What favors orbit or collision of two planetoids ?

[dougettinger]

Assume that two sizable planetoids are in similar orbits traveling in the same direction. Assume that one is 1/4 the size of the other in mass. Three possible scenarios could possibly occur. One is a collision between the two bodies; another is the ejection of one or both from their orbital region; and the third scenario would be that one starts orbiting the other. What are the differences in the basic parameters needed to cause each scenario ? Supposely, all these scenarios occurred in the Asteroid Belt. Some asteroids may be shepherded by larger asteroids and do not actually orbit, but are closely bound by gravitational forces.

Doug Ettinger, Pittsburgh, PA 02/15/2011

[Chris Peterson]

Assume that two sizable planetoids are in similar orbits traveling in the same direction. Assume that one is 1/4 the size of the other in mass. Three possible scenarios could possibly occur. One is a collision between the two bodies; another is the ejection of one or both from their orbital region; and the third scenario would be that one starts orbiting the other. What are the differences in the basic parameters needed to cause each scenario ? Supposely, all these scenarios occurred in the Asteroid Belt. Some asteroids may be shepherded by larger asteroids and do not actually orbit, but are closely bound by gravitational forces.

There is no evidence of planetoids colliding in the asteroid belt. Certainly there have been many collisions between asteroids, but those collisions are random events. The actual orbits of bodies in the asteroid belt is determined by body position, with perturbations from the gas giants, mainly Jupiter. Individual asteroids don't perturb one another.

In a pure three-body system like you outline, you can't make any generalizations. Except for a few very special cases (which would not likely occur naturally) the system is chaotic, and very small changes in any orbital parameters can produce any of the scenarios you suggest. You have left out what is perhaps the most likely scenario, that both bodies simply end up in different orbits. A collision is extremely unlikely, and a capture only slightly less so.

[dougettinger]

I am alluding to certain examples in the solar system. They are irregular satellites of Mars and the outer planets that were mostly captured. Also, the moons of dwarf planets including those of Pluto are other examples. In the Asteroid Belt, I remember seeing photography from space probes of at least one asteroid having a nearby partner that was gravitationally bound to the larger body. In our time there was the collision of a comet with Jupiter.

In the nebula hypotheses the accretion process requires collisions of both small and large objects. Numerous and massive collisions were required over short periods of cosmic time in order to produce the planets. What are the differences in parameters when objects coming close enough to orbit the other or be shepherded by the larger body and not smash into each other ? I am looking for such parameters as - 1) there must always be an N-body criteria; 2) their vector velocities must be in the same plane; 3) their passing distance and and masses must have a certain ratio; 4) their passing distance and velocity difference must have a certain ratio; etc. Are there any cookbook parameters for cause of the shepherding or the orbiting of two celestial bodies ?

Doug Ettinger, Pittsburgh, Pa 02/15/2011

[Chris Peterson]

I am alluding to certain examples in the solar system. They are irregular satellites of Mars and the outer planets that were mostly captured. Also, the moons of dwarf planets including those of Pluto are other examples. In the Asteroid Belt, I remember seeing photography from space probes of at least one asteroid having a nearby partner that was gravitationally bound to the larger body. In our time there was the collision of a comet with Jupiter.

But none of these are suggestive of extrasolar bodies. Moons can be captured by planets because that is an inherently three-body situation: moon-planet-Sun. And as previously noted, collisions do occur in the asteroid belt, although they are rare.

In the nebula hypotheses the accretion process requires collisions of both small and large objects. Numerous and massive collisions were required over short periods of cosmic time in order to produce the planets. What are the differences in parameters when objects coming close enough to orbit the other or be shepherded by the larger body and not smash into each other ? I am looking for such parameters as - 1) there must always be an N-body criteria; 2) their vector velocities must be in the same plane; 3) their passing distance and and masses must have a certain ratio; 4) their passing distance and velocity difference must have a certain ratio; etc. Are there any cookbook parameters for cause of the shepherding or the orbiting of two celestial bodies ?

No. Two bodies will collide if their orbits intersect and their locations along each orbit coincide within a narrow time window. You don't need more than two bodies, they don't need their velocity vectors on the same plane, their masses and distance apart are largely irrelevant, except for the case where their distance is less than their sizes- which is what defines a collision!

