6 Years of Saturn (2009 September 4)

[zbvhs]

If you think about it, the Sun has a ring as well (the Asteroids). Curious how the four inner planets are so very different from the four outer gas giants and the Asteroids are in between. How do you suppose that happened?

[Chris Peterson]

If you think about it, the Sun has a ring as well (the Asteroids). Curious how the four inner planets are so very different from the four outer gas giants and the Asteroids are in between. How do you suppose that happened?

There has been a lot of research in the area of how planetary systems form, with huge progress made in the last few years as computer power has increased and computer models have improved (this is something that pretty much requires simulation techniques to study). While much remains to be understood, what it probably boils down to is that during the formation of a stellar system, there is a gradient of conditions (temperature, density, type of material, etc) extending outwards from the central star or protostar. Details aside, it seems very reasonable that if you have a range of conditions like this, you're likely to see a range of different planet types condense.

Once you have some planets- especially a gas giant or two- the gravitational interactions between them create resonances and zones of stability and instability. This results in a rapid clearing of material from much of the intervening space, and the possible creation of rubble zones like the asteroid belt (which does share some similarity to planetary ring systems, but is also different in important ways).

[neufer]

If you think about it, the Sun has a ring as well (the Asteroids).

Two major rings: The Kuiper belt & The Main asteroid belt

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The Kuiper belt, set against the four Gas giants
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The Main asteroid belt, set against the four rocky terrestrials:

[orin stepanek]

Don't look like Jupiter cleared it's orbit; what with the Trojans and the Greeks still out there. Aww; just making a case for Pluto! 8)

Orin

[bystander]

Don't look like Jupiter cleared it's orbit; what with the Trojans and the Greeks still out there. Aww; just making a case for Pluto! 8)

Just as long as they stay on their own sides. Don't want them to start fighting again. Helen isn't worth it.

[neufer]

Don't look like Jupiter cleared it's orbit; what with the Trojans and the Greeks still out there. Aww; just making a case for Pluto! 8)

Just as long as they stay on their own sides. Don't want them to start fighting again. Helen isn't worth it.

Ah, but is Hilda worth it?

<<The Hilda family of asteroids consists of asteroids with a semi-major axis between 3.7 AU and 4.2 AU,
an eccentricity greater than 0.07, and an inclination less than 20°.

They do not form a true asteroid family, in the sense that they do not descend from a common parent object. Instead, this is a dynamical family of bodies, made up of asteroids which are in a 2:3 orbital resonance with Jupiter. Hildas move in their elliptical orbits so that their aphelia put them opposite Jupiter, or 60 degrees ahead of or behind Jupiter at the L4 and L5 Lagrangian points. Over three successive orbits each Hilda asteroid passes through all of these three points in sequence. The namesake is 153 Hilda, discovered by Johann Palisa in 1875.

• ------------------------------------------------------------
  A schematic of the orbit of 153 Hilda (green), with Jupiter (red)
  
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The asteroids of the Hilda group (Hildas) are in 3:2 mean motion resonance with Jupiter. That is, their orbital periods are 2/3 that of Jupiter. They move along the orbits with a semimajor axis near 4.0 AU and moderate values of eccentricity (up to 0.3) and inclination (up to 20°). Unlike the Trojan asteroids they may have any difference in longitude with Jupiter, nevertheless avoiding dangerous approaches to the planet.

The Hildas taken together constitute a dynamic triangular figure with slightly convex sides and trimmed apexes in the triangular libration points of Jupiter - the "Hildas Triangle". The "asteroidal stream" within the sides of the triangle is about 1 AU wide, and in the apexes this value is 20-40 % greater.

Each of the Hilda objects moves along its own elliptic orbit. However, at any moment the Hildas together constitute this triangular configuration, and all the orbits together form a quite predictable ring. Figure 2 illustrates this with the Hildas positions (black) against a background of their orbits (gray).

Left: The Hildas Triangle against a background of all known asteroids up to Jupiter's orbit.
Right: The positions of the Hildas against a background of their orbits.

For the majority of these asteroids their position in orbit may be arbitrary except for the external parts of the apexes (the objects near aphelion) and the middles of the sides (the objects near perihelion). The Hildas Triangle has proven to be dynamically stable for a long time span.

The typical Hilda object has a retrograde perihelion motion. On average the velocity of perihelion motion is greater as the orbital eccentricity is lesser, while the nodes move more slowly. All typical objects in aphelion would seemingly approach closely to Jupiter, which should be disstabilising for them. But the adjustment of orbital elements over time helps to avoid this, and conjunctions with Jupiter occur only near the perihelion of Hilda asteroids. Moreover the apsidal line oscillates near the line of conjunction with different amplitude and a period of 2.5 to 3.0 centuries.

