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Jupiter and the Sun are the two largest objects in our Solar System, and as they orbit around one another, they create regions where their gravity roughly cancels out. These are the Lagrangian points, created whenever two objects orbit one another: places where gravity is such that another small object can follow along in the orbit without being pulled in or out. And since things aren't getting pulled out of there, they get stuck in there as well: and so we have two large clumps of asteroids (and miscellaneous smaller space debris) in Jupiter's orbit. These are called the Trojan Asteroids; the group ahead of Jupiter is known as the Greek Camp, and the group behind it the Trojan Camp, with the asteroids in each camp being named after famous people in that war. Together, these two camps have as many asteroids as the Asteroid Belt.

Other stable patterns are possible, too: another one is what's called a 3:2 resonance pattern, asteroids whose motion gets confined to a basically triangular shape by the combined pull of Jupiter and the Sun. This group (for Jupiter) is called the Hilda Family, and their route forms a triangle with its three points at the two Lagrange points and at the point on Jupiter's orbit directly opposite it from the Sun. 

None of these orbits are perfectly stable, because each of these asteroids is subject to pulling from everything in the Solar System; as a result, an asteroid can shift from the Lagrange points to the Hilda family, and from the Hilda family to the Asteroid Belt (not shown), especially if it runs into something and changes its course. 

The reason that Pluto was demoted from planet to dwarf planet is that we realized that these things are not only numerous, but some of them are quite big. Some things we formerly called asteroids are actually bigger than Pluto, so the naming started to seem a little silly. So our Solar System has, in decreasing order of size, four gas giant planets (Jupiter, Saturn, Neptune and Uranus); four rocky planets (Earth, Venus, Mars, and Mercury); five officially recognized dwarf planets (Eris, Pluto, Haumea, Makemake, and Ceres); and a tremendous number of asteroids. (We suspect that there are actually about 100 dwarf planets, but the job of classifying what's an asteroid and what's actually a planet is still in progress -- see the "dwarf planet" link below if you want to know the details)

Ceres orbits in the Asteroid Belt, about halfway between Mars and Jupiter, just inside the triangle of the Hilda Family; Pluto and Haumea are both in the distant Kuiper Belt, outside the orbit of Neptune but shepherded by its orbit in much the same way that the Hildas are shepherded by Jupiter; Makemake is what's called a "cubewano," living in the Kuiper Belt but unshepherded, orbiting independently; and Eris is part of the Scattered Disc, the even more distant objects whose orbits don't sit nicely in the plane of the Solar System at all, having been kicked out of that plane by (we believe) scattering off large bodies like Jupiter.

But mostly, I wanted to share this to show you how things orbit. This picture comes from the amazing archive at http://sajri.astronomy.cz/asteroidgroups/groups.htm, which has many other such pictures, and comes to me via +Max Rubenacker

More information about all of these things:
http://en.wikipedia.org/wiki/Lagrangian_point
http://en.wikipedia.org/wiki/Trojan_(astronomy)
http://en.wikipedia.org/wiki/Hilda_family
http://en.wikipedia.org/wiki/Dwarf_planet
http://en.wikipedia.org/wiki/Kuiper_belt
http://en.wikipedia.org/wiki/Scattered_disc

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126 comments
 
+Arthur Gwynne your list says it's sorted by diameter, but it appears to be sorted by orbit distance. Great site, though. Really liked that read.
 
Good point, +Arthur Gwynne. Updated the post to highlight that we have five official dwarf planets, but there are probably about 100 all told.
 
Never saw this in a visual/chronological reference. Very cool!
 
Anyone know the name of that lone Trojan hanging out around the third point of the Hilda triangle?
 
Very cool. While I was familiar with the 5 Lagrangian points, I had never seen a good visualization of the 3:2 resonance.

FWIW: Lagrangian points aren't the point where gravity cancels out: there's only one such point, and at that point the orbit isn't stable (since an object there would move in a straight line, not in a circle).
 
+Jean-Baptiste Quéru Yeah, I wasn't quite sure what the best way to explain a Lagrangian point was. "A point where the gravitational fields of the two primary objects are such that a smaller object can be in a stable orbit around the joint COM" is accurate, but a bit hard to visualize. Got a suggestion?
 
