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What's this bit about not forming a true asteroid family because they don't "descend from a common parent body"? As I understand, an asteroid family is defined by having common orbital elements--anyway, is it even commonly accepted that any of the asteroids have a common parent body? I'm going to comment it out as OR. -- Aelffin 17:06, 30 August 2006 (UTC)
I think the article should point out that the orbit of each Hilda asteroid is generally elliptic, and the apparent triangle is just a dynamic sum of all Hildas at each point in time with a reference rotating along Jupiter's orbit. A figure should be included to illustrate a single Hilda's orbit demonstrating that it travels through all of Jupiter's L3, L4 and L5 through 3 cycles (2 Jupiter cycles).
Background: As an amateur astronomer I am well aware of Kepler's laws, and so it astonished me to read this article about a special group of asteroids apparently moving in triangular orbits. This misunderstanding was based on the following text and also the graphs:
Hildas move in their 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.
Not really believing it I sketched possible orbits by hand and realised: These asteroids, as most celestial bodies, generally demonstrate elliptic orbits where the speed is slower at aphelion (at a Hilda triangular vertex, near Jupiter's L3, L4 or L5) and faster at perihelion (at the middle of a Hilda triangular edge). Indeed each object passes through L3, L5 and L4 in that order in 3 orbits, but each elliptic orbit remains relatively constant.
I believe the concentration of Hildas at the L3, L4 and L5 points is explained partly by the generally slower speed of objects at their respective aphelia and partly by the special gravitation potentials at the Lagrange points. Assuming this is substantiated by literature it should also be included in the article.
-- Eddi ( Talk) 02:49, 24 November 2007 (UTC)
Such a diagram is easy enough to make, but is style consistancy important? I usually make plots with GNUplot, which means they look vaguely like the one on the right (which I made). What's that plot made with? Super Mongo? Wily D 14:47, 24 November 2007 (UTC)
Very well! (And the restart is just fine.) I suppose the sun, planet and asteroid can be shown as dots or something instead of crosses. It would also be neat if the Trojan, Greek and Hilda regions could be indicated on the outer circle orbiting along with Jupiter, so that the asteroid's passing through or near all those regions can be observed. -- Eddi ( Talk) 23:58, 4 December 2007 (UTC)
Since I don't know how to make animations I made a series of 12 drawings that span 2 orbits of Jupiter and 3 orbits of Hilda. One constellation is shown to the right; click here for all 12. With this series I try to show that Jupiter's Lagrange points move in orbits that overlap exactly with Jupiter's orbit, only at −60, +60 and 180 degrees angles to the planet, and that successive aphelia of Hilda coincide with L5, L4 and L3. My 12 steps are of course very crude, but I think this principle can be animated rather smoothly. The plot would include 5 objects travelling around the sun, of which 4 with identical orbits (Jupiter, L3, L4 and L5) and one with a smaller orbit (Hilda). If there is no limit to the number of objects in a plot, they could just be represented by different symbols, for example big dots for Jupiter and Hilda, and circles for the Lagrange points. -- Eddi ( Talk) 00:31, 6 December 2007 (UTC)
So I animated that to poor result - I think to do anything like this effectively, we'd need to be in jupiter's frame, and I'm not sure how well that'd go - it'd probably also need to be less jumpy. Wily D 19:40, 13 December 2007 (UTC)
In one place this article says the Hilda asteroids are in 2:3 resonance with Jupiter; in another it is 3:2. Which is it? -- 23:26, 5 August 2009 (UTC)~ltaylor@csub.edu Larry Taylor —Preceding unsigned comment added by 66.75.198.179 ( talk)
The eytomology needs to be included. 174.3.123.220 ( talk) 04:26, 20 May 2010 (UTC)
Most of the orbital resonance points in the astroid belt are devoid of asteroids. These are called the Kirkwood gaps. But the Hildas are apparently the exceptions to this rule. Does anybody know why? If so, it should be in the article, if not, it should be mentioned as an unanswered question. — MiguelMunoz ( talk) 06:25, 15 June 2012 (UTC)
The Article should say whether similar families are known to exist, for other planets and/or other resonance ratios. 94.30.84.71 ( talk) 10:10, 16 June 2012 (UTC)
Dear main authors; thank you for the good work. I am not happy with the sentence: "Consequently, a Hilda's orbit has a semi-major axis between 3.7 AU and 4.2 AU, an eccentricity less than 0.3, and an inclination less than 20°."
