Re: Is Titan a saturnian Europa/Ganymede?

From: Henry Spencer (henry_at_spsystems.net)
Date: 07/04/04 

Date: Sun, 4 Jul 2004 17:36:06 GMT

In article <fdVFc.6903$JR4.3306@attbi_s54>,
Jack <merde44spinks@yahoo.com> wrote:
>My memory was a little fuzzy on this, I forgot that the reason
>Io is heated is because of its orbital resonance with Europa, which
>causes it to slow down or speed up at different parts of it's orbit.

Well, kind of sort of. The more usual way of saying this is that the
resonance with Europa is what keeps Io's orbital eccentricity non-zero,
and it's the eccentricity that causes the changes in both orbital rate and
orbital radius, shifting the tidal bulges around and causing internal
heating. (You can't change the speed of an orbiting object without also
changing the shape of the orbit.)

>Both Io and Titan have synchronous orbits...

Uh, no, synchronous *orbits* are another story; both moons are far above
the altitude required for that. They both have synchronous *rotations*,
rotating once per orbit.

>it's the slight nodding
>back and forth of Io in the strong gravity close to Jupiter that
>does it. But eccentricity per se or synchronous orbits per se
>are not the cause (or the prevention).

Eccentricity is precisely what does it -- that's what prevents the
synchronous rotation from exactly matching the orbital rate at all times,
in which case the tidal bulges would be stationary. The "nodding", which
moves the bulges around, occurs precisely because of the eccentricity.
(There is also a rather smaller contribution from changing orbital radius,
again due to eccentricity, which changes the height of the bulges.)

A contributing factor is that there's a threshold effect in tidal melting.
For a solid moon, the heating is strongly concentrated at the core. If
the core gets hot enough to *melt*, the moon loses some of its structural
strength, and so starts flexing more in response to the tidal forces,
increasing the heating rate. So more of the interior melts, and you get
runaway melting until essentially the whole moon is molten. That's what
happened to Io, as predicted in a paper published just weeks before Io's
volcanos were discovered.

(Ref: Murray&Dermott, "Solar System Dynamics".)

>I don't know if Titan's orbit is affected by other moons or not.

Not substantially. Saturn only has one big moon, Titan itself. The
others are much too small to have the sort of effects seen at Jupiter.

>But if it is, the effect would not have to be nearly as great
>to cause methane volcanism because the temperatures involved
>are much lower than for sulfur volcanism.

Again, it's not the effect of the other moons that causes the heating,
it's the orbital eccentricity. The role of the other moons at Jupiter is
to *maintain* Io's orbital eccentricity, which otherwise would quickly be
reduced to zero.

In Titan's case, it simply doesn't see sufficiently drastic tidal effects
to circularize its orbit rapidly. So its rather lower level of internal
heating will persist without other moons pumping up its orbit. However,
it doesn't get enough heating to cause runaway melting. Its *interior*
isn't methane. Any methane volcanism would be a local thing, not the
result of an entirely molten interior like the Io volcanism. 

-- 
"Think outside the box -- the box isn't our friend."    |   Henry Spencer
                                -- George Herbert       | henry@spsystems.net

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