This is fascinating! Thank you for sharing it. The image is mesmerizing. 

How does the Asteroid Belt fit into this? Is there any shepherding that affects those bodies or is it primarily the Sun and their own influence on each other? 
 
Thank you Jupiter, for saving our puny little human asses over and over!
 
That's an awesome animation.  I knew about the Trojan asteroids (the Jovian Chronicles RPG setting has colonies in them, called Vanguard Mountain for L4 and Newhome for L5), but I had no idea that the astroid belt was roughly triangular.
 
+Yonatan Zunger - I totally agree that it's really hard to explain them.

I'd try "those are the points there the gravity fields of the Sun and Jupiter combine to create stable orbits around the Sun that have the same period as Jupiter" for lack of a better explanation that applies to all 5 of them.
 
The general thing that's going on here is that whenever you have two big bodies orbiting each other, generally Jupiter and the Sun when you're talking about the Inner Solar System, or Neptune and the Sun when you're talking about the Outer Solar System, you get semi-stable points (the Lagrangian points), and a bunch of shepherded orbits that are defined by orbital ratios -- how many times they go around per orbit of the big primary. The Hilda Family, for example, is in a 3:2 resonance with Jupiter, meaning that they orbit 3 times for every 2 orbits of Jupiter's.

The Asteroid Belt is actually a bunch of different groups; e.g., the Cybele Group is 7:4. Similarly, the Kuiper Belt is in a bunch of different ratios with Neptune and the Sun; the Plutinos, for example (the group that includes Pluto) are 3:2 in that family. 
 
The visualization of the orbits is oddly soothing. Thank you for it.
 
Really fantastic animation.  Thank you for posting.
 
This is excellent, thanks!
 
What is this "bodies orbiting each other" business? I thought it was simply planets orbiting the Sun? I'm having trouble visualizing a mutual orbiting. 
 
+Matija Pa Now I have a mental image of two people holding hands and spinning around and around. But that helps, actually. 
 
+Christina Talbott-Clark Exactly. You can consider the Sun a superfat chick who's trying to face us all the time, and her sole turning is causing a small orbit in itself.
Any which way you turn, your arse remains on the back, as we say :)
 
the earth is going fast Jupiter is going slow
 
+nancy coleman that's because Jupiter's orbit is quite a bit larger than Earth's. The smaller the orbit, the faster the rotation. 
 
My immediate thoughts on seeing the graphic before reading the explanation:

1) Cooooool.

2) Reminds me of a screen saver I had on my IBM PC Jr.

:D
Zach W.
 
For a moment I thought these spots sounded like great orbital mining platforms...Then as I understood it, they would drift too much between the Trojan Camps and the Hilda Family, making it somewhat difficult to ensure any needed supplies get to them...I think? Unless maybe you put them/one at the Lagrangian Points?
 
This is fascinating and something I have thought about from time to time.  I just didn't know they had a name for it.  +brian naasz - have you seen this?
 
+Christina Talbott-Clark Every object in the Universe exerts gravitational force on every other object in the Universe. Because the Sun is so much more massive than the planets, the easiest way to visualize the Solar System is through the approximation that the planets orbit the Sun. To be a little bit more precise, the Sun and each planet orbit the center of mass of the system formed by the Sun and that planet.

To be more precise than that we'd have to take into account the gravitational effect of each planet on the orbits of each of the other planets. Unfortunately that would require mathematics that we haven't invented yet.

This animation is possible because the asteroids are so much smaller than Jupiter and the Sun that their locations can be plotted without taking into account the effect of the gravitation due to their mass on the orbits of the planets.
Zach W.
 
+Chuck Karish, wait, we actually haven't developed mathematics to calculate the overlapping gravitational fields/forces between massive bodies like planets? That's pretty interesting, if true.
 
This image greatly expands (...) the physical scale of what would obviously need to be written off together with Jupiter if Jupiter was to be subtracted from the Solar System.

Can the physics of such a counterfactual subtraction be unequivocally defined? Not fully... looks about right :)
 
This made me dizzy. Interesting however.
 
+Zach Wilks We have the math, definitely -- that's where things like this animation (and the ability of spaceships to fly) comes from. What we can't do is solve it as an equation; all we can do is numerical calculations. The actual dynamics are chaotic and very complex.
 
