<p>When the Sun becomes a red giant there will be some mass loss, making Jupiter's orbit wider and slower. The extent is fairly small during the initial expansion, but about 50% of the mass at the end. <a href="https://www.sciencedirect.com/science/article/abs/pii/S0019103598959620" rel="nofollow noreferrer">Simulations suggest</a> Jupiter does end up with about twice the current semimajor axis, and hence up to 4 times the period it has now (<span class="math-container">$P\propto \sqrt{a^3/M_\odot}$</span>).</p>
<p>When <a href="https://www.liebertpub.com/doi/abs/10.1089/153110703769016406" rel="nofollow noreferrer">the habitable zone passes the Jupiter region depends a bit on stellar model</a>, but it is in about 5 gigayears. This is a long time compared to the slow evolution of the orbits.</p>
<p>Currently the inner Galilean moons are in a 1:2:4 orbital resonance (the Laplace resonance). However, there is a lot of tidal dissipation in Io, making the system slowly shift. <a href="https://arxiv.org/abs/2001.01106" rel="nofollow noreferrer">(Lari, Sailenfest &amp; Fenucci 2020)</a> model the future evolution of the moons. During the first billion years the periods go up a small amount as the moons become a bit more distant but retain their resonance. However, after 1.4 Gyr, Ganymede approaches the 2:1 mean-motion resonance with Callisto and chaotic effects show up. At this point various scenarios of resonance can play out, but practically for this question the effects are minor: the moons keep on slowly expanding their orbits.</p>
<p><a href="https://i.sstatic.net/h62Vi.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/h62Vi.png" alt="Fig 5 from Lari et al 2020" /></a></p>
<p>So when Europa becomes warm, it will likely have an orbit maybe 11 Juiter radii out rather than 10, with a period of about 100 hours rather than 85. Not too diifferent.</p>

CC BY-SA 4.0
2022-03-21T10:11:07.207Z
2022-03-21T10:11:07.207Z
Anders Sandberg
<p>We know that the Sun gets so big billions of years later and the Earth will get destroyed.</p>
<p>What will the orbital period of Jupiter (Sun-Jupiter system) and its moon Europa (Jupiter-Europa system) be when the habitable zone reaches Europa? Also, what will the side-real rotation period be for the two objects?</p>
<p>Is there a way to calculate them?</p>

<rotation><jupiter><europa><future><sidereal-period>
The orbital period of Jupiter and Europa billions of years later
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# The orbital period of Jupiter and Europa billions of years later

(Asked by: username_0 on 2022-03-19)

We know that the Sun gets so big billions of years later and the Earth will get destroyed.

What will the orbital period of Jupiter (Sun-Jupiter system) and its moon Europa (Jupiter-Europa system) be when the habitable zone reaches Europa? Also, what will the side-real rotation period be for the two objects?

Is there a way to calculate them?

**Tags:** rotation, jupiter, europa, future, sidereal-period

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## 1 answers

### Answer by username_1 on 2022-03-21. Score: 4 | Accepted answer

When the Sun becomes a red giant there will be some mass loss, making Jupiter's orbit wider and slower. The extent is fairly small during the initial expansion, but about 50% of the mass at the end. [Simulations suggest](https://www.sciencedirect.com/science/article/abs/pii/S0019103598959620) Jupiter does end up with about twice the current semimajor axis, and hence up to 4 times the period it has now ($P\propto \sqrt{a^3/M\_\odot}$).

When [the habitable zone passes the Jupiter region depends a bit on stellar model](https://www.liebertpub.com/doi/abs/10.1089/153110703769016406), but it is in about 5 gigayears. This is a long time compared to the slow evolution of the orbits.

Currently the inner Galilean moons are in a 1:2:4 orbital resonance (the Laplace resonance). However, there is a lot of tidal dissipation in Io, making the system slowly shift. [(Lari, Sailenfest & Fenucci 2020)](https://arxiv.org/abs/2001.01106) model the future evolution of the moons. During the first billion years the periods go up a small amount as the moons become a bit more distant but retain their resonance. However, after 1.4 Gyr, Ganymede approaches the 2:1 mean-motion resonance with Callisto and chaotic effects show up. At this point various scenarios of resonance can play out, but practically for this question the effects are minor: the moons keep on slowly expanding their orbits.

[![Fig 5 from Lari et al 2020](https://i.sstatic.net/h62Vi.png)](https://i.sstatic.net/h62Vi.png)

So when Europa becomes warm, it will likely have an orbit maybe 11 Juiter radii out rather than 10, with a period of about 100 hours rather than 85. Not too diifferent.


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