Regards, Herbmuell ( talk) 03:15, 27 January 2016 (UTC)
I made a plot of two 3:2 orbits in the rotating frame. (I disregarded effects of Jupiter's gravity, though that's kinda contrary to the spirit.) The two differ in eccentricity: the black one touches the Trojan points, and the red one has a cusp where it "stands still" at aphelion. I'd like to add one for the eccentricity below which the curve is everywhere convex, but don't know how to find it. — Tamfang ( talk) 08:22, 9 February 2016 (UTC)
Ref. 4 of the article, Brož, M.; Vokrouhlický, D. (2008), can be downloaded from arxiv. These authors call the Hilda asteroids a group, and so does the beginning of this article. The group consists of two families, the Hilda family and the Schubart family; the article also says so. Clearly, this article is about the Hilda group, and not the family. I suggest therefore to rename it "Hilda group". If we can agree on this terminology, the articles 153 Hilda and 1911 Schubart would then also have to be corrected similarly (distinction between group and family). See also the articles Asteroid family and List of minor-planet groups on this topic. -- Herbmuell ( talk) 15:07, 19 November 2016 (UTC)
How stable are the orbits of these asteroids? The main article sort of SUGGESTS, without actually explicitly saying, that they are stable for a long time. That is, that their Keplerian elements change only very "slowly". But how "long" is "long? Hundreds of years? Thousands? Millions? And how do their orbits "decay"?
On a related topic ... "The Hildas Triangle has proven to be dynamically stable over a long time span". What exactly does this mean? Is this the same thing as the previous question? If not, then what is it? And again, what is a "long time" in this context? So many questions... — Preceding unsigned comment added by 2001:8003:E422:3C01:BCD6:9922:BB24:C3D0 ( talk) 09:22, 30 December 2021 (UTC)
It needs to be explicitly stated that these asteroids orbit around THE SUN, not Jupiter. Even though the animations and the diagrams make this clear, well at least to me. I say this because in the Talk section for the Trojan asteroids, which whilst of course different from the Hildas, do arguably share some common factors with Hildas, there is quite a bit of confusion about this. — Preceding unsigned comment added by 2001:8003:E422:3C01:BCD6:9922:BB24:C3D0 ( talk) 09:27, 30 December 2021 (UTC)
There should be a bit of a discussion of this. In this discussion shoudl be included something like the following:
From the diagram with the red and green orbits, it can be seen that the closest approach between asteroid and Jupiter - that is, when Jupiter is in opposition - occurs when the asteroid is at perihelion, and thus at its furthest from Jupiter. This would presumeably minimise the gravitational perturbation of Jupiter.
Also .... is this the case for ALL Hilda asteroids, or only Hilda itself? — Preceding unsigned comment added by 2001:8003:E422:3C01:C2D:60A8:DA74:74FD ( talk) 22:33, 30 December 2021 (UTC)
You have: "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, averaging 2.5 to 3.0 years. "
This seems very incorrect. If you look at the animated gif, the aphelion "rest" is more like 2-3 years, and the "rapid siding" is more like 5-6 years.
