<p>When the Galilean moons formed, they weren't in resonance with each other. All of them were in slightly smaller orbits than they are now. Over time after their formation, Io's orbit slowly moved outward due to tides from Jupiter. This is the same effect that is causing our moon to slowly move away from the Earth (at about the same rate your fingernails grow). It goes like this. The Moon's gravity causes tides to form in Earth's oceans. This bulge of water gets carried forward with Earth's rotation, because the Earth is spinning faster than the Moon is orbiting. Because the moon is still attracting the bulge, it causes a drag on the Earth, slowing its spin. At the same time, the bulge is attracting the moon, causing it to go faster in its orbit. As the moon speeds up, its orbit gets bigger. So essentially, the Earth's spin energy is getting transferred into the Moon's orbital energy. The same thing happens with Jupiter and Io, with a bulge in Jupiter's atmosphere causing Io's orbit to get bigger.</p>
<p>As Io's orbit expanded, its 'year' got longer, until it approached a 2/1 resonance with Europa. Once they reached resonance, they got 'locked in', their mutual gravity acting on each other reinforced it. Io was still raising tides on Jupiter, though, and its orbit was still trying to expand. As Io's orbit kept expanding, it gave a gravitational kick to Callisto on each pass, expanding both of their orbits until Ganymede reached a 2/1 resonance with Callisto. This is where the inner 3 Galilean moons got their resonance. The orbits are still expanding, but much more slowly because with each one you add on, it gets harder to transfer the energy. Given enough time, all 4 Galilean moons would probably reach resonance, although the sun will die before that happens.</p>
<p>I may have some of the minor details wrong here, but this is the story as I understand it.</p>
<p><strong>EDIT:</strong>  Seven years later, <a href="https://astronomy.stackexchange.com/questions/40701/when-will-callisto-be-in-orbital-resonance-with-the-rest-of-jupiters-big-moons">When will Callisto be in orbital resonance with the rest of Jupiter&#39;s big moons?</a> was asked.  The newest answer for when the first four moons will be in orbital resonance is much sooner than the Sun will die.  Specifically, about 1.5 billion years from now.</p>

CC BY-SA 4.0
2021-02-04T21:31:10.687Z
I think the names of the jupiter moons have to be corrected in the second paragraph.
eftshift0
CC BY-SA 3.0
2014-03-18T16:51:43.997Z
The link in the comments above describes why resonance holds, but this is a beautiful revelation of why orbiting bodies are likely to find that resonance to begin with.
Mark Bailey
CC BY-SA 4.0
2014-01-29T20:15:44.143Z
2022-01-10T13:55:10.997Z
2022-01-10T13:55:10.997Z
gargoylezoo
<p>Three of the <a href="http://en.wikipedia.org/wiki/Galilean_moons">first four moons</a> ever discovered outside of our own planetary sphere of gravitational influence orbit in very close to perfect resonance. Europa's orbit is almost exactly twice as long as Io's, and Ganymede's is almost exactly twice as long as Europa's. Perhaps it is just coincidence. If you look at enough random things, you start to see patterns that aren't necessarily there. But it would be a pretty big coincidence. When I see something like this in nature, I have to wonder if there is an underlying cause.</p>

<p>The ratios aren't quite exactly 2, so if there is a gravitational influence or something that pulls them into this resonance, the influence must not be overpowering enough to force exact resonance. Or maybe it is, given enough time, but "recent" collisions or the pull of other satellites in the system may have driven them a little bit off of their resonance. Has anyone studied this and found a probable reason for this phenomenon?</p>

CC BY-SA 3.0
2013-12-06T17:35:30.290Z
I'm sorry but I have to ask. Does your question by chance have anything to do with yesterday's [Galilean Moons XKCD](http://xkcd.com/1300/)? Because that comic is actually wrong (well, intentionally, see what happens to Callisto in it if that was true), Io Europa and Ganymede are never in triple conjunction, and [Laplace resonance](https://en.wikipedia.org/wiki/Orbital_resonance#The_Laplace_resonance) gives equation for why that is impossible. Good question tho, and answers will be a pleasure to read! :)
TildalWave
CC BY-SA 3.0
2013-12-06T19:17:10.353Z
I do read XKCD, and love it. I know that when all three align, one is actually always on the opposite side of Jupiter. It shows that on the wiki that I referenced above. But I think Laplace resonance is actually the answer to my question.
Mark Bailey
CC BY-SA 3.0
2013-12-06T19:50:07.120Z
Yes, it would be, but is notoriously difficult to explain well. Way beyond my capabilities I'm afraid. :}
TildalWave
CC BY-SA 3.0
2013-12-06T19:57:56.723Z
http://en.wikipedia.org/wiki/Orbital_resonance
Envite
CC BY-SA 3.0
2013-12-06T20:14:22.317Z
Yeah @Envite. I see the page. That must be the answer. One day I'll spend enough time to understand what that means.
Mark Bailey
<orbit>
Does anyone know why three of Jupiter's largest moons orbit in 1:2:4 resonance?
Mark Bailey
# Does anyone know why three of Jupiter's largest moons orbit in 1:2:4 resonance?

