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Headshot of Emily Lakdawalla

Where are the big Kuiper belt objects?

Posted by Emily Lakdawalla

16-02-2012 17:35 CST

Topics: trans-neptunian objects, Pluto, scale comparisons, Eris, dwarf planets beyond Neptune, trojans and centaurs

Earlier today I wrote a post about how to calculate the position of a body in space from its orbital elements. The particular reason I wanted this information now was because, for a project I'm working on, I'm trying to get a big-picture view of what's going on in trans-Neptunian space. Planets are in fairly circular orbits mostly confined to the ecliptic, so to understand their position in the solar system you really only need one piece of information: their average distance from the Sun. Earth is at 1 AU, Mars at about 1.5, Jupiter 5, and Saturn, Uranus, and Neptune at about 10, 20, and 30. Of course at different times they're at different positions in their orbits, but to a great extent you can predict the properties of a planet just by knowing how far from the Sun it is.

But Pluto and its neighbors generally have much more elliptical and inclined orbits, so average distance from the Sun just isn't enough information to let me form a mental picture of what's going on out there. I want to know: how far away are they now? How far and close do they get? And are they now going farther away or getting closer? Of the big eight objects that we know about (Pluto, Eris, Haumea, Makemake, Quaoar, Varuna, Orcus, and 2007 OR10), do any of them share similar orbits?

You can write down a table of basic orbital information -- semimajor axis, eccentricity, inclination -- but I can't make a picture of the solar system by staring at that table. I know that Pluto is relatively close and actually is sometimes closer to the Sun than Neptune, and I know that Eris is really far, but other than that, I've got no idea where these things are.

I have seriously spent day and night for almost a week ruminating about which orbital information is useful, and how to present it, and finally today I came up with a way that helps me begin to get a sense for what's going on out there. Here's the diagram I came up with; an explanation follows it. I think that this is just the start of what will be a very detailed diagram that gives a snapshot of the Kuiper belt, and I'd welcome input on it. I do ask that you not reproduce it without asking, as it's very much a work in progress and there's lots of things I want to do with it.

The X-axis is range from the Sun, in astronomical units (AU). The Y-axis is heliocentric latitude (the angular elevation of the object above the planet of the ecliptic). The closed loops show the path in range-latitude space that the eight biggest objects travel over time. The loops actually represent 600 years' worth of HORIZONS predictions of orbital positions (from 1600 to 2200), which loop repeatedly for the closer bodies but barely more than once for the most distant bodies.

Infographic: Kuiper belt object orbits (ver. 1)

Emily Lakdawalla

Infographic: Kuiper belt object orbits (ver. 1)
This infographic is an attempt to illustrate the current positions of the eight largest known Kuiper belt objects and the range of positions that they may occupy.

The loops are not ellipses around the Sun; they show how near and how far the objects get over time, but they ignore longitude (that is, they ignore the distance traveled around the Sun over the course of a year).

Let's start at the left-hand side. On this particular diagram, planets, like Neptune, have nearly circular orbits (little change in range from the Sun) with low inclination. So Neptune's orbit makes a very short, thick, black slash near 30 AU. Kuiper belt objects usually have elliptical orbits with higher inclinations. More vertical loops indicate more circular orbits. Shorter loops indicate less-inclined orbits.

The most up-and-down and least-tall of the loops are for Quaoar and Varuna. These are classical Kuiper belt objects, with nearly circular orbits ranging from 40-45 AU. They're doing their own thing, with, apparently, little influence from Neptune.

All the other bodies on this diagram are in various orbital resonances with Neptune. Pluto and Orcus are "plutinos" in 2:3 orbital resonances, meaning that they orbit twice for every three Neptune years. One thing that I like about this diagram is that Pluto's "loop" doesn't intersect Neptune's, so it shows that although Pluto's and Neptune's orbits "overlap," with Pluto sometimes being a teeny bit closer to the Sun than Neptune, in fact the two bodies definitely never actually get near each other.