[dougettinger]

I am alluding to certain examples in the solar system. They are irregular satellites of Mars and the outer planets that were mostly captured. Also, the moons of dwarf planets including those of Pluto are other examples. In the Asteroid Belt, I remember seeing photography from space probes of at least one asteroid having a nearby partner that was gravitationally bound to the larger body. In our time there was the collision of a comet with Jupiter.

But none of these are suggestive of extrasolar bodies. Moons can be captured by planets because that is an inherently three-body situation: moon-planet-Sun. And as previously noted, collisions do occur in the asteroid belt, although they are rare.

In the nebula hypotheses the accretion process requires collisions of both small and large objects. Numerous and massive collisions were required over short periods of cosmic time in order to produce the planets. What are the differences in parameters when objects coming close enough to orbit the other or be shepherded by the larger body and not smash into each other ? I am looking for such parameters as - 1) there must always be an N-body criteria; 2) their vector velocities must be in the same plane; 3) their passing distance and and masses must have a certain ratio; 4) their passing distance and velocity difference must have a certain ratio; etc. Are there any cookbook parameters for cause of the shepherding or the orbiting of two celestial bodies ?

No. Two bodies will collide if their orbits intersect and their locations along each orbit coincide within a narrow time window. You don't need more than two bodies, they don't need their velocity vectors on the same plane, their masses and distance apart are largely irrelevant, except for the case where their distance is less than their sizes- which is what defines a collision!

I may have been too general in my line of questioning. Firstly, I only am referring to solar system objects in this topic.
I will become more specific. What were the differences in the parameters that caused a comet to spiral inward and hit Jupiter and caused numerous irregular moons to orbit Jupiter at some time in the distant past ? Why did the larger asteroid shepherd a smaller asteroid and not collide with it ? It is truly unbelievable that those two asteroids did not smash each oher or zip past each other with their different trajectories and velocities.

Doug ettinger, Pittsburfgh, PA 02/15/2011

[Chris Peterson]

What were the differences in the parameters that caused a comet to spiral inward and hit Jupiter and caused numerous irregular moons to orbit Jupiter at some time in the distant past ?

I don't understand the question. What "parameters" are you referring to? SL-9 did not spiral inward and hit Jupiter. It was captured by Jupiter, and ended up in a very eccentric orbit (nearly hyperbolic) with its periapsis just above Jupiter's cloud tops. That was inside the Roche limit, and subsequent perturbations were sufficient to tweak the orbit so that periapsis was less than Jupiter's radius.

All of the gas giants have large enough masses that capturing orbiting bodies as moons is possible- indeed, probable given enough time.

Why did the larger asteroid shepherd a smaller asteroid and not collide with it ? It is truly unbelievable that those two asteroids did not smash each oher or zip past each other with their different trajectories and velocities.

What asteroids are you talking about?

[dougettinger]

What were the differences in the parameters that caused a comet to spiral inward and hit Jupiter and caused numerous irregular moons to orbit Jupiter at some time in the distant past ?

I don't understand the question.

What "parameters" are you referring to? SL-9 did not spiral inward and hit Jupiter. It was captured by Jupiter, and ended up in a very eccentric orbit (nearly hyperbolic) with its periapsis just above Jupiter's cloud tops. That was inside the Roche limit, and subsequent perturbations were sufficient to tweak the orbit so that periapsis was less than Jupiter's radius.

All of the gas giants have large enough masses that capturing orbiting bodies as moons is possible- indeed, probable given enough time.

If I know the masses of a possible parent planet and "the near-eccounter-passing object", the minimum passing distance, and the velocity of the passing object, is there any reference or equation(s) that can predict whether it will be captured into an elliptical orbit or simply pass by in an hyperbolic or parabolic trajectory ?

Why did the larger asteroid shepherd a smaller asteroid and not collide with it ? It is truly unbelievable that those two asteroids did not smash each oher or zip past each other with their different trajectories and velocities.

What asteroids are you talking about?

From my files I found Asteroid 87 Sylvia with her two moons (SN:7/28/01,p. 61) that apparently orbit. Then there is Asteroid 243 Ida and its moon Dactyl listed in Wikipedia. Then there is the statement in SN: 728/01, p.61 that claims about one out of every eight asteroids orbiting near Earth travels with a compainion.