I think a serious study comparing this phenomenon with weather patterns would yield some noteworthy results.
 
+Christina Talbott-Clark Some people have already answered various parts of this, but I'll add a bit more explanation of "orbiting each other" -- if you have two bodies in orbit, each is pulling on the other. What's really happening is that they're both orbiting their mutual center of mass. If one body is much heavier than the other, like the Sun and the Earth, (or for that matter, an electron and a proton in an atom) then the center of mass is pretty close to the center of the heavier item, so it looks like the light object is circling the heavy object. (And if you look closely, like the heavy object is wobbling as well: that's simply its own motion around its own center of mass) On the other hand, if you have two bodies of equal size orbiting each other, then the center of mass would be bang in the middle between them, so they both appear to be orbiting that central point. 

Two people holding hands and spinning around on an ice rink do the exact same thing. 
Zach W.
 
+Yonatan Zunger That makes...A little sense. I'm not exactly adept with math, so I don't follow how that works, in all honesty. Without getting too caught up on the mathematical side of it, I'm guessing that it must be an extensive series of measurements to gather this information, as opposed to set data that can be used to predict the patterns?
 
Fascinating, thank you for posting, +Yonatan Zunger!  The nifty graphic really puts in perspective just how fast we are zooming along on our mother Earth... I think I'm getting motion sickness now!
 
+Zach Wilks As far as the numerics? It's basically simple -- if you know the mass, position, and velocity of the various objects, you can run a big computation to plot their trajectories. The challenge is that, because the system is chaotic, even small errors in any of those parameters can quickly turn into big errors in the trajectory plots. Fortunately, with gravitational trajectories, if you get the motions of the big objects right, then errors in the data about a small object lead to errors in the predictions for that object, but not errors in the predictions for every other object. And we're pretty good about measuring positions and so on within our solar system, now. That's all core astronomy work, basically taking lots of pictures through telescopes and watching how things move.
 
So does every body in our solar system has 5 lagrange points like the Earth? Didn't we put satellites in ours? I remeber reading we have something looking at the sun in one of them. Oh and Pluto is a planet (and also Mickey's friend)! Anyone who disagrees can go walk into Mount Doom. 
 
+Matt Kiener Yup; whenever two bodies orbit each other, they form five Lagrange points. Points 1-3 are "unstable" points, which means that if you're exactly on that spot you're in a stable orbit, but if you deviate even by a tiny bit you fall out of it; points 4 and 5 (the ones ahead of and behind the smaller mover, respectively, in this picture) are the "stable" Lagrange points, where the point itself is the heart of stability but there's a whole basin of stable regions. The Wikipedia article I linked to tells you more, and has pictures.

We have plenty of satellites sitting in both the Earth-Moon Lagrange points and the Earth-Sun ones.
 
The Sol/Jupiter Lagrangian points look like a pretty tenuous place to put asteroid mining facilities...  They'd be mobbed and destroyed pretty quickly.
 
This is my favourite G+ post so far.  Superb.
 
So what about comets, do they have 5 lagrange points that would be constantly moving? Park something there and it would be a good way to look around without using much energy, maybe? Unless they aren't stable. 
 
+Michael Vaughan They're really no worse than any other asteroid. The dots are overlapping on this picture mostly because of pixel size limitations: space is really, really big. There's always the risk of asteroid collisions, but that's going to be the case in any belt; a mining operation would have to be able to mitigate that no matter what. The Lagrange points could actually be good in a lot of ways, because it means that you could have a bunch of mines relatively close to one another and thus simplify transit. That said, it's not clear whether these particular asteroids have anything in particular on them worth mining.
 
+Matt Kiener Comets orbit the Sun, so technically there are Sun-Comet Lagrange points -- but comets are so small, and their own gravity is so weak, that nothing much more than dust is likely to float around in them. 
 
Comets are tiny and their orbits are very large, which together mean that the gravitational forces involved aren't large enough to make this an interesting possibility.
Zach W.
 
Gotcha +Yonatan Zunger, that sounds like what I was trying to think of but didn't have adequate knowledge to describe.
 
+Alexandre Pellerin It's not my model, but I suspect that this particular model didn't do any collisions; those are actually fairly rare. Space is big, and asteroids are small.
 
