keep the exit closed and compress the air. The force which keeps you from compressing it to zero, is what keeps the planets as-is, too. It's also the same force which keeps gravity from crushing you.
planetmaker
CC BY-SA 4.0
2022-07-22T05:15:59.053Z
Related: https://astronomy.stackexchange.com/questions/39620/why-has-saturn-stopped-contracting-gravitationally ... https://astronomy.stackexchange.com/questions/44398/arent-denser-bodies-more-likely-to-collapse-into-hydrostatic-equilibrium
Nilay Ghosh
<planet>
Are gas planets in hydrostatic equilibrium?
Faeze Moosazade
# Are gas planets in hydrostatic equilibrium?

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

Why don't gas planets get bigger and smaller over time? Are their sizes constant? Are they in hydrostatic equilibrium like the Sun? Is there an internal force against gravity that does not allow gravity to compress the planet?

**Tags:** planet

> **Comments:**
> **username_1**: take a manual tire pump, keep the exit closed and compress the air. The force which keeps you from compressing it to zero, is what keeps the planets as-is, too. It's also the same force which keeps gravity from crushing you.  
> **username_2**: Related: https://astronomy.stackexchange.com/questions/39620/why-has-saturn-stopped-contracting-gravitationally ... https://astronomy.stackexchange.com/questions/44398/arent-denser-bodies-more-likely-to-collapse-into-hydrostatic-equilibrium  

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## 1 answers

### Answer by username_3 on 2022-07-21. Score: 14

Like the Sun, gas giant planets are *approximately* in hydrostatic equilibrium - a pressure *gradient* in their interiors balances the gravitational forces acting towards the centre.

However, there is a big difference between the Sun and a gas giant planet - both the Sun and planets are losing energy from their surfaces. In the Sun, this energy output is almost exclusively provided by nuclear reactions in its core - that is, the luminosity of the Sun equals the energy generation rate by nuclear reactions in its interior. This means that the Sun's interior temperature, structure and radius are stable on timescales for the nuclear energy generation rate to change (billions of years). In a gas giant planet there are no nuclear reactions and so the only source of heat is from the gas in its interior, ultimately heated by the release of gravitational potential as the planet contracts.

A complication is that the gas in the deep interior of a gas giant planet is so dense that it becomes electron-degenerate. This breaks the direct connection between temperature and pressure and means that as time goes on, a gas giant planet will cool-off at almost constant radius, because the electron-degenerate gas can maintain its pressure regardless of temperature.

Giant planets are more similar to contracting protostars - which also derive their luminosity from gravitational contraction. The difference is that a giant planet's interior becomes electron degenerate at a temperature much lower tahn required to start nuclear fusion.

Here is an example of a model for the time-evolution of the radii of Jupiter and Saturn (from [Fortney at al. 2011](https://iopscience.iop.org/article/10.1088/0004-637X/729/1/32)); the black and red curves are for different assumptions about the atmospheres and the vertical dotted line represents the present day.

[![Radii of Jupier and Saturn](https://i.sstatic.net/tRf1o.jpg)](https://i.sstatic.net/tRf1o.jpg)

Thus, the answer to your question is that gas giant planets are more dynamic than (main sequence) stars. They are gradually contracting, but at a decreasing rate, in order to maintain hydrosttaic equilibrium as they lose heat from their surfaces.

> **Comments:**
> **username_4**: The linked article is not Fortney+2011.  
> **username_3**: @username_4 fixed  
> **username_5**: On a related note, stars like the Sun are in this “quasi-hydrostatic” state (slowly contracting due to energy loss at the surface) in the first part of their lives, before they reach the main sequence and core H fusion begins.  The exact amount of time varies with mass, but for 1 solar mass it’s about 100 million years.  
> **username_3**: @EricJensen it's about 10 Myr for a 1 solar mass star. The difference between a contracting pre-main sequence star and a giant planet is that the the core of the star become hot enough to burn hydrogen *before* it become electron-degenerate.  
> **username_5**: @username_3  Looking at stellar models ([MIST isochrones](https://waps.cfa.harvard.edu/MIST/interp_tracks.html)), at 10 Myr, the H-burning luminosity is 0.2% of the total stellar luminosity.  It surpasses 50% of total L at about 30 Myr.  So I was a bit high, but I'd argue 10 Myr is a bit low.  But you are correct that H fusion has begun at 10 Myr - earlier than I remembered.  
> **username_3**: @EricJensen agreed. 10 Myr is more like an "ignition age". 30-50 Myr is where a 1 solar mass star transitions to being totally supported by nuclear reactions.  

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