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Message started by Mal on 09/22/08 at 01:32:35

Title: Kirkwood gaps?
Post by Mal on 09/22/08 at 01:32:35

Has anyone tried to use GravSim to simulate/recreate the Kirkwood Gaps in the asteroid belt? I guess it'd have to be done with a lot less asteroids (say 100-1000?) but it could be interesting to see how a load of objects randomly scattered between Mars and Jupiter evolve over time... would you get something similar to the real asteroid belt here (with Kirkwood gaps and the 3:2 asteroids)? GS can handle resonances, right?

More interestingly, would you get the same features in belts in others planetary systems with different planets and orbital parameters?

I don't know how computationally painful it'd be to try to simulate it, but it could be interesting to try.

Title: Re: Kirkwood gaps?
Post by frankuitaalst on 09/22/08 at 07:28:05

I think GS can handle this . Maybe Tony has done it already ?
Maybe it will take a lot of time before this gaps really appear ( they won't appear visually , but one has to look for the SMA of each object ) . Nice sim to let work at night .

Edit : this sim may take a lot of time , if one considers the orbital period of Jupiter is 10 years and if it takes lets say 100 revolutions to get some resonace pattern one gets 1000 years of simulation at least .

Title: Re: Kirkwood gaps?
Post by Mal on 09/22/08 at 09:12:25

Actually the best way to see them is to plot the inclination or eccentricity vs the semimajor axis (on the x-axis). They're really obvious shown like that.

Incidentally, if anyone knows of a spreadsheet program that can show more than 32,000 rows of data can you point me to it? I've got the orbital data for over 100,000 asteroids but Excel refuses to plot more than the first 32k of them (it's enough to show the structure, but not ALL of them).

Here's the eccentricity vs SMA for the first 32,000 asteroids in the main belt:

Title: Re: Kirkwood gaps?
Post by Mal on 09/22/08 at 09:13:21

And here's the inclination vs the SMA - you can really see the asteroid families here too. (the clump at 5.2 AU in both graphs are the Trojans in Jupiter's orbit). I'll discuss it more later on when I have the time.


Title: Re: Kirkwood gaps?
Post by frankuitaalst on 09/22/08 at 09:44:55


Mal wrote:
Actually the best way to see them is to plot the inclination or eccentricity vs the semimajor axis (on the x-axis). They're really obvious shown like that.

Incidentally, if anyone knows of a spreadsheet program that can show more than 32,000 rows of data can you point me to it? I've got the orbital data for over 100,000 asteroids but Excel refuses to plot more than the first 32k of them (it's enough to show the structure, but not ALL of them).

Here's the eccentricity vs SMA for the first 32,000 asteroids in the main belt:

In which format do you have the data ?
It's possible to write some code to represent them in various ways .

Title: Re: Kirkwood gaps?
Post by Tony on 09/22/08 at 12:55:32

I've done some partial Kirkwood gap simulations.  I'll dig it up for you later.  But I'll briefly describe it now.  I computed the semi-major axis of one of the resonant zones.  Let's just say for example that it is 3 AU (I'll look up the exact answer later).  I placed 100 objects evenly spaced from 2.9 to 3.1 AU, every 0.1 AU.  I ran it for a few million years.  When I was finished, all the objects between 2.99 and 3.01 were ejected, and the others were virtually undisturbed.  This confirmed that Jupiter will clear the gap at that resonance.

You can probably plot all the points you want in IDL.  Additionally, I've made my own graph creator in Visual Basic.  It doesn't have many features, but if you can give me the semi-major axes in text format, I can plot all of them for you.  One issue that might be a problem, is that the graph might be too crowded with over 100,000 points.  Even the gaps might appear full because of screen resolution.

Title: Re: Kirkwood gaps?
Post by frankuitaalst on 09/22/08 at 13:06:37

Nice to have a graph generator .
I've just finished a gsim with 600 bodies from 3AU+/- 40% . Result output every 10 years . Can you make a graph out of this ? ( a, e are saved in the file ) . Size: <2MB .