Makemake and Haumea have similar orbits and are in 6:11 and 7:12 resonances with Neptune, respectively. Although 2007 OR10 and Eris seem to be in a class all their own, with very long loops and high inclinations, they both do return to Neptune's neighborhood as Pluto, Orcus, Haumea, and Makemake do, and they are probably also in orbital resonances with Neptune (3:10 and 5:17, respectively).

The labeled circles/ellipses show the current positions of the eight objects as well as their relative sizes. The skinny black triangles point in the direction along the loop that the bodies are currently headed. I think that the aspect of this diagram that I'm least happy with is the size of the ellipses representing the positions of the bodies, because they obscure details of the orbital loops. And also because sizes are so much more uncertain than orbital data. I think that probably when I work on this some more I will replace those ellipses with dots, and then have callouts -- boxes of information for each of the bodies (magnitude, number, provisional designation, color, albedo, whatever people have managed to measure) that point to little dots with arrows representing the position and sense of motion of each body.

What do you guys think? Is this useful? Do you have any suggestions for improvements or additions?

See other posts from February 2012


Or read more blog entries about: trans-neptunian objects, Pluto, scale comparisons, Eris, dwarf planets beyond Neptune, trojans and centaurs


Waterbergs: 04/17/2013 05:09 CDT

HI Emily - great diagram, very helpful. Two suggestions: I agree with you that the circles/elipses around the objects do obscure - and confuse a little at first reading. Also, it would help to just add the extra 25 AU to the left. I think the extra space gained by trunctaing the axis there adds less value than the lost sense of persective from not seeing the sun at zero. Two questions: From your diagram it doesn't look as if Pluto is ever closer to the sun than Neptune. Maybe I'm missing something, but imagining an arc centred in the sun passing through Neptune (again would help to see the sun there to try this) it would seem to never intersect Pluto on this diagram. Also, I like the resonance stuff, has a sort of beauty to it. Can you tell us anything more about the ratios? Are these rather arbitrary? What is our best guess about how they get "selected"? Is it simply that the relative orbits were close to these integer ratios and then just got fine-tuned to the nearest? Thanks so much for your work on all this - absolutely fascinating.

Emily Lakdawalla: 04/17/2013 10:50 CDT

There's more discussion of this diagram (including a version with the rest of the solar system) here: Your confusion about Pluto has to do with the fact that you're imagining it's a polar-coordinate plot but it is a cartesian-coordinate plot. So draw any vertical line on it, and that's a constant distance from the Sun. Something that was in a perfectly circular orbit that was tilted with respect to the ecliptic would appear as a vertical line segment on this diagram. The little slash that represents Neptune is at about 30 AU, and you can see that Pluto's orbit does cross within 30 AU at its top left. To me, this diagram helps illustrate how Pluto can get closer to the Sun than Neptune but actually doesn't "cross" Neptune's orbit -- it is never anywhere close to Neptune. Regarding your questions about the orbital resonances, they're likely a result of the migration of Neptune into the Kuiper belt. Do a Google search on the "Nice model" (Nice = the French city) to learn more about this.

Waterbergs: 04/18/2013 11:55 CDT

Thanks Emily - got the axis thing now.

Waterbergs: 04/18/2013 01:35 CDT

Thanks for the link - very interesting diagram. A few thoughts occur: The angle each "planetary stripe" presents on your diagram is very similar for Mars, Jupiter and Neptune (whereas obviously the eccentricities of the orbits vary substantially for these objects) is this due to some underlying physics? Is it also relevant that Uranus (with its strange axial tilt) leans the other way on this plot? Finally, I can't quite grasp what the pattern for Saturn is showing. It crosses the ecliptic at two places whose distances to the sun differ by nearly 1 AU from each other. Is that right? If so why so and not with any other planets?