Also, it is perhaps way too simplistic to describe this with one set of values. Orbits with low eccentricities, such as Hilda herself, have "sharp" apices, like the red one, and the "rest" period is relatively short. Orbits with larger eccentricities have "lobes" at their apices, like the black one, and the "rest" period is much longer. — Preceding unsigned comment added by 2001:8003:E422:3C01:B5C0:7521:E3E5:C5E7 ( talk) 03:29, 1 January 2022 (UTC)
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What's this bit about not forming a true asteroid family because they don't "descend from a common parent body"? As I understand, an asteroid family is defined by having common orbital elements--anyway, is it even commonly accepted that any of the asteroids have a common parent body? I'm going to comment it out as OR. -- Aelffin 17:06, 30 August 2006 (UTC)
I think the article should point out that the orbit of each Hilda asteroid is generally elliptic, and the apparent triangle is just a dynamic sum of all Hildas at each point in time with a reference rotating along Jupiter's orbit. A figure should be included to illustrate a single Hilda's orbit demonstrating that it travels through all of Jupiter's L3, L4 and L5 through 3 cycles (2 Jupiter cycles).
Background: As an amateur astronomer I am well aware of Kepler's laws, and so it astonished me to read this article about a special group of asteroids apparently moving in triangular orbits. This misunderstanding was based on the following text and also the graphs:
Hildas move in their 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.
Not really believing it I sketched possible orbits by hand and realised: These asteroids, as most celestial bodies, generally demonstrate elliptic orbits where the speed is slower at aphelion (at a Hilda triangular vertex, near Jupiter's L3, L4 or L5) and faster at perihelion (at the middle of a Hilda triangular edge). Indeed each object passes through L3, L5 and L4 in that order in 3 orbits, but each elliptic orbit remains relatively constant.
I believe the concentration of Hildas at the L3, L4 and L5 points is explained partly by the generally slower speed of objects at their respective aphelia and partly by the special gravitation potentials at the Lagrange points. Assuming this is substantiated by literature it should also be included in the article.
-- Eddi ( Talk) 02:49, 24 November 2007 (UTC)
Such a diagram is easy enough to make, but is style consistancy important? I usually make plots with GNUplot, which means they look vaguely like the one on the right (which I made). What's that plot made with? Super Mongo? Wily D 14:47, 24 November 2007 (UTC)
Very well! (And the restart is just fine.) I suppose the sun, planet and asteroid can be shown as dots or something instead of crosses. It would also be neat if the Trojan, Greek and Hilda regions could be indicated on the outer circle orbiting along with Jupiter, so that the asteroid's passing through or near all those regions can be observed. -- Eddi ( Talk) 23:58, 4 December 2007 (UTC)
Since I don't know how to make animations I made a series of 12 drawings that span 2 orbits of Jupiter and 3 orbits of Hilda. One constellation is shown to the right; click here for all 12. With this series I try to show that Jupiter's Lagrange points move in orbits that overlap exactly with Jupiter's orbit, only at −60, +60 and 180 degrees angles to the planet, and that successive aphelia of Hilda coincide with L5, L4 and L3. My 12 steps are of course very crude, but I think this principle can be animated rather smoothly. The plot would include 5 objects travelling around the sun, of which 4 with identical orbits (Jupiter, L3, L4 and L5) and one with a smaller orbit (Hilda). If there is no limit to the number of objects in a plot, they could just be represented by different symbols, for example big dots for Jupiter and Hilda, and circles for the Lagrange points. -- Eddi ( Talk) 00:31, 6 December 2007 (UTC)
So I animated that to poor result - I think to do anything like this effectively, we'd need to be in jupiter's frame, and I'm not sure how well that'd go - it'd probably also need to be less jumpy. Wily D 19:40, 13 December 2007 (UTC)
In one place this article says the Hilda asteroids are in 2:3 resonance with Jupiter; in another it is 3:2. Which is it? -- 23:26, 5 August 2009 (UTC)~ltaylor@csub.edu Larry Taylor —Preceding unsigned comment added by 66.75.198.179 ( talk)
The eytomology needs to be included. 174.3.123.220 ( talk) 04:26, 20 May 2010 (UTC)
Most of the orbital resonance points in the astroid belt are devoid of asteroids. These are called the Kirkwood gaps. But the Hildas are apparently the exceptions to this rule. Does anybody know why? If so, it should be in the article, if not, it should be mentioned as an unanswered question. — MiguelMunoz ( talk) 06:25, 15 June 2012 (UTC)
The Article should say whether similar families are known to exist, for other planets and/or other resonance ratios. 94.30.84.71 ( talk) 10:10, 16 June 2012 (UTC)
Dear main authors; thank you for the good work. I am not happy with the sentence: "Consequently, a Hilda's orbit has a semi-major axis between 3.7 AU and 4.2 AU, an eccentricity less than 0.3, and an inclination less than 20°."