Off topic, but I find myself constantly muting interesting threads (like this one) because of animated gifs.  On a very fast Retina MacBook Pro running Mac OS X Mountain Lion, Chrome's CPU usage jumps from negligible to 33% when a single animated gif is visible in my stream.  A configurable click-to-play option would be nice.
 
Hahahahaha, +Yonatan Zunger, I showed this to your pupil too and she loved it.  So then we read your whole post together and went to the Dwarf planet link.  She was peeved that there was no listing for "Santa" on that because she says +Mike Brown's book mentions one named "Santa" so I googled for that and found the entry on Haumea, which the team was calling Santa immediately after discovery.  Which taught me something important: never question Peo's knowledge of anything pertaining to Brown.

Then she wanted to watch the graphic for a bit longer.  She said, "It's kind of hypnotizing."  I said that's fine but I did want my computer back.  She sighed and said, "Fine, two more orbits by Jupiter and then you can have your computer back."  She counted them down and ran off at the end calling, "You can have your computer back now!  Wait, was that cheeky?"
 
The Solar System consists of four planets and some debris. We live on one of the larger chunks of debris.
 
A memorable graphic. Is it dynamic or an animated gif?
If an animated gif is there a URL to see a real dynamic
video of what physicists know is happening even in our own
solar system?
 
+Kimberly Chapman if the Duckling ever refuses to stop watching videos of planetary orbits, I'm going to leave her there. Of course I also have plenty of devices to play with. :)
 
I think the nerdy children of this social group need to have a playdate at Doctor Zed's Playhouse and Science Emporium.
 
Wow, reminds me of a rotary engine...
 
I was worried that I would sound like a wankel if I called it by it's proper name...
 
Oh and speaking of things that go around, +Yonatan Zunger you should check out this great song by +Monty Harper called "Roundy Round" about everything from planetary bodies to atoms going around: Roundy Round by Monty Harper

That was one of the first Harper songs I heard on the Parenting Beyond Belief podcast by +Rob Tarr, and it's why I had to go find more.  I believe he said that it was inspired by a kid spinning around joyfully, but maybe he can clarify the story (and will likely dig this post).
 
Ha ha, I keep returning to the image, somehow expecting to see a different pattern emerge...
 
Thank you, +Yonatan Zunger.

I can only understand half of it
but that's enough
to be touched by it's magic...
 
We've another Near-Earth Asteroid making its closest approach to Earth on Saturday (9th March).  2013 ET was only discovered a few days ago.  I imaged it a couple of nights ago and there's a time-lapse of it whizzing across the sky in my G+ post here:  https://plus.google.com/u/0/113293976957750950702/posts/Fd7KLts84Z4

I'll also be using the same robotic telescopes in the Canary Islands to image the asteroid live as it makes its closest approach.  The live images will be broadcast on a free public show on Saturday.
 
For what it's worth, we can put satellites in the Lagrange points that exist within the earth-moon system. Pretty cool idea doing that. Saves gas...:)
 
Such simulations bug me immensely because they give the impression that all bodies in the solar system rotate around a single axis; that is to say, that the motions of the planets adhere to the ecliptic plane, which they do not.
 
Jupiter is the ANDROID
 
Like stirring some sandy oil. inertia, friction, centrifugal force...
 
Thank you for this mesmerizing video.  

Interestingly, L3, L4 and L5 are acting as aphelia attractors of Hilda Family asteroids which may be the key to understanding long-period Oort cloud comets.

While Pluto is vastly more massive than all the asteroids together, even Jupiter may pale in size next to a hypothesized companion star to the Sun, Proxima (Centauri), perhaps merely on a temporary hyperbolic orbit around the passing binary star, Alpha Centauri.  And Proxima at a former distance of 182,600 AU from the Sun would place the solar-system barycenter (SS-barycenter) at 20,000 AU, perhaps explaining the typical 20,000 aphelia of the long-period Oort cloud comets as an alternative explanation for a Jupiter-sized planet, 'Tyche', orbiting at 20,000 AU (Matese and Whitman, 1999) and (Matese and Whitmire, 2011).