Doug Ettinger, Pittsburgh, PA 02/16/2011

[Chris Peterson]

If I know the masses of a possible parent planet and "the near-eccounter-passing object", the minimum passing distance, and the velocity of the passing object, is there any reference or equation(s) that can predict whether it will be captured into an elliptical orbit or simply pass by in an hyperbolic or parabolic trajectory ?

A capture is not possible in that scenario. Neither will the pass change the orbital elements with respect to the large body at all (unless it is so close that the smaller body is tidally broken up, or experiences atmospheric drag).

From my files I found Asteroid 87 Sylvia with her two moons (SN:7/28/01,p. 61) that apparently orbit. Then there is Asteroid 243 Ida and its moon Dactyl listed in Wikipedia. Then there is the statement in SN: 728/01, p.61 that claims about one out of every eight asteroids orbiting near Earth travels with a compainion.

I doubt these are captures. A simpler explanation is that they are asteroids which have come apart, probably as the result of being spun up to high rotation speeds.

[dougettinger]

If I know the masses of a possible parent planet and "the near-eccounter-passing object", the minimum passing distance, and the velocity of the passing object, is there any reference or equation(s) that can predict whether it will be captured into an elliptical orbit or simply pass by in an hyperbolic or parabolic trajectory ?

A capture is not possible in that scenario. Neither will the pass change the orbital elements with respect to the large body at all (unless it is so close that the smaller body is tidally broken up, or experiences atmospheric drag).

The irregular satellites of Mars and the outer planets were not part of the primordal proto-planetary disk. These satellites were captured possibly from perturbations of objects originally in the Asteroid Belt. Very simply - how did these captures occur ?

From my files I found Asteroid 87 Sylvia with her two moons (SN:7/28/01,p. 61) that apparently orbit. Then there is Asteroid 243 Ida and its moon Dactyl listed in Wikipedia. Then there is the statement in SN: 728/01, p.61 that claims about one out of every eight asteroids orbiting near Earth travels with a compainion.

I doubt these are captures. A simpler explanation is that they are asteroids which have come apart, probably as the result of being spun up to high rotation speeds.

One explanation in Wikipedia is that two objects collided and then somehow the bigger pieces came closer together after the initial splattering because escape velocity was never attained. Your so-called simpler explanation seems to be even more improbable. I have seen real meteorites, and it would take immense spinning to break them apart. Where does the energy come from to create this angular momentum ?

Doug Ettinger, Pittsburgh, PA 02/16/2011

[Chris Peterson]

The irregular satellites of Mars and the outer planets were not part of the primordal proto-planetary disk. These satellites were captured possibly from perturbations of objects originally in the Asteroid Belt. Very simply - how did these captures occur ?

It is by no means certain that the satellites of Mars are captured bodies. It is very possible, however. In order to end up in orbit around Mars, they needed to exchange energy with a third body- most likely Jupiter.

One explanation in Wikipedia is that two objects collided and then somehow the bigger pieces came closer together after the initial splattering because escape velocity was never attained. Your so-called simpler explanation seems to be even more improbable. I have seen real meteorites, and it would take immense spinning to break them apart. Where does the energy come from to create this angular momentum ?

Very gentle collisions are a possibility, but are likely to be rare events.

It is now believed that most asteroids are not solid rock, but basically piles of loosely bound rubble. The rotational speed of asteroids tends to increase due to the Yarkovsky effect (now extended to the Yarkovsky–O'Keefe–Radzievskii–Paddack effect). An asteroid absorbs energy from the Sun and radiates it as heat. The radiated photons carry momentum, and radiate non-isotropically. The result is that small asteroids get spun-up, and eventually break apart. This is suspected to be a (maybe the) major source of non-cometary meteorites. It is the most likely explanation for binary asteroids, as well.

[dougettinger]

The irregular satellites of Mars and the outer planets were not part of the primordal proto-planetary disk. These satellites were captured possibly from perturbations of objects originally in the Asteroid Belt. Very simply - how did these captures occur ?

It is by no means certain that the satellites of Mars are captured bodies. It is very possible, however. In order to end up in orbit around Mars, they needed to exchange energy with a third body- most likely Jupiter.

