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How does jupiter's moon get so hot?

by ehab_s
Tags: jupiter, moon
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ehab_s
#1
Nov1-13, 10:53 PM
P: 5
This question is really starting to bug me!!

Consider for example Io is orbiting Jupiter and the force of the gravity pulling the moon towards the planet vs the momentum pulling in the other direction creates friction in the moon's core.
First of all, this should heat up the moon. But where exactly did the energy come from? Gravity isn't an example of energy, energy can only be 'held' in gravity as a potential energy if a force acts against it.The force against it in this case is the 'centrifugal' force acting on the moon. You'd assume that it is caused by the kinetic energy of the moon, only it seems as if it never runs out even though it obviously heating it? Where does the energy actually come from?

It seemed like a really trivial and simple question at first but the more I thought of it the more it confused me. I have a limited understanding of physics as I have just turned 14 and it's early in the morning.

P.S about 7:53 where I live on a weekend not 3:53 soo yeah.
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Simon Bridge
#2
Nov1-13, 11:44 PM
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Welcome to PF;
Io is heated primarily through tides - the tidal forces get complicated because there are other large moons present to change things about.
http://www.astro.washington.edu/user...als/TidalHeat/

Note: the time stamp on the posts is the tie at the server - the local time of day does not matter as much as knowing how long ago the post was made.

So I posted this 1745 NZDT - the time stamp reads 0445. (give or take)
You posted at 0753 or 1953 your local time and the time-stamp is 0353
That means I posted the reply an hour and 8 mins after you asked the question.
See?
pixelpuffin
#3
Nov2-13, 12:13 AM
P: 41
Quote Quote by Simon Bridge View Post
Welcome to PF;
Io is heated primarily through tides - the tidal forces get complicated because there are other large moons present to change things about.
http://www.astro.washington.edu/user...als/TidalHeat/

Note: the time stamp on the posts is the tie at the server - the local time of day does not matter as much as knowing how long ago the post was made.

So I posted this 1745 NZDT - the time stamp reads 0445. (give or take)
You posted at 0753 or 1953 your local time and the time-stamp is 0353
That means I posted the reply an hour and 8 mins after you asked the question.
See?
this explains the mechanism but wouldn't the orbit or orbits of the moons slow down as the energy is turned into heat

SteamKing
#4
Nov2-13, 01:10 AM
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How does jupiter's moon get so hot?

The orbital characteristics of Io about Jupiter are complicated by the orbits of the other large moons.

This article explains how these interactions contribute to the heating of Io and to its orbit's stability:

http://en.wikipedia.org/wiki/Io_%28moon%29
Simon Bridge
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Nov2-13, 02:06 AM
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Quote Quote by pixelpuffin View Post
this explains the mechanism but wouldn't the orbit or orbits of the moons slow down as the energy is turned into heat
Sort of. The have gravitational PE and regular KE to exchange for heat. It can't go on forever but it can go on for a very long time - especially considering that Io-Jupiter-Europa-etc are not a closed system.

Of course things can get arbitrarily complicated.
We've got it easy with just the one big moon.
Borek
#6
Nov2-13, 03:53 AM
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Another thing to ponder: in the past Earth rotated much faster then it does today (the day was shorter, there were more days in the year). What happened to the rotational energy?

(no, I am not asking you to explain it to me, I want OP to think about it for a moment, as it gives partial answer to his original question)
Bandersnatch
#7
Nov2-13, 04:30 AM
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I think Borek's question might put the OP on a wrong track, since Earth's rotation was certainly not all slowed by heating. So let me clarify.

The heating siphons energy from the rotation and revolution of the system's components. Tidal forces cause exchange of angular momentum between the interacting bodies, but due to heating it is not a 100% efficient process.

Take Earth-Moon system as it is today for an example that is simpler to analyse than multi-satellite system of Jupiter. Currently, with the Moon tidally locked, and disregarding libration, precession, and slight excentricity of its orbit, the only process still going on is the reduction of Earth's rotation (making days longer) and simultainous raising of the Moon's orbit(so it drifts away). If not for the tidal heating, the total angular momentum would be conserved, and the Moon's increased contribution would match exactly the decreased contribution of Earth. But since there is heating, Earth loses more angular momentum than it imparts to its satellite.

With Jupiter and its moons, it becomes much harder to pinpoint wchich way the angular momenta exchanges go, but you can be sure of one thing: the TOTAL angular momentum of the whole system gets reduced as a result of tidal heating.
D H
#8
Nov2-13, 12:04 PM
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Quote Quote by Bandersnatch View Post
With Jupiter and its moons, it becomes much harder to pinpoint wchich way the angular momenta exchanges go, but you can be sure of one thing: the TOTAL angular momentum of the whole system gets reduced as a result of tidal heating.
What makes you say that? The total angular momentum of the Jovian system is going to be very close to a conserved quantity. It's the energy of the Jovian system that is not conserved.

The three innermost Galilean moons are slowly migrating outward from Jupiter. This means their angular momentum is increasing, which in turn means Jupiter's rotational angular momentum is decreasing. The total is very close to constant. You'd have to look to interactions between Jupiter and the Sun, and between Jupiter and the other planets to see whether the total angular momentum of the Jovian system is increasing or decreasing.
Borek
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Nov2-13, 12:51 PM
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Quote Quote by D H View Post
It's energy that is not conserved.


