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Tranquility
2004-Jun-15, 01:54 AM
The first question is regarding Miranda, the moon of Uranus.
The structural enigma it is is really though-provoking. I heard that it is possible the satellite was broken up and remoulded, but what scale may such an event require, indeed, what is the required scale of such a catastrophe to be able to break up Miranda and then allow it to assemble? (there seem to be some similar groove patterns on Ariel but on a much smaller scale) Whats everyone's take on this particular enigma?

Another question, is regarding the other moons of Uranus. They seem to be mainly captured asteroids, can they be regarded as KBOs, being outside the Asteroid belt and might have had initial orbits taking them outside the orbit of Neptune? And can the same be said about Neptune's satellites, like Thalassa, Proteus, etc. where many seem to be captured asteroids?

The last question (thanks for reading this far!) is regarding Triton. Why does it orbit Neptune in the opposite direction to Neptune's other moons? Is the probable event again catastrophic?

Sorry about all these questions, but may God bless the kind souls who forgive my ignorance :)

Tranquility
2004-Jun-16, 12:47 AM
So no loving soul is going to take mercy on my ignorance :D ?

Candy
2004-Jun-16, 03:04 AM
The first question is regarding Miranda, the moon of Uranus.
The structural enigma it is is really though-provoking. I heard that it is possible the satellite was broken up and remoulded, but what scale may such an event require, indeed, what is the required scale of such a catastrophe to be able to break up Miranda and then allow it to assemble? (there seem to be some similar groove patterns on Ariel but on a much smaller scale) Whats everyone's take on this particular enigma?

Another question, is regarding the other moons of Uranus. They seem to be mainly captured asteroids, can they be regarded as KBOs, being outside the Asteroid belt and might have had initial orbits taking them outside the orbit of Neptune? And can the same be said about Neptune's satellites, like Thalassa, Proteus, etc. where many seem to be captured asteroids?

The last question (thanks for reading this far!) is regarding Triton. Why does it orbit Neptune in the opposite direction to Neptune's other moons? Is the probable event again catastrophic?

Sorry about all these questions, but may God bless the kind souls who forgive my ignorance :) I would love to talk about Ur-anus, but I'd rather talk about mine. :o

Hamlet
2004-Jun-16, 03:12 AM
The first question is regarding Miranda, the moon of Uranus.
The structural enigma it is is really though-provoking. I heard that it is possible the satellite was broken up and remoulded, but what scale may such an event require, indeed, what is the required scale of such a catastrophe to be able to break up Miranda and then allow it to assemble? (there seem to be some similar groove patterns on Ariel but on a much smaller scale) Whats everyone's take on this particular enigma?

I'm not sure if this will address your ignorance or expose mine. But here goes. :D

Given the mass of Miranda: 6.3E19kg and its radius: 236,000m we can calculate its gravitational binding energy (http://www.internet-encyclopedia.org/wiki.php?title=Gravitational_binding_energy).

GBE = 3/5(GM^2/r) = 3/5 * (G * 6.3E19kg^2 / 236,000m) = 6.7E23 J

The above equation assumes a uniform spherical mass, which Miranda is not, but it gives us a ball park number. This amount of energy would blow Miranda apart. Since we know that Miranda was able to re-form, this number is only an upper bound.

For comparison, a 1 megaton detonation is equivalent to 4.2E15 J. This would be about 1.6E8 Megatons.



Another question, is regarding the other moons of Uranus. They seem to be mainly captured asteroids, can they be regarded as KBOs, being outside the Asteroid belt and might have had initial orbits taking them outside the orbit of Neptune? And can the same be said about Neptune's satellites, like Thalassa, Proteus, etc. where many seem to be captured asteroids?

I haven't heard this before, but it doesn't seem unreasonable.



The last question (thanks for reading this far!) is regarding Triton. Why does it orbit Neptune in the opposite direction to Neptune's other moons? Is the probable event again catastrophic?

Sorry about all these questions, but may God bless the kind souls who forgive my ignorance :)

IIRC, the theory is that Triton was captured by Neptune. Its highly inclined and retrograde orbit was a result of its orbit before is was captured. I don't think this qualifies as catastrophic, but it is very odd. :D

Candy
2004-Jun-16, 03:23 AM
I'm not sure if this will address your ignorance or expose mine. But here goes. :D What no photos?

milli360
2004-Jun-16, 05:37 AM
So no loving soul is going to take mercy on my ignorance
You got that right. :)

Miranda (http://www.solarviews.com/eng/miranda.htm)'s chevroning and deep canyons has been fascinating a lot of people. Once, at an AGU (http://www.agu.org) meeting, Bob Pappalardo (http://www.colorado.edu/news/releases/2003/340.html) heard my spiel about spherical harmonics in the Earth geoid, and told me about his theory of 3,2 spherical harmonic (l=3, m=2) (http://stephan.sugarmotor.org/harmonics/) convection on Miranda. It took only a few minutes to persuade him that that wouldn't work--I think he figured it out when I began to talk.

Tranquility
2004-Jun-16, 10:36 AM
You got that right :)
Yes, well at least that's something. :) Its weird though that people only reply once Candy does. :lol: The bloody threat was sitting dormant for two days until she breathed life into it. :o


Given the mass of Miranda: 6.3E19kg and its radius: 236,000m we can calculate its gravitational binding energy.

GBE = 3/5(GM^2/r) = 3/5 * (G * 6.3E19kg^2 / 236,000m) = 6.7E23 J

The above equation assumes a uniform spherical mass, which Miranda is not, but it gives us a ball park number. This amount of energy would blow Miranda apart. Since we know that Miranda was able to re-form, this number is only an upper bound.