Why cannot astrophysists be certain about the capture of the iregular moons of Mars ? And more than likely they came from the Asteroid Belt. What other mechanism exists for the reason for these Martian moons ?

Likewise, the highly inclined, sometimes retrograde, irregular moons of the outer planets have to be captured bodies. What other option exists ?

It is now believed that most asteroids are not solid rock, but basically piles of loosely bound rubble. The rotational speed of asteroids tends to increase due to the Yarkovsky effect (now extended to the Yarkovsky–O'Keefe–Radzievskii–Paddack effect). An asteroid absorbs energy from the Sun and radiates it as heat. The radiated photons carry momentum, and radiate non-isotropically. The result is that small asteroids get spun-up, and eventually break apart. This is suspected to be a (maybe the) major source of non-cometary meteorites. It is the most likely explanation for binary asteroids, as well.

I read about the Yarkovsky effect and the YORP effect . Thank you for these references. Spin-up that you mentioned where some asteroids would break apart was only suggested for smaller objects and objects within 1 AU of the Sun. It seems that the Yarkovsky effect was utilized more so to explain why some asteriods could move away from their stable orbits into other orbits and then be possibly perturbed by other asteroids. There is a strong need to explain why asteroids have so many different orbits other than those inside the Asteroid Belt. And then there is a pressing need to know how some of the asteroids gained extra energy to be kicked into the outer solar system and be captured by the outer planets.

Doug ettinger, Pittsburgh, PA 02/19/2011

[Chris Peterson]

Why cannot astrophysists be certain about the capture of the iregular moons of Mars ? And more than likely they came from the Asteroid Belt. What other mechanism exists for the reason for these Martian moons ?

The moons may have coalesced in place, during or shortly after the formation of Mars. They may also be the product of a collision between a large body and Mars- something like the way the Moon was formed, but on a smaller scale. The problem is that from a material standpoint, the Martian moons don't seem very much like asteroids.

Likewise, the highly inclined, sometimes retrograde, irregular moons of the outer planets have to be captured bodies. What other option exists ?

I don't know of any theories other than that they are captured bodies. But they were probably captured when these planets still had protolunar discs (the source of their inner moons). These discs provided environments where passing asteroids/planetoids could shed energy, allowing them to be captured. Captures in today's Solar System environment are much more difficult.

I read about the Yarkovsky effect and the YORP effect . Thank you for these references. Spin-up that you mentioned where some asteroids would break apart was only suggested for smaller objects and objects within 1 AU of the Sun.

Not at all. The effect is size dependent, and it is the apparent cause of otherwise high rotation rates for most asteroids (in the asteroid belt). The effect is very strong at that distance for objects smaller than a few kilometers. As I noted, this YORP spin-up is currently the favored theory for the production of a large amount of small debris that eventually produces sporadic meteors.

It seems that the Yarkovsky effect was utilized more so to explain why some asteriods could move away from their stable orbits into other orbits and then be possibly perturbed by other asteroids. There is a strong need to explain why asteroids have so many different orbits other than those inside the Asteroid Belt. And then there is a pressing need to know how some of the asteroids gained extra energy to be kicked into the outer solar system and be captured by the outer planets.

YORP helps explain a lot of dynamics. I don't think there is any mystery surrounding the observed orbits of asteroids outside the belt. And asteroids are not being sent to the outer system and captured by planets. Those captures occurred billions of years ago, when the entire environment of the Solar System was very different from today.

[dougettinger]

Why cannot astrophysists be certain about the capture of the iregular moons of Mars ? And more than likely they came from the Asteroid Belt. What other mechanism exists for the reason for these Martian moons ?

The moons may have coalesced in place, during or shortly after the formation of Mars. They may also be the product of a collision between a large body and Mars- something like the way the Moon was formed, but on a smaller scale. The problem is that from a material standpoint, the Martian moons don't seem very much like asteroid.

I did not know that the Martian moon material differed greatly from asteroids. I remember a report that stated the materials of these moons and Mars was not similar. Would you remember this reference or where I could search ?

Likewise, the highly inclined, sometimes retrograde, irregular moons of the outer planets have to be captured bodies. What other option exists ?