I guess you mean kinetic
D H
#10
Nov2-13, 01:01 PM
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I edited my post to say "It's mechanical energy that is not conserved.", but I think I should change it back. Energy is not conserved. The Jovian system is not a closed system. Why should energy be conserved? The heat generated by tidal stresses is eventually radiated away.
Borek
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Nov2-13, 01:51 PM
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While I understand what you are saying, I strongly disagree with the statement. Energy is conserved - period. Some of the energy is radiated away, so it is not conserved inside of the system, but it doesn't mean it disappeared in general.

I was always taught "Energy is conserved. If you miss some energy, it wasn't lost - it is just somewhere else, or in some other form." And I have a feeling every other approach is pedagogically either wrong or at least dangerous - as it suggests energy conservation is something that sometimes works, sometimes not. Say

Quote Quote by D H View Post
Energy is not conserved.
and then try to convince an over unity crackpot he can't be right, as energy is conserved.
pixelpuffin
#12
Nov2-13, 07:47 PM
P: 41
i tried to make a program for the duration of the cycle but it gives me all sorts of errors because the numbers are too long :/
pixelpuffin
#13
Nov2-13, 08:45 PM
P: 41
just fixed my program using the difference in escape velocity from the surface to their orbit to calculate that the system would last a bit over 2 billion years on it's own at it's current rate
exact info is in the text file
this is assuming a scenario in which all the major moons contribute all of their energy
Attached Files
File Type: txt majormoons.txt (1.3 KB, 5 views)
Simon Bridge
#14
Nov2-13, 10:07 PM
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@Borek - this was my take on it too ... it is pedagogically dangerous. The way the "elastic collisions" topic gets taught is bad enough but at east they say it's kinetic energy that isn't conserved.

The observation that the Jovian system, considered alone, is not closed is valid, but still tricky pedagogically for the same sorts of reasons: it's too easy for the student to miss the proviso. Anyway - how "non-closed" is it?

@pixelpuffin: you mean 2 billion years from now - assuming the system changes at a constant rate?
That constant rate over 2by is a big ask though... is the rate expected to accelerate or decelerate over time? (i.e. do the influences on the rate get bigger or smaller?)
pixelpuffin
#15
Nov2-13, 10:50 PM
P: 41
i would expect the process to go exponentially faster as they get closer to jupiter however the 2 billion years doesn't account for that it also assumes a system where all the moons contribute
that answer is the longest it could potentially go given it taps all of the energy from the moons around it that it can
i would expect based on my math that it lasts 400,000,000 to 500,000,000
D H
#16
Nov3-13, 02:21 AM
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Quote Quote by Simon Bridge View Post
The observation that the Jovian system, considered alone, is not closed is valid, but still tricky pedagogically for the same sorts of reasons: it's too easy for the student to miss the proviso. Anyway - how "non-closed" is it?
I disagree. Tidal migration necessitates that the total energy (thermal + kinetic + potential) of a planet and its moons not be a conserved quantity. There can be no tidal migration unless some mechanism by which the system loses energy exists. How does it lose energy? Simple: Mechanical energy is converted to heat by some mechanically lossy mechanism, and that generated heat is eventually radiated into space. The universe makes for a very, very large and very, very cold heat sink to which lots of energy can be transferred.

In the case of Io, the mechanism by which mechanical energy is converted to heat is the viscoelastic-plastic nature of semi-molten rock. Io's orbit is somewhat eccentric. This eccentricity means Io is subject to significant tidal stresses. Coupled with the nature of the material that forms Io, those tidal stresses result in heat. If Jupiter had no other moons, these tidal stresses and the resultant heat generation would act to circularize Io's orbit. Jupiter does have other moons. The three innermost moons, Io, Europa, and Ganymede, are locked in a 1:2:4 orbital resonance. Europa and Ganymede collectively act to increase the eccentricity of Io's orbit. The tidal stresses act to decrease Io's eccentricity. The end result is that Io's orbit is slightly eccentric, and that all three of those innermost Galilean moons are *slowly* migrating outward. Eventually they'll move far enough out that Io, Europa, Ganymede, and Callisto will be in a 1:2:4:8 orbital resonance. That won't happen for a long, long time.
D H
#17
Nov3-13, 02:24 AM
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Quote Quote by pixelpuffin View Post
i would expect the process to go exponentially faster as they get closer to jupiter however the 2 billion years doesn't account for that it also assumes a system where all the moons contribute
that answer is the longest it could potentially go given it taps all of the energy from the moons around it that it can
i would expect based on my math that it lasts 400,000,000 to 500,000,000
That's just wrong. Look at it this way: The Galilean moons have been in existence for over 4.5 billion years.

With regard to your calculations, where's the Q and k2 Love numbers of Jupiter and the Galilean moons?
ehab_s
#18
Nov3-13, 01:23 PM
P: 5
Thanks for all the interesting replies! I wasn't really expecting this kind of response (maybe it's because i'm used to yahoo and the likes..)

Anyway, an answer to what someone said

What makes you say that? The total angular momentum of the Jovian system is going to be very close to a conserved quantity. It's the energy of the Jovian system that is not conserved.
Correct me if I'm wrong but I thought that the total angular momentum of Jupiter's system would be lost if the total energy is lost. e.g. if our moon was moving away from the Earth, my assumption would be that rather than the moon's angular momentum increasing and Earth's decreasing, both of them were decreasing however it was mostly the Earth's rotational angular momentum decreasing because of the energy lost through tides. Otherwise energy wouldn't be conserved in the system, it would have to be created.

What is really confusing to me is that if Io's orbit is eccentric, it must have to be losing its kinetic energy at a quicker rate than the other moons around jupiter. So why is it moving away from Jupiter, surely the planet couldn't be losing angular momentum faster than Io (After all, Jupiter is massive compared to it)?


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