"If [Eugene] Shoemaker was correct in his estimate that virtually all terrestrial craters of diameter >100 km are produced by long period comets, then the phase and plane crossing period of the solar system about the Galactic disk should be consistent with the ages of accurately dated large craters. A time series analysis of these ages in which the solar oscillation phase is fixed to be consistent with observations indicates a maximal correlation for a period of 36±2 Myr."  (Matese et al, 1998)

Proxima at 182,600 from the Sun would orbit the SS-barycenter with a period of 73.8 Myr, twice the 36±2 Myr periodicity of >100 km and larger comet craters on earth.  And long-period comets with 20,000 aphelia pinned to the SS-barycenter (as the Hilda Family asteroids are pinned to the 3 Lagrange points) would have their major axes aligned with the tidal influence of the Galactic core twice per 73.8 Myr orbit of the Sun around the SS-barycenter, stretching their semi-major axes pinned to the SS-barycenter, causing their perihelia to spiral down into the planetary realm with a periodicity of about 36.4 Myr.
 
+David Carlson Huh... that's an interesting thought. I haven't run through any of the calculations and so don't have an opinion off the top of my head, but the idea that the Sol-Proxima (or even Sol-Alpha) resonance could be driving Oort cloud instabilities makes a certain sense. I'll check out some of those papers.
 
Where is MOON ???????????????
 
+Yonatan Zunger There hasn't been a lot of research on Alpha and Proxima, perhaps because they're only visible from the southern hemisphere, but the Hipparcos satellite of the European Space Agency measured the proper motion of more than 100,000 stars and published the Hipparcos Catalogue in 1997, and from this new data, Wertheimer and Laughlin, 2006, calculated the probability of a bound state of Proxima with Alpha Centauri.  In a Monte Carlo simulation, 44% of the trial systems are bound, with an unbound probability of 55%.

I'm a firm believer that science doesn't like coincidences suggesting that the following calculations are meaningful in which Proxima relates 90377 Sedna to 4 Vesta at Jupiter:

Sedna Period * Sedna Mass/Proxima mass = 2.64E-7
518.57^(2/3) * 1E21 kg / (.123 Ms * 1.989E30 kg/Ms)  = 2.64E-7

Vesta Period * Vesta mass/Jupiter mass = 2.42E-7
2.362^(2/3) * 2.59E20 kg / 1.899E27 kg  = 2.42E-7

This implies that Sedna was to Proxima as Vesta was to Jupiter when, hypothetically, both Jupiter and Proxima were binary objects spiraling out from the Sun/SS-barycenter, such that 4 Vesta formed in Jupiter's 5:2 to 3:1 resonant nursery, where 1 Ceres now presides, and fell through the 3:1 resonance when its (period x mass) reached a threshold, and similarly, Sedna fell through Proxima's 3:1 resonance.

This implies an alternative formation mechanism for binary companion stars, binary planets and binary planetesimals which may unify their formation processes, with 'core accretion' playing at best a secondary role in resonant nurseries of giant planets and companion stars.

Accordingly, as protostars contract, excess angular momentum is understood to cause 'bifurcation', forming close-binary stellar pairs, but if the bifurcation process is fractal and messy, smaller gravitationally-bound masses may also spin off, forming giant protoplanets.  These protoplanets in turn may bifurcate as they contract, spinning off smaller protomoons etc., with each generation having a higher metallicity than the previous generation due to volatile diffusion.

Then core-collapse perturbation causes binary objects to spiral out from their progenitors as their close-binary components spiral in, conserving energy and angular momentum, until they merge, forming solitary objects.  If binary progeny spiral out of their progenitor's Roche spheres, they assume heliocentric orbits, otherwise they remain gravitationally bound as moons.

In a linear-log plot of binary Proxima spiraling out from the SS-barycenter:
89 AU at 4,567 Ma
182,600 AU at 542 Ma
The SS-barycenter is aligned over the Plutinos (in a 2:3 resonance with Neptune) at 3,830 Ma, explaining the late heavy bombardment (LHB).  The two end dates are also significant, with the binary Sun in a luminous red nova (LRN) at 4,567 Ma, creating the short-lived radionuclides of the early solar system and binary Proxima merging at 542 Ma, causing the Cambrian Explosion and the Great Unconformity.
 
thanks for posting, these are things I never knew. I hope I can use this knowledge one day. Say if ever anyone puts a gun to my head and asks me about the greek and trojan camps.
 