I don't know of any theories other than that they are captured bodies. But they were probably captured when these planets still had protolunar discs (the source of their inner moons). These discs provided environments where passing asteroids/planetoids could shed energy, allowing them to be captured. Captures in today's Solar System environment are much more difficult.

You speak of environments where passing planetoids could shed energy and be captured. Currently, would not the existing family of captured satellites around Jupiter, Jupiter's dust rings, and Jupiter's magnetosphere provide an environment that could aid in shedding energy from a closely passing planetoid to avoid a approximate 2-body event?

I am very curious about the trajectory path of the Shoemaker-Levy 9 Comet that broke apart and struck Jupiter. This comet had a very elliptical orbit that extended from the interior of the Asteriod Belt to some short distance past Jupiter's orbit. It supposely was estimated to have orbited in this manner since the 60's or 70's. The question that seemed not to get answered was what was its origin and how did it find this particular orbit around Jupiter. The pundits of the day made out Jupiter to be a great vacuum cleaner that has saved the inner solar system from being repeatly bombarded by comets. Comets from where ? The SL-9 comet seems to have come from the asteroid belt. Can you shed some light on this puzzle ?

Doug Ettinger, Pittsburgh, PA 02/20/2011

[BMAONE23]

Doug
Have you seen this
http://www.sciencedirect.com/science?_o ... archtype=a
Abstract
Comet D/Shoemaker–Levy 9 orbited Jupiter for decades (P. W. Chodas and D. K. Yeomans 1995,Bull. Am. Astron. Soc.27, 1111–1112; L. A. M. Benner and W. B. McKinnon 1995,Icarus118, 155–168) and was tidally disrupted during the orbit before impact. To estimate the rate of such events and to infer the implications for the comet's previous orbit, we have performed numerical integrations of test particles with orbits similar to those of Jupiter-family comets.

[Chris Peterson]

You speak of environments where passing planetoids could shed energy and be captured. Currently, would not the existing family of captured satellites around Jupiter, Jupiter's dust rings, and Jupiter's magnetosphere provide an environment that could aid in shedding energy from a closely passing planetoid to avoid a approximate 2-body event?

Not really. The magnetosphere is irrelevant, the dust rings are far too tenuous to provide significant drag, and the moons are not massive enough to be effective perturbers outside of a near-miss, which would be unlikely, and would leave a signature in the form of an eccentric orbit for the perturbing body.

I am very curious about the trajectory path of the Shoemaker-Levy 9 Comet that broke apart and struck Jupiter. This comet had a very elliptical orbit that extended from the interior of the Asteriod Belt to some short distance past Jupiter's orbit. It supposely was estimated to have orbited in this manner since the 60's or 70's. The question that seemed not to get answered was what was its origin and how did it find this particular orbit around Jupiter. The pundits of the day made out Jupiter to be a great vacuum cleaner that has saved the inner solar system from being repeatly bombarded by comets. Comets from where ? The SL-9 comet seems to have come from the asteroid belt. Can you shed some light on this puzzle ?

There is no suggestion that SL-9 originated in the asteroid belt. It appears to have been a short period, Jupiter family comet (of which there are many) that was barely captured by Jupiter. The orbit was extremely unstable and chaotic, which makes deterministic back integration of its orbital characteristics impossible; the analysis of the orbital history of the comet has a range of possible solutions. But all are consistent with a Jupiter family comet, as far as I know.

[dougettinger]

So how did the Jupiter family of comets come to be ? By theory they came from the Oort Cloud 5 to 10 thousand years ago. On one of their orbits about the Sun they eventually had near crossings with Jupiter in its orbit and were captured in elliptical orbits with high eccentricity around Jupiter. All these type of comets are eventually destined to fall into Jupiter as comets or as asteroids that have lost their volatiles.

Can we safely say that these captures were made without any serious drag that would occur in a proto-star disk ?

Doug Ettinger, Pittsburgh, PA 02/21/2011

[Chris Peterson]

So how did the Jupiter family of comets come to be ? By theory they came from the Oort Cloud 5 to 10 thousand years ago. On one of their orbits about the Sun they eventually had near crossings with Jupiter in its orbit and were captured in elliptical orbits with high eccentricity around Jupiter. All these type of comets are eventually destined to fall into Jupiter as comets or as asteroids that have lost their volatiles.

Jupiter family comets are not seen as originating in the Oort cloud, which is approximately spherical, but in the Kuiper belt, which is coplanar with the ecliptic. Kuiper belt objects are perturbed into orbits taking them into the inner system, and because they lie on the ecliptic, they will cross the orbit of Jupiter, offering the possibility of additional perturbations. They are not typically captured by Jupiter (SL-9 was a rare exception), but remain in orbit around the Sun, with orbits modified by Jupiter. These are unstable orbits, so Jupiter family comets are short lived, eventually being ejected from the Solar System or colliding with the Sun or a planet.

Can we safely say that these captures were made without any serious drag that would occur in a proto-star disk ?

Yes, since they are observed to be recent additions to their current orbits, and since it is easy enough to construct the conditions of an inner system capture of a Kuiper belt object.

[dougettinger]

That leaves one final question in this matter. Where did the Kuiper belt objects including its dwarf planets come from ? From the Oort Cloud ? Or from the leftover remains of the proto-star disk ? Or from ejected objects of the regular solar system (objects inside Neptune's orbit) ?

Doug Ettinger, Pittsburgh, PA, 02/22/2011

[Chris Peterson]

That leaves one final question in this matter. Where did the Kuiper belt objects including its dwarf planets come from?

And it remains an unanswered question. Most likely it consists of material remaining from the protoplanetary disc from which the planets formed. But accurately modeling that process remains a work in progress. It is worth noting, however, that regions like the Kuiper belt may be common, as they have been observed around quite a few other stars.

[dougettinger]

I hope you do not mind another question which you just have given me. How do astronomers observe Kuiper belt regions around other stars ? I certainly know how exo-solar planets are observed because of their size, mass, and ecclipses. But how do you observe Kuiper objects such as comets and dwarf planets at 30 to 50 AU from their star ?

Doug Ettinger, Pittsburgh, PA 02/22/2011

[Chris Peterson]

I hope you do not mind another question which you just have given me. How do astronomers observe Kuiper belt regions around other stars ? I certainly know how exo-solar planets are observed because of their size, mass, and ecclipses. But how do you observe Kuiper objects such as comets and dwarf planets at 30 to 50 AU from their star ?

Some observations are in visible bands, but most are in IR. Remember that you don't have to resolve individual objects in order to detect a structure they make up. That is, it isn't the objects that are being detected, but the belt of objects. It is no different from our ability to detect the rings of Saturn from Earth, even though we can't resolve any of the individual objects that form it.

[dougettinger]

How do these detected belts compare in density to the our Kuiper Belt and how far away can they be detected ?

Chris, what is a cloud angler ? I know you have an observatory but do not understand the connection. Perhaps when you visit your observatory you may take side trips to go fishing ?

Doug

[Chris Peterson]

How do these detected belts compare in density to the our Kuiper Belt and how far away can they be detected?

I think similar and higher densities are inferred. For resolved belts, stars must be necessarily close- within 100 ly or so. Farther than that and planetary system sized structures are too small to resolve. But many stars similar to the Sun show an IR signature that is believed to come from structures similar to the Kuiper belt. This observation doesn't require high optical resolution, and can be made over any distance that sun-like stars can be observed- many thousands of light years.

Chris, what is a cloud angler ? I know you have an observatory but do not understand the connection. Perhaps when you visit your observatory you may take side trips to go fishing ?

It's a bit of word play on my observatory name, Cloudbait. The name comes from the (anecdotal) observation that the more you invest in astronomical equipment, the more cloudy weather you'll have. Thus, my observatory might be seen as bait for clouds. And whichever moderator provided my forum rank obviously imagined me as the angler of those clouds.

[dougettinger]

I remember buying my first snow skis. They were bait for extremely warm winter for about two years.

Well, I am pleased to know that other stars have Kuiper Belts. It confirms my personal opinion that the outskirts of stars systems with outer planets, which I believe to be the typical case, are "bait" for interstellar objects. I know you have been working very hard to dispel my opinion. Your very objective reasoning is appreciated; this prevents me from going too far beyond the box.

A fellow angler, Doug