For comparison, a 1 megaton detonation is equivalent to 4.2E15 J. This would be about 1.6E8 Megatons.

Thanks a lot for showing the calculations. Wouldn't it seem though, that a catastrophic event that seems to have broken up Miranda and "knocked over" Uranus would annihilate Miranda instead of just breaking it up into pieces that would soon reassemble? And wouldn't it have done considerable damage to the rest of the moons of Uranus?


Once, at an AGU meeting, Bob Pappalardo heard my spiel about spherical harmonics in the Earth geoid, and told me about his theory of 3,2 spherical harmonic (l=3, m=2) convection on Miranda. It took only a few minutes to persuade him that that wouldn't work--I think he figured it out when I began to talk.

Okay I started to get the gist of 3,2 spherical harmonics from the link you gave, but I didnt understand anything else. :D

Jason Thompson
2004-Jun-16, 11:13 AM
Wouldn't it seem though, that a catastrophic event that seems to have broken up Miranda and "knocked over" Uranus would annihilate Miranda instead of just breaking it up into pieces that would soon reassemble? And wouldn't it have done considerable damage to the rest of the moons of Uranus?

Why assume that the event that knocked Uranus over was the same as the one that shattered Miranda?

I suspect (and I'm no astronimcal whizz, so I'm open to correction) that Uranus was pelted early on, and the moons formed or were captured later. To me it seems unlikely that knocking over Uranus would neatly bring all the moons and rings with it if they were there before the event took place, though perhaps the system has had time to settle down from such a major disruption.

As for the impact that shattered Miranda, it only needs to have provided just enough energy to break the moon, not send all its constituent parts flying off in separate directions. The larger fragments would soon drift back together again and fuse under their own gravity.

As for Triton, it probably orbits retrograde because it is a captured KBO.

milli360
2004-Jun-16, 12:08 PM
Okay I started to get the gist of 3,2 spherical harmonics from the link you gave, but I didnt understand anything else.
Convection can have favored modes, like the resonant frequencies of bells or drums. Sounds from bells are represented by sine curves of various frequencies--the modes of drums can be two-dimensional functions, and convection in the Earth can be two-dimensional spherical harmonics, as in the illustration. Those spherical harmonics are the same ones used to model the electron orbits in physical chemistry.

He was suggesting that 3,2 convection mode might have been favored for some reason, on Miranda.

The same thing can happen in very large earthquakes, they excite certain modes, and the Earth rings like a bell.

Tranquility
2004-Jun-16, 12:37 PM
Okay I started to get the gist of 3,2 spherical harmonics from the link you gave, but I didnt understand anything else.
Convection can have favored modes, like the resonant frequencies of bells or drums. Sounds from bells are represented by sine curves of various frequencies--the modes of drums can be two-dimensional functions, and convection in the Earth can be two-dimensional spherical harmonics, as in the illustration. Those spherical harmonics are the same ones used to model the electron orbits in physical chemistry.

He was suggesting that 3,2 convection mode might have been favored for some reason, on Miranda.

The same thing can happen in very large earthquakes, they excite certain modes, and the Earth rings like a bell.

Got that. Thanks a lot for the info, something amazing every day :wink: .


Why assume that the event that knocked Uranus over was the same as the one that shattered Miranda?

I suspect (and I'm no astronimcal whizz, so I'm open to correction) that Uranus was pelted early on, and the moons formed or were captured later. To me it seems unlikely that knocking over Uranus would neatly bring all the moons and rings with it if they were there before the event took place, though perhaps the system has had time to settle down from such a major disruption.

As for the impact that shattered Miranda, it only needs to have provided just enough energy to break the moon, not send all its constituent parts flying off in separate directions. The larger fragments would soon drift back together again and fuse under their own gravity.

Got that as well. Thanks for clearing it up. :)

Hamlet
2004-Jun-16, 02:32 PM
You got that right :)
Yes, well at least that's something. :) Its weird though that people only reply once Candy does. :lol: The bloody threat was sitting dormant for two days until she breathed life into it. :o

Actually I started my reply before I saw Candy's, but she beat me to the post button. :D




Given the mass of Miranda: 6.3E19kg and its radius: 236,000m we can calculate its gravitational binding energy.

GBE = 3/5(GM^2/r) = 3/5 * (G * 6.3E19kg^2 / 236,000m) = 6.7E23 J

The above equation assumes a uniform spherical mass, which Miranda is not, but it gives us a ball park number. This amount of energy would blow Miranda apart. Since we know that Miranda was able to re-form, this number is only an upper bound.

For comparison, a 1 megaton detonation is equivalent to 4.2E15 J. This would be about 1.6E8 Megatons.

Thanks a lot for showing the calculations. Wouldn't it seem though, that a catastrophic event that seems to have broken up Miranda and "knocked over" Uranus would annihilate Miranda instead of just breaking it up into pieces that would soon reassemble? And wouldn't it have done considerable damage to the rest of the moons of Uranus?

I don't think we have evidence that these events were caused by the same interloper. I think it's more likely that Miranda was hit be a different impactor than the one that laid out Uranus.

Tranquility
2004-Jun-16, 02:33 PM
What an unfortunate planet :D

Hamlet
2004-Jun-16, 02:34 PM
I'm not sure if this will address your ignorance or expose mine. But here goes. :D What no photos?

You're a naughty girl, aren't you? :D