The N-Body problem is only worked with massive array calculations. Best handled by computer code... for each body, you need current location, vector, and mass; in 2d, 5 variables per body, and in 3d, 7 variables. Work through the array calulating vector change due to other bodies, then go back through and apply the calculated vectors. Most of the "gravity simulations" for PC's do it in a single pass, resulting in errors due to altered position. Your level of accuracy makes a huge difference, too... To get the differences in scale you need mass on a minimum 32 bit float; 64 bit is better still. Solar mass is 1.9E30kg, while Ceres is 8.95E20 - about 2.1E9 difference... just a hair shy of 31 bits. And Ceres is a HUGE asteroid - a proper dwarf planet (most asteroids are not).
 
What is the cause of the third vortex though opposite of Jupiter on its orbit?
 
Hope that Jupiter's double shift as sentinel and shepherd never ends, so that nothing is willing to pay a visit to Earth.
 
I like what i ignored but i to se the picture..

 
The universe will never cease to amaze.
 
I'm not smart enough to add to this conversation but it was neat watching the little dots go round and round :) 
 
The forces that's amongst us is remarkable
 
Orbit around each other? Jupiter orbits the Sun.
 
This is some of the most interesting information and imparted so clearly. Thanks for all the time spent.
 
+Joshua McDonald Gravity works both ways -- whenever two things are in orbit, they each orbit around the other. If one is much bigger than the other (like the Earth and the Sun) then the heavier one's motion is very small, but even that's still there: the main way we detect extrasolar planets is by watching the way they make their stars wobble. When they're both bigger, it becomes more obvious: the center that the Sun and Jupiter both orbit around is close to the edge of the Sun. And for Pluto and its moon Charon, the center is somewhere between the two, so it's really obvious that they're both moving. (If the two orbiting bodies weighed the same as each other, the center would be smack in the middle)
 
Das jetzt noch in einer 3D version, aber ansonsten ein cooler Bericht.
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Those little pieces of rock and ice must be protecting the inner planets to some degree. 
 
+Jonathan Raabe Not so much as "protecting" as "occasionally running in to." What with all the things pulling on them, and their own tendency to sometimes break rather violently (especially the ones made of ice, which are getting unevenly heated by the Sun) these things tend to fall out of orbit, at which point they either get pulled inwards by the Sun or fly out into some other part of the Solar System. At which point they tend to collide with things, rather a lot.
 
+Yonatan Zunger Can you please link me to some information regarding Jupiter and the Sun orbiting each other. It has always been taught to me that while celestial bodies do exert gravity on each other. For example the moon's effects on earth's ocean's. All bodies will orbit the largest mass.

With the exception of bodies close to the same mass. Just with the sheer difference in size you would think any effect of gravity on the sun would be null and void.

I understand what your saying. I just can't visualize it.
 
+Joshua McDonald Whenever two bodies orbit, they really are both orbiting around their mutual center of mass. If one object is much heavier than the other -- say, the Earth and the Sun -- then the center of mass is so close to the center of the heavier object that it appears that the heavier object is stationary. But when their masses become more equal, the difference is more pronounced; if you imagine two equal masses orbiting each other, their center of mass is dead between them, so they're both spinning about an invisible point in the middle. For Jupiter and the Sun, the center of mass is actually just outside the outer edge of the Sun itself, and so the Sun's wobble due to Jupiter's motion is quite detectable. (In fact, it's this kind of wobble that's one of the best ways to detect planets orbiting other stars) 

Jupiter is quite large. :)
 
Yeah thanks. That makes more sense now. Is there a term used for this so I may read more about it?
 
+Joshua McDonald There's no particular term for it; it's just part of orbital mechanics, which is part of classical mechanics. I can point you at good textbooks if you want to see more of the math.
 
+Joshua McDonald A good relatively basic book is Taylor's Classical Mechanics. A more hardcore book is Jose & Saletan's Classical Dynamics. Neither of these are non-technical, though; I'm afraid I don't know a good non-tech book on this off the top of my head. Someone else might.
 
ヒンズー教占星術でも木星と太陽は重要な役割を持っています--------------参考になりました・・ありがとうございました・・これですね・・
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