In addition to the fact that the Hildas triangle revolves in connection to Jupiter the quasi-periodical waves of the stream density of asteroids in every point are noticed, as if the triangle "breathes". At any time the density of objects in the triangle's apexes is more than twice the density within the sides. The Hildas rest at their aphelia in the apexes for an average of 5.0-5.5 years whereas they move along the sides more quickly for 2.5 to 3.0 years. The orbital periods of these asteroids are approximately 7.9 years, or 2/3 that of Jupiter.>>

[bystander]

Ah, but is Hilda worth it?

IMHO, no. She's a little too full figured for my tastes. Reminds me of my mother, and contrary to the song, I don't want a girl like dad married. Besides, she seems to be playing both the Trojans and the Greeks off against Jupiter. Of course, Jupiter is a god.

http://en.wikipedia.org/wiki/Hildas

On a more serious note, what strange dynamics. Seems like there would be destructive interaction with the Greeks and the Trojans, as well as with the outer part of the main astroid belt. Are the numbers of Greeks, Trojans, and Hildas changing?

[neufer]

Ah, but is Hilda worth it?

IMHO, no. She's a little too full figured for my tastes. Reminds me of my mother, and contrary to the song, I don't want a girl like dad married. Besides, she seems to be playing both the Trojans and the Greeks off against Jupiter.

Still, neither Hilda nor the Trojan or Greeks camps have enough mass in themselves to gravitationally affect the others (or themselves).
[I'm sure the same applies to your mom. ]

http://en.wikipedia.org/wiki/Hildas

On a more serious note, what strange dynamics. Seems like there would be destructive interaction with the Greeks and the Trojans, as well as with the outer part of the main asteroid belt.

A "destructive interaction with the Greeks and the Trojans!" What a great idea for an epic novel!

Stabilizing 3:2 & 2:3 triangular resonances allow for a careful choreographed dance around the point of closest orbital contact with the nearest large perturber. This is the basis of Plutinos.

A 3:2 triangular resonance can also stabilize a shepherding satellite like Pandora which, in turn, forms a sharp outer edge to a ring system that contains destabilizing 2:1 and 3:1 resonance ring gaps:

<<Mimas is responsible for clearing the material from the Cassini Division, the gap between Saturn's two widest rings, A ring and B ring. Particles at the inner edge of the Cassini division are in a 2:1 resonance with Mimas. They orbit twice for each orbit of Mimas. The repeated pulls by Mimas on the Cassini division particles, always in the same direction in space, force them into new orbits outside the gap. Other resonances with Mimas are also responsible for other features in Saturn's rings: the boundary between the C and B ring is at the 3:1 resonance and the outer F ring shepherd, Pandora, is at the 3:2 resonance. More recently, a 7:6 corotation eccentricity resonance has been discovered with the G ring, whose inner edge is about 15 000 km inside the orbit of Mimas.>>

[bystander]

A "destructive interaction with the Greeks and the Trojans!" What a great idea for an epic novel!

Or an epic poem, though why anybody would want to read a novel length poem is beyond me, or write one for that matter.

Still, with all the Hildas flirting with all the Greeks and Trojans, it seems it would go bad at least once, and once one went bad ...

[orin stepanek]

My neighbor lady was Hilda. She was tiny; but her sons were big. They could probably keep the Trojans and the Greeks at bay.

Orin

[neufer]

My neighbor lady was Hilda. She was tiny; but her sons were big.
They could probably keep the Trojans and the Greeks at bay.

An Indian chief had three wives, each of whom was pregnant.

The first gave birth to a boy.
The chief was so elated he built her a teepee made of deer hide.

A few days later, the second gave birth, also to a boy.
The chief was very happy. He built her a teepee made of antelope hide.

The third wife gave birth a few days later, but the chief kept the details a secret.
He built this one a two-story teepee, made out of hippopotamus hide.

The chief then challenged members of the tribe to guess what had occurred.
Many tried, unsuccessfully.

Finally, one young brave declared that the third wife had given birth to twin boys.

“Correct,” said the chief. “How did you figure it out?”

The warrior answered, “It's elementary.
The value of the squaw of the hippopotamus
is equal to the sons of the squaws of the other two hides.”

[bystander]

The value of the squaw of the hippopotamus
is equal to the sons of the squaws of the other two hides.

[sic]