(Asked by: username_0 on 2013-12-06)

Three of the [first four moons](http://en.wikipedia.org/wiki/Galilean_moons) ever discovered outside of our own planetary sphere of gravitational influence orbit in very close to perfect resonance. Europa's orbit is almost exactly twice as long as Io's, and Ganymede's is almost exactly twice as long as Europa's. Perhaps it is just coincidence. If you look at enough random things, you start to see patterns that aren't necessarily there. But it would be a pretty big coincidence. When I see something like this in nature, I have to wonder if there is an underlying cause.

The ratios aren't quite exactly 2, so if there is a gravitational influence or something that pulls them into this resonance, the influence must not be overpowering enough to force exact resonance. Or maybe it is, given enough time, but "recent" collisions or the pull of other satellites in the system may have driven them a little bit off of their resonance. Has anyone studied this and found a probable reason for this phenomenon?

**Tags:** orbit

> **Comments:**
> **username_1**: I'm sorry but I have to ask. Does your question by chance have anything to do with yesterday's [Galilean Moons XKCD](http://xkcd.com/1300/)? Because that comic is actually wrong (well, intentionally, see what happens to Callisto in it if that was true), Io Europa and Ganymede are never in triple conjunction, and [Laplace resonance](https://en.wikipedia.org/wiki/Orbital_resonance#The_Laplace_resonance) gives equation for why that is impossible. Good question tho, and answers will be a pleasure to read! :)  
> **username_0**: I do read XKCD, and love it. I know that when all three align, one is actually always on the opposite side of Jupiter. It shows that on the wiki that I referenced above. But I think Laplace resonance is actually the answer to my question.  
> **username_1**: Yes, it would be, but is notoriously difficult to explain well. Way beyond my capabilities I'm afraid. :}  
> **username_2**: http://en.wikipedia.org/wiki/Orbital_resonance  
> **username_0**: Yeah @username_2. I see the page. That must be the answer. One day I'll spend enough time to understand what that means.  

---

## 1 answers

### Answer by username_3 on 2014-01-29. Score: 8 | Accepted answer

When the Galilean moons formed, they weren't in resonance with each other. All of them were in slightly smaller orbits than they are now. Over time after their formation, Io's orbit slowly moved outward due to tides from Jupiter. This is the same effect that is causing our moon to slowly move away from the Earth (at about the same rate your fingernails grow). It goes like this. The Moon's gravity causes tides to form in Earth's oceans. This bulge of water gets carried forward with Earth's rotation, because the Earth is spinning faster than the Moon is orbiting. Because the moon is still attracting the bulge, it causes a drag on the Earth, slowing its spin. At the same time, the bulge is attracting the moon, causing it to go faster in its orbit. As the moon speeds up, its orbit gets bigger. So essentially, the Earth's spin energy is getting transferred into the Moon's orbital energy. The same thing happens with Jupiter and Io, with a bulge in Jupiter's atmosphere causing Io's orbit to get bigger.

As Io's orbit expanded, its 'year' got longer, until it approached a 2/1 resonance with Europa. Once they reached resonance, they got 'locked in', their mutual gravity acting on each other reinforced it. Io was still raising tides on Jupiter, though, and its orbit was still trying to expand. As Io's orbit kept expanding, it gave a gravitational kick to Callisto on each pass, expanding both of their orbits until Ganymede reached a 2/1 resonance with Callisto. This is where the inner 3 Galilean moons got their resonance. The orbits are still expanding, but much more slowly because with each one you add on, it gets harder to transfer the energy. Given enough time, all 4 Galilean moons would probably reach resonance, although the sun will die before that happens.

I may have some of the minor details wrong here, but this is the story as I understand it.

**EDIT:** Seven years later, [When will Callisto be in orbital resonance with the rest of Jupiter's big moons?](https://astronomy.stackexchange.com/questions/40701/when-will-callisto-be-in-orbital-resonance-with-the-rest-of-jupiters-big-moons) was asked. The newest answer for when the first four moons will be in orbital resonance is much sooner than the Sun will die. Specifically, about 1.5 billion years from now.

> **Comments:**
> **username_0**: The link in the comments above describes why resonance holds, but this is a beautiful revelation of why orbiting bodies are likely to find that resonance to begin with.  
> **username_4**: I think the names of the jupiter moons have to be corrected in the second paragraph.  

---