Emily Lakdawalla: 04/19/2013 11:48 CDT

Those angles essentially tell you how their orbits are angled with respect to Earth's orbit. (Earth's orbit is a teeny horizontal slash because the ecliptic is defined to be the plane of Earth's orbit). The eccentricities of all of the planets are very close to zero, which is why their orbits appear mostly like lines -- they are actually closed loops on this diagram, just like the KBOs, but the loops are very thin. Saturn's orbit is the most eccentric of the outer planets which is why its loop appears open. If we expanded the X-axis so you could see the inner solar system better, you'd see the planets' loops open up; Mercury would have the most-open loop, Mars the next-most-open. This is why I didn't include the inner solar system on the diagram I put in the post; it is compressed into oblivion on this scale, and the point of this exercise was to explore the shapes of the orbits of things in the outer solar system. There's no linear scale that works well for everything.

Waterbergs: 04/20/2013 06:11 CDT

Thanks for your response Emily, however, I am still a little confused by the form of the planetary orbit markers. As I understand it the following should be true: For a circular orbit completely in the plane of the ecliptic you would get a single point. For a circular orbit inclined to the plane of the ecliptic you would get a vertical stripe. For an eliptical orbit you will always get a horizontal varitation; if in the plane of the ecliptic then a pure horizontal one, if inclined to the ecliptic then at some angle to the horizontal. If the periapsis is above the ecliptic then the stripe will be top-left to bottom-right (as for Uranus), otherwise the opposite (as for Mars, Jupiter and Neptune). The one that puzzles me is Saturn - how do you get a loop like that? It implies that Saturn crosses the ecliptic at two points with significantly different distances to the sun - about 1 AU apart. I can't see how that happens easily. I can't see that an eccentricity alone does it - that should only increase the fractional distance between the two ends of the "stripe" relative to the total distance out from the sun (for example, the eccentricity of the planets Mars, Jupiter and Neptune decreases in that order - hence the "stripe angle" remains approximately the same for all three - even though the distance out from the sun increases). For a standard eliptical orbit the heliocentric lattitude should be a function of distance from the sun - and single valued. A loop implies there are two positions (one above the other below the ecliptic) for each value of distance from the sun. I can't get my head around that. Does it represent a tilt in the eliptical orbit about the major axis relative to the ecliptic? That would seem to do it, but it would have to be very large to produce the effect seen.

Chang: 01/04/2014 08:31 CST

Your diagram strikes me as innovative and informative. Unlike the most common diagram, which shows us longitude and distance but not latitude, this graph shows us latitude and distance from the sun (but not longitude). For a complete picture of these orbits, it would be ideal to combine this graph with two others: A graph of longitude and distance plotted on polar coordinates, and a graph of latitude as a function of longitude (which would tell us, for example, where each orbit crosses the plane of each other orbit). Your diagram reveals something about the argument of perihelion: If perihelion occurs near either minimum or maximum latitude, then distance is closely correlated with latitude, and the orbit will cross the ecliptic at nearly the same distance when ascending as when descending. The result is a narrow loop for Varuna, for example. If perihelion occurs near the ecliptic instead, then distance at the ascending node is very different than at the descending node. The result is a wide loop for Eris or 2007 OR10.

Chang: 01/04/2014 08:35 CST

We can also see whether perihelion occurs closer to the ascending node or the descending node. For most of these KBOs, perihelion occurs closer to the descending node, which results in KBOs moving counterclockwise on your diagram. For others, however, perihelion occurs closer to the ascending node, which causes them to move clockwise instead. Your diagram also conveys some information on which orbits pass inside of other orbits. We see that all these KBOs (even Pluto) always pass through the plane of Neptune’s orbit outside of that orbit. But we also see that both Eris and 2007 OR10 pass inside of Quaoar’s orbit when descending through the plane of that orbit but outside of the orbit when ascending. Quaoar’s orbit and the orbit of either Eris or 2007 OR10 form interlocking rings. We cannot tell whether the other pairs of orbits are interlocking, however, without information on longitude. I would like to see Sedna included on these graphs, at least the portion of Sedna’s orbit that passes through the domain relevant for the KBOs you have included. If the graphs get crowded, then I would suggest deleting the smallest two KBOs (Varuna and Orcus).

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