Regards, Herbmuell ( talk) 03:15, 27 January 2016 (UTC)
I made a plot of two 3:2 orbits in the rotating frame. (I disregarded effects of Jupiter's gravity, though that's kinda contrary to the spirit.) The two differ in eccentricity: the black one touches the Trojan points, and the red one has a cusp where it "stands still" at aphelion. I'd like to add one for the eccentricity below which the curve is everywhere convex, but don't know how to find it. — Tamfang ( talk) 08:22, 9 February 2016 (UTC)
Ref. 4 of the article, Brož, M.; Vokrouhlický, D. (2008), can be downloaded from arxiv. These authors call the Hilda asteroids a group, and so does the beginning of this article. The group consists of two families, the Hilda family and the Schubart family; the article also says so. Clearly, this article is about the Hilda group, and not the family. I suggest therefore to rename it "Hilda group". If we can agree on this terminology, the articles 153 Hilda and 1911 Schubart would then also have to be corrected similarly (distinction between group and family). See also the articles Asteroid family and List of minor-planet groups on this topic. -- Herbmuell ( talk) 15:07, 19 November 2016 (UTC)
How stable are the orbits of these asteroids? The main article sort of SUGGESTS, without actually explicitly saying, that they are stable for a long time. That is, that their Keplerian elements change only very "slowly". But how "long" is "long? Hundreds of years? Thousands? Millions? And how do their orbits "decay"?
On a related topic ... "The Hildas Triangle has proven to be dynamically stable over a long time span". What exactly does this mean? Is this the same thing as the previous question? If not, then what is it? And again, what is a "long time" in this context? So many questions... — Preceding unsigned comment added by 2001:8003:E422:3C01:BCD6:9922:BB24:C3D0 ( talk) 09:22, 30 December 2021 (UTC)
It needs to be explicitly stated that these asteroids orbit around THE SUN, not Jupiter. Even though the animations and the diagrams make this clear, well at least to me. I say this because in the Talk section for the Trojan asteroids, which whilst of course different from the Hildas, do arguably share some common factors with Hildas, there is quite a bit of confusion about this. — Preceding unsigned comment added by 2001:8003:E422:3C01:BCD6:9922:BB24:C3D0 ( talk) 09:27, 30 December 2021 (UTC)
There should be a bit of a discussion of this. In this discussion shoudl be included something like the following:
From the diagram with the red and green orbits, it can be seen that the closest approach between asteroid and Jupiter - that is, when Jupiter is in opposition - occurs when the asteroid is at perihelion, and thus at its furthest from Jupiter. This would presumeably minimise the gravitational perturbation of Jupiter.
Also .... is this the case for ALL Hilda asteroids, or only Hilda itself? — Preceding unsigned comment added by 2001:8003:E422:3C01:C2D:60A8:DA74:74FD ( talk) 22:33, 30 December 2021 (UTC)
You have: "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, averaging 2.5 to 3.0 years. "
This seems very incorrect. If you look at the animated gif, the aphelion "rest" is more like 2-3 years, and the "rapid siding" is more like 5-6 years.
Also, it is perhaps way too simplistic to describe this with one set of values. Orbits with low eccentricities, such as Hilda herself, have "sharp" apices, like the red one, and the "rest" period is relatively short. Orbits with larger eccentricities have "lobes" at their apices, like the black one, and the "rest" period is much longer. — Preceding unsigned comment added by 2001:8003:E422:3C01:B5C0:7521:E3E5:C5E7 ( talk) 03:29, 1 January 2022 (UTC)