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To answer the other half of your question (mafribe already said why the moons are tectonically active): what's needed for heating due to tidal friction is not o
by Udo 10y ago
To answer the other half of your question (mafribe already said why the moons are tectonically active): what's needed for heating due to tidal friction is not only strong gravity, but a strong gravity gradient that changes over time.
I was doing some back-of-the-envelope calculations just now to show how Io experiences much more tidal stress than Mercury due to a stronger change in gradient, when I discovered my assumptions were wrong, but I'm posting the results anyway:
Mercury's orbit has a huge eccentricity, and its distance to the sun varies between 0.47 AU at Aphelion and 0.307 AU at Perihelion. Taking Mercury's size into account, that should work out to a difference in solar gravity between its near and far side of about 0.000004 m/s^2 at Aphelion and 0.000013 m/s^2 at Perihelion! That's actually quite the squeeze!
Now comparing that to Io, which has often been reported as having this wild orbit, upon looking up the actual numbers I saw that Io's orbit around Jupiter is actually nearly circular: 420000km at Periapsis and 423400km at Apoapsis. The moon itself has a radius of 1800km, that means its orbit is so circular its variation falls within the size of the actual moon. Furthermore, plugging in the numbers, Io's gravity gradient between its near and far side remains pretty much stable at 0.000014 m/s^2 no matter where it is, varying only by a factor of about -1.37x10^-08.
So the gradient change itself is not dramatic in Io, but reasonably pronounced in Mercury - didn't expect that. Taking a look at the orbital period of both objects, Io completes about 50 orbits in the same time it takes Mercury to orbit once, but even a factor of 50 isn't enough to blow up Io's tidal action to make up for the observed difference in tidal heating.
My only conclusion at this point is that I either made a careless mistake somewhere (which is likely) or that Io's squeezing action must come almost entirely from its interaction with the other Jupiter moons.
In the end, a heat source is not required for Mercury to experience tectonic activity though. As described in the article, the cooling and shrinking of the planet itself are sufficient to cause disturbances on the surface.
- mcguire 10y agoShouldn't Mercury have reached thermal equilibrium already?
- Arnt 10y agoIf Mercury is in an eccentric orbit, then the sun's gravity changes depending on where in its orbit is is. Adding to that, when it'a closer, the difference between the gravity on the bright side and dark side is more pronounced than when it's farther away.
- mturmon 10y agoClearly the eccentricity is one key here, but I'm not sure that the acceleration difference is the right metric. The basic paper that pointed out the likelihood of volcanoes on Io is not that complex -- http://www.es.ucsc.edu/~pkoch/EART_206/09-0205/Peale%20et%2079%20Science%20203-892.pdf http://www.es.ucsc.edu/~pkoch/EART_206/09-0205/Peale%20et%20... The key is equation (7), which gives the energy dissipated by a solid body due to its eccentric orbit. It's quadratic in eccentricity, but there are other key factors that would vary from Mercury to Io. The paper above is remarkable. It's an amazing chain of basically armchair logic that leads to the likelihood of volcanism on Io.
- Udo 10y agoWhy would acceleration difference not be the right metric? The Peale model is different because it takes material properties like rigidity into account - but let's keep in mind here that Mercury's eccentricity is 0.2 whereas Io's is 0.004!
- mturmon 10y agoNot arguing, just observing that acceleration does not seem to be explaining the issue.
- Udo 10y agoThat's kind of a bold statement though. If tidal heating is in your opinion not caused by a gravity differential, you're going far beyond and outside the source you linked to, and I would like to hear what alternative you're proposing. The "conventional" explanation for tidal heating is that a body is being squeezed repeatedly, for which the changing gravity gradient I calculated does seem an appropriate measure. The paper you linked to used eccentricity, whereas I used periapsis and apoapsis - it's the same thing mathematically. Not sure where this "clearly eccentricity is the key" thing comes from when I just told you that Io's orbit is nearly circular. I do like the materials science aspect of the article you linked to in regard to taking rigidity of the body into account, but at a very basic level the problem remains that Io's orbital shape alone doesn't yield enough of a change over time to account for a lot of tidal heating - certainly not compared to Mercury.