Title: Re: Kirkwood gaps?
Post by Tony on 09/23/08 at 01:26:15

First, a disclaimer: The Kirkwood Gaps are not visible gaps like the Cassini Division in Saturn's rings. There are pleanty of asteroids in the Kirkwood Gaps. However, most of them are asteroids with semi-major axes that do not equal the gap distance, but with enough eccentricity that they can cross the gaps.  There are very few of them that possess semi-major axes equal to those of certain resonances. So the Kirkwood Gaps are only gaps in a histogram of semi-major axes like the image Mal posted.

Here's the simulations I promised you:

Asteroids in Jupiter's 3:1 interior resonance go around the sun three times for every time one time Jupiter goes around the sun. So their periods should be 1/3 Jupiter's period. Jupiter's orbital period is 4331.572 days. So their orbital periods should be 4331.572 /3 = 1443.85733333333 days. Using the formula http://orbitsimulator.com/gravity/a3.GIF, and converting everything into proper units (just use the calculator here: http://orbitsimulator.com/gravity/articles/formula55.html , enter 1443.85733333333 for P, choose "d" for units, enter 1 for mass and choose "solar masses" for unit, and choose AU for output units), asteroids in Jupiter's 3:1 interior resonance should have semi-major axes of 2.50 AU.

The simulation http://orbitsimulator.com/gravity/simulations/j3_1.gsim begins with an accurate representation of the solar system's 8 planets, plus Earth's moon and Pluto. Then 90 massless objects are added near Jupiter's 3:1 interior resonance. There are 10 each at:

2.46 AU
2.47 AU
2.48 AU
2.49 AU
2.50 AU
2.51 AU
2.52 AU
2.53 AU
2.54 AU

The objects are color-coded and are given names that reflect their initial semi-major axis. For example, "2p47 28" has an initial semi-major axis of 2.47, and it is the 28th asteroid in the simulation.

Let the simulation run at a time step of 16384 seconds, and in 3 million years, you'll find that most of the objects that started at semi-major axes of 2.50 and 2.51 (2p50 nn & 2p51 nn) are no longer in circular orbits, and many have very high inclinations. All other asteroids are virtually unchanged.

If you don't want to wait the simulated 3 million years, the simulation http://orbitsimulator.com/gravity/simulations/j3_1_3millionYears.gsim shows this system 3 million years later.  This simulation begins in "ecliptic view" so you can see the high inclinations.  Drag the scroll bar to the top to return to a top-down view.





Title: Re: Kirkwood gaps?
Post by Tony on 09/23/08 at 09:08:20

Here's some screen shots of the above simulations.

http://www.orbitsimulator.com/gravity/images/kw01.GIF
This is the beginning of the simulation.  The 90 asteroids orbit the sun in Jupiter's 3:1 interior resonance, +- .04 AU

http://www.orbitsimulator.com/gravity/images/kw02.GIF
This is after 3 million years, looking top-down on the ecliptic plane.  The blue objects were originally in orbits with semi-major axes of 2.50 AU, and the purple ones, 2.51.  Four of them have been ejected out of the solar system.  Eight of them are still in circular orbits (ecc < 0.1).  Some of these have had their semi-major axes perturbed out of the 3:1 resonance, so they are protected for now.


http://www.orbitsimulator.com/gravity/images/kw03.GIF
This is a view from within the ecliptic plane, showing the very high eccentricities of some of these asteroids.

Title: Re: Kirkwood gaps? - Clearance
Post by frankuitaalst on 09/23/08 at 13:11:42

The following animation is the result of a gsim simulation .
600 bodies were created at 3AU+/- 40% , so simulating an asteroid belt ( 0 incl , 0 eccentricity) .
The a and e of each body were saved in an output file , every 10 years .
The sim was run for 8500 years at 16000 seconds.
I wrote a small programm able to read the Gsim-output file and able to represent the a and e value of ech body . ( a is represented from left to right , e is represented bottom up ) .
So each dot represnts a body .
Pasting each screenshot ( every 100 years ) gives the following animation ....
One can see the bodies originally at e=0 .
The eccentricity of each body increases with time .
The 4 little dots at the left are Mercury ,...Mars . The stationary dot at the right represents Jupiter .
One can see also some gaps are created ( fi 2 cm to the right of Mars ) . .
The screenshot which doesn't erase every previous picture shows the gaps more clearly than this animation . I'll try to post it also .

Title: Re: Kirkwood gaps?
Post by frankuitaalst on 09/23/08 at 13:22:45

Perhaps this is a better representation : The following picture represents the final distribution of a,e of the simulated bodies .
As the color of the bodies was changed from red at start to white at the end of the simulation one can see some gaps are created ar certain distances .
The four lines at the left are the inner planets, where Jupiter is the line at the right .
Furthermore the eccentricity of each body seems to change largely with time .

Edit : is it due to my vision that I'm seeing a kind of bow starting at the right end of the belt and going upwards to the left ? Can  this mean that a decreasing sma goes together with an increasing e ?

Title: Re: Kirkwood gaps?
Post by Mal on 09/23/08 at 21:17:40

Cool, those are really interesting sims and graphs. (I'd play more with this myself but I don't have the time right now... but thanks for trying these things out!). It's interesting how you can watch the eccentricities increase over time in the animation that frankuitaalst did. What might be interesting is to see if including Saturn in the system makes any difference - I think there are some secular resonances (the nu 6 one?) that can affect the inclination - these are mentioned on page 315 of Solar System Dynamics.

I got the asteroid data from astorb.dat , which can be found here: ftp://ftp.lowell.edu/pub/elgb/astorb.html

I stripped out the asteroid number, semimajor axis, eccentricity and inclination and used those to make the graphs. Note that the data contains asteroids outside the main belt, so if you're showing them on a graph and want to focus on the belt you have to trim the range of the graph axes. I'll attach the data in the next posts.

Title: Re: Kirkwood gaps?
Post by Mal on 09/23/08 at 21:18:18

Here's the #, SMA, Ecc, and Inc for asteroids 1-99999 in csv format

Title: Re: Kirkwood gaps?
Post by Mal on 09/23/08 at 21:18:59

Here's the #, SMA, Ecc, and Inc for asteroids 100000-199999 in csv format

Title: Re: Kirkwood gaps?
Post by Mal on 09/23/08 at 21:19:45

Here's the #, SMA, Ecc, and Inc for asteroids 200000-299999 in csv format

Title: Re: Kirkwood gaps?
Post by Mal on 09/23/08 at 21:20:36

Here's the #, SMA, Ecc, and Inc for asteroids 300000-399999 in csv format

Title: Re: Kirkwood gaps?
Post by Mal on 09/23/08 at 21:22:40

And here's the #, SMA, Ecc, and Inc for asteroids 400000-423291 in csv format.

You can merge them together using Programmer's File Editor, which is a really good, basic text editor (written by someone at my old Uni!) that can open huge text files.
http://www.lancs.ac.uk/staff/steveb/cpaap/pfe/pfefiles.htm

Title: Re: Kirkwood gaps?
Post by Mal on 09/23/08 at 21:26:06

And here's a table showing all of Jupiter's big resonances:


Code:
res multiple Period(s) distance(m) distance(AU)
6:1      0.17      6.24E+07      2.358E+11      1.58
5:1      0.20      7.49E+07      2.662E+11      1.78
4:1      0.25      9.37E+07      3.090E+11      2.07
3:1      0.33      1.25E+08      3.743E+11      2.50
2:1      0.50      1.87E+08      4.904E+11      3.28
3:2      0.67      2.50E+08      5.941E+11      3.97
4:3      0.75      2.81E+08      6.426E+11      4.30
5:4      0.80      3.00E+08      6.709E+11      4.48
1:1      1.00      3.75E+08      7.785E+11      5.20 <<<<<<<<<<<< Jupiter
4:5      1.25      4.68E+08      9.034E+11      6.04
3:4      1.33      5.00E+08      9.431E+11      6.30
2:3      1.50      5.62E+08      1.020E+12      6.82
1:2      2.00      7.49E+08      1.236E+12      8.26
1:3      3.00      1.12E+09      1.619E+12      10.82
1:4      4.00      1.50E+09      1.962E+12      13.11
1:5      5.00      1.87E+09      2.276E+12      15.22
1:6      6.00      2.25E+09      2.571E+12      17.18

Title: Re: Kirkwood gaps?
Post by Mal on 09/23/08 at 21:48:28

This is interesting - I plotted the first 32,000 asteroids of the 300k group (i.e. numbers 300,000 to 332,000) as a graph of asteroid number vs SMA. You can clearly see some gaps in here. They mostly seem to correspond to the Kirkwood Gaps but I'm not sure what's going on between 2.8 and 3.0 AU. Apparently the 5:2 and 7:3 resonances (which I didn't list on the table are in this region (5:2 is at 2.83 AU and 7:3 is at 2.96) so these are probably responsible for the "thinning out" there - see also the graph at http://en.wikipedia.org/wiki/Kirkwood_gap . I'm not sure what's so special about those particular resonances that they result in gaps though.

I guess those trails of asteroids stretching down toward the sun are the result of specific searches that found a lot of earth-crossers? (because they must be close in asteroid number, and therefore discovery date?).

Title: Re: Kirkwood gaps?
Post by frankuitaalst on 09/23/08 at 22:57:13


Mal wrote:
What might be interesting is to see if including Saturn in the system makes any difference - I think there are some secular resonances (the nu 6 one?) that can affect the inclination - these are mentioned on page 315 of Solar System Dynamics.

I got the asteroid data from astorb.dat , which can be found here: ftp://ftp.lowell.edu/pub/elgb/astorb.html

I stripped out the asteroid number, semimajor axis, eccentricity and inclination and used those to make the graphs. Note that the data contains asteroids outside the main belt, so if you're showing them on a graph and want to focus on the belt you have to trim the range of the graph axes. I'll attach the data in the next posts.
Thanks for the link , I'll add them to my favorites  :).
Actually the data above include already Saturn as I used the onlyplanets.gsim and added the bodies between mars and jupiter .

Title: Re: Kirkwood gaps?
Post by frankuitaalst on 09/24/08 at 05:01:18

Hallo Mal , can you repost the 400k.zip ?  It contains the 400k.csv instead of the 500k.csv

Title: Re: Kirkwood gaps?
Post by frankuitaalst on 09/24/08 at 05:32:32

Here's a picture of the Sma and ecc of the first 400k asteroids Mal provided .
1 line represents 1AU .
Eccentricity goes from 0 to 1 .
Its interesting to see how the planets clear the gaps.

Title: Re: Kirkwood gaps?
Post by frankuitaalst on 09/24/08 at 06:14:52

Zooming in into the 2 to 3 AU range gives the following picture ....

Title: Re: Kirkwood gaps- evolution
Post by frankuitaalst on 09/24/08 at 06:51:30

The animation herunder shows the evolution of 600 bodies in 3AU+/-40% , as above , but this time with a time-step of 5 years in a SMA-Eccentricity plot .
400 years are simulated in total .
Again the "stationary" points are planets ( Jupiter at the right ) .

It is clear that some regions are triggered very quickly ( 2.5 Au and 3.25 Au)
Interesting is the region in the middle between Mars and Jupiter where some bodies seem to decrease their sma and increase their eccentricity ...

EDIT : new animation attached

Title: Re: Kirkwood gaps - Inclination
Post by frankuitaalst on 09/24/08 at 07:25:23

The plot herunder shows the Inclination - SMA distribution of the data provided by Mal .
Max incl is 179.
Its amazing how there seems to be a stratification .
Apparently some regions are forbidden ?

Title: Re: Kirkwood gaps- evolution
Post by Mal on 09/24/08 at 17:05:13


frankuitaalst wrote:
It is clear that some regions are triggered very quickly ( 2.5 Au and 3.25 Au)
Interesting is the region in the middle between Mars and Jupiter where some bodies seem to decrease their sma and increase their eccentricity ...

EDIT : new animation attached


That's mindboggling...!  :o

I mean, that big "fold up" between 3 and 3.5 AU looks like it's right at the 2:1 resonance, and there's a smaller 'spike' that develops later at 2.5 AU that corresponds to the 3:1 resonance. I wonder why everything's compressing in and folding up on the 2:1 though, or is that just an illusion caused by the animation?

Fascinating stuff! (it's weird, I was never really interested in the Kirkwood Gaps but I'm really getting sucked in by all this now!)

Title: Re: Kirkwood gaps - Inclination
Post by Mal on 09/24/08 at 17:07:18


frankuitaalst wrote:
The plot herunder shows the Inclination - SMA distribution of the data provided by Mal .
Max incl is 179.
Its amazing how there seems to be a stratification .
Apparently some regions are forbidden ?


Yeah, I think some of those are caused by the "nu" resonances that I mentioned earlier. What would be really interesting would be to see how these graphs would look for an asteroid belt in a different system, but I guess we're running into computational problems because there's no way even any current computer could handle running a simulation of 10,000 (never mind 400,000) asteroids before we die of old age... is there??

Title: Re: Kirkwood gaps?
Post by Mal on 09/24/08 at 19:33:33

OK, i've checked and updated the attached files in the earlier posts, they should all be correct now.

Title: Re: Kirkwood gaps?
Post by frankuitaalst on 09/25/08 at 08:10:29


Mal wrote:
OK, i've checked and updated the attached files in the earlier posts, they should all be correct now.

Thanks , I'll integrate yhem into the other fle .
BTW : the total file in zip has about 6.15 MB. Anyone feels interested to receive it ?

About the output Mal , do you have special wishes about the range of output : is SMA 0 - 7 AU ok ? or should it be larger ?

Title: Re: Kirkwood gaps?
Post by Mal on 09/25/08 at 08:36:10

Well I'm mostly interested in the main belt... 1.5 to 5.5 AU should be fine to see what's going on there. Thanks!

I'd also be curious to see an animation (like your eccentricity one) to see what happens to the inclinations of your bodies between Mars and Jupiter. And also to see what happens to your bodies if you fill the space completely between Mars' and Jupiter's orbits (rather than just fill part of the space between them) to see what happens to bodies that start off closer to the planets.

Title: Re: Kirkwood gaps?
Post by frankuitaalst on 09/25/08 at 09:44:30

Here's the SMA-Ecc distribution of the data provided by Mal ( more than 420000 bodies )

Title: Re: Kirkwood gaps?
Post by frankuitaalst on 09/25/08 at 09:47:00

Same data as above but in SMA- Incl representation ...
The trojans of Jupiter are represented at around 5.1 AU .

Title: Re: Kirkwood gaps?
Post by frankuitaalst on 09/25/08 at 10:06:02


Mal wrote:
Well I'm mostly interested in the main belt... 1.5 to 5.5 AU should be fine to see what's going on there. Thanks!

I'd also be curious to see an animation (like your eccentricity one) to see what happens to the inclinations of your bodies between Mars and Jupiter. And also to see what happens to your bodies if you fill the space completely between Mars' and Jupiter's orbits (rather than just fill part of the space between them) to see what happens to bodies that start off closer to the planets.

If you want a more "zoomed" picture than provided above it can be made .

I'll try to represent also the inclination . My guess is there will be not much variation while IJup is close to zero .
If I fill the gap between Jupiter and Mars completely I think the objects close to Jupiter will drift away very quickly .
I'll give it a try in the weekend .
Question fo Tony : if I make objects with AU 3 +/-50% will this then result in a range of 1.5 Au to 4.5 AU ?

Title: Re: Kirkwood gaps - Inclination
Post by frankuitaalst on 09/25/08 at 10:35:34


Mal wrote:
What would be really interesting would be to see how these graphs would look for an asteroid belt in a different system, but I guess we're running into computational problems because there's no way even any current computer could handle running a simulation of 10,000 (never mind 400,000) asteroids before we die of old age... is there??

I think you're right .
But there may be a solution which can reduce the computing time.
Lets say we want to compute p bodies and add n asteroids ( p=10 , n=10000) .
The computing time goes up as : T = a. (n+p)*(n+p) , so kwadratic .
10 times more bodies gives 100 times longer run ...

But : if one runs the simulation once with the p bodies and stores the obtained data , then a separate program can calculate an additional body in a time T2= b*p . ( if the asteroid is small it has no influence upon the other bodies , so they don't have to be calculated ; their previous orbits which are known reman valid ) .
So if we run this program n times we have a total time of : T2 = n*b*p . This is the time to integrate the n asteroids .
T2/T gives : b*p/(a*n) , or if a=b then : T2/T = p/n .
If p=10 and n=10000 asteroids then the simulation in this way may be performed 10000/10 = 1000 times faster ...
Of course this requires a lot of reprogramming ....
I think jpl calculates orbits of asteroids in this way , assuming an asteroid doesn't influence the major bodies ...


Title: Re: Kirkwood gaps- Inclination change
Post by frankuitaalst on 09/25/08 at 12:11:01

Adding the inclination change to the animation gives the following picture :
Eccentricity in red , inclination in green .
Animation covers 100 years after the initial circular orbits between Mars and Jupiter .
Each frame covers 1 year . Total of 100 frames .
The inclination change is at maximum closer to Jupiter .
As may be seen the changes in eccentricity appear to come in waves as the eccentricity is pumped up by the resonances .

Title: Re: Kirkwood gaps?
Post by Mal on 09/25/08 at 20:08:30

what's causing the "spurts" in eccentricity? It's like there's a rhythmic increase in one set of asteroids, then in another set, then back to the first one... is the periodicity of that down to Jupiter's orbital period or something?

Title: Re: Kirkwood gaps?
Post by Mal on 09/26/08 at 08:07:48


frankuitaalst wrote:
Here's the SMA-Ecc distribution of the data provided by Mal ( more than 420000 bodies )


Is it me or is there a slight clumping of asteroids going between about 1 AU (at zero eccentricity) to 2 AU (at 0.5 eccentricity)?

Title: Re: Kirkwood gaps?
Post by frankuitaalst on 09/26/08 at 11:17:21


Mal wrote:
what's causing the "spurts" in eccentricity? It's like there's a rhythmic increase in one set of asteroids, then in another set, then back to the first one... is the periodicity of that down to Jupiter's orbital period or something?

It's intruiging isn't it ? I don't know exactly what happens here but my guess is that these bodies which are in a 1:2 resonance to Jupiter get a boost every time they are close to Jupiter , increasing their eccentricity ..
Those which are lagged for 180 get also a boost , but later .
This might explain the waves ??

Title: Re: Kirkwood gaps?
Post by frankuitaalst on 09/26/08 at 13:19:44

What causes the spurts as Mal asked ? Sure some resonance interaction, or the lack of at other distances .
But its very hard to visualize this .
Is a body at a certain position changing its eccentricity or does it change its sma over time ?
Both .
The animation in annex shows the variation of SMA/Year as a function of SMA of the above simulation .
One can see  bodies having the same SMA at a certain time can decrease or increase their SMA .
The plot is centered on dSMA/year =0 .
The resonance mechanism must be very complex .
I can only draw one conclusion : the dynamical behaviour becames stronger the more the body is near to Jupiter .

Title: Re: Kirkwood gaps?
Post by Mal on 09/26/08 at 14:59:30

That's bizarre... it looks like there's a central core that oscillates a small amount around 0 there, but as you get toward Jupiter the rest of the asteroids fluctuate in a more extreme way. I have no idea what's going on there - and there doesn't seem to be a link to the resonant distances either.

Title: Re: Kirkwood gaps?
Post by Mal on 09/29/08 at 23:11:02

OK, I just made my computer cry a bit...

I've now got a text file about 200 years of sma, ecc, and inc data for 500 asteroids between Mars and Jupiter (2.8 AU +/- 40%, starting at ecc 0 an inc 0 on 1/1/2005, set at uniform distribution), sampled every 150 days. I started with the fullsystem.gsim, deleted everything except the 8 planets (and Pluto) and added the 500 asteroids. I also, for a twist, replaced Mars with another Jupiter, so there's a Jupiter inside and outside the belt. I just wanted to see if that had any effect.

Unfortunately I have no idea what to do with the data. I have a big 17MB text file that compresses down to about 7 MB (too big to attach), and my text editor (that has been known to handle 1GB text files) actually crapped out on opening the file, which was weird!

So... frank, can I send this to you somehow and you can maybe work your graph magic on it? I'd be curious to see how this looks.

Title: Re: Kirkwood gaps?
Post by frankuitaalst on 10/01/08 at 13:15:08

yes you can send it to me by mail . I think my mail can handle 10MB . The visualisation program can handle more than 40MB , so I guess this is not a problem .

Title: Re: Kirkwood gaps?
Post by Mal on 10/01/08 at 23:47:09

OK, frank - thanks! Check your PMs, I've put it on an FTP site for you to download (easier that way!).

Title: Re: Kirkwood gaps?
Post by frankuitaalst on 10/02/08 at 04:01:50

Here's the plot you requested showing the e vs Sma over the 200 years .
The asteroids seem to have a hard time  :)

Title: Re: Kirkwood gaps?
Post by frankuitaalst on 10/02/08 at 09:10:58

An animation over the first 50 years shows that the asteroids below 2AU are unstable from the beginning .
Further around 3.5AU there is some kind of resonance .

Title: Re: Kirkwood gaps?
Post by frankuitaalst on 10/02/08 at 10:30:53

The evolution of inclination of the 500 asteroids can be seen hereunder .
Seems totally chaotic .
Many asteroids are also injected inside Earths orbit .

Title: Re: Kirkwood gaps?
Post by Mal on 10/02/08 at 13:34:47

Thanks a lot... very interesting (what the heck is with that massive 'tail' of stuff going into high ecc/high sma space on the first graph??) - from the animation it looks like it's composed of asteroids that have been ejected there by the second Jupiter in Mars' orbit.

Guess I should have left it running for longer to see what happened later, but it really was grinding my machine to a halt...Can you do an animation over the whole 200 year period at all?

Title: Re: Kirkwood gaps?
Post by frankuitaalst on 10/02/08 at 13:37:59


Mal wrote:
Thanks a lot... very interesting (what the heck is with that massive 'tail' of stuff going into high ecc/high sma space on the first graph??) - from the animation it looks like it's composed of asteroids that have been ejected there by the second Jupiter in Mars' orbit.

Guess I should have left it running for longer to see what happened later, but it really was grinding my machine to a halt...Can you do an animation over the whole 200 year period at all?

I can do an animation for the 200 years , but the file will have 1.2MB unless I reduce the size or compress it even more in resolution . I'll give it a try .

Title: Re: Kirkwood gaps?
Post by frankuitaalst on 10/02/08 at 13:50:10

The next 70 years of the above animation shows that the big tail in fact is the result of quickly moving bodies ...

Title: Re: Kirkwood gaps?
Post by Mal on 10/02/08 at 20:04:44

Interesting... I think the big bump around 3.25 AU must be the 2:1 resonance with (the outer) Jupiter, but the smaller bump around 2.4 AU seems a bit off from the 3:1 resonance (which should be at 2.5 AU). However... at 2.42 AU we have the 1:2 resonance with the inner Jupiter (we'll call it "Marspiter") - so I wonder if that's causing it...

that big tail is also interesting... it looks like "Marspiter" is kicking asteroids that are in and around its orbit into orbits with higher sma and higher eccentricity, and into orbits with lower sma and higher eccentricity (it even looks like a freeze-frame of an impact crater blast centred on 1.524 AU in the sma/ecc graph). What I don't get is why it looks like some of them are coming back into more normal orbits periodically...

Title: Re: Kirkwood gaps?
Post by frankuitaalst on 10/02/08 at 22:02:46

The next "50" years :
watch the behaviour of the peak around 3.5 AU , Due to the eccentricity of the Marspiter ?

Title: Re: Kirkwood gaps?
Post by Mal on 10/02/08 at 22:52:10

Oh yeah, that's weird - the 2:1 peak is shearing a bit! Could be due to the eccentricity maybe...?

The 2.42 peak is definitely real though... so I guess that's evidence that a 1:2 would cause a Gap too? (which we don't have in the real solar system since there's no belt beyond Jupiter's orbit).

Do you have a way of seeing if the Marspiter captured any trojans?

Title: Re: Kirkwood gaps?
Post by frankuitaalst on 10/05/08 at 13:44:14


Mal wrote:
Do you have a way of seeing if the Marspiter captured any trojans?

I think there are no trojans to  Marspiter in the above animation around 1.52 AU .
Some bodies come close , but there is none which stays there .


Title: Re: Kirkwood gaps?
Post by Mal on 10/05/08 at 14:15:33

I wonder if that's because they're not stable closer to the sun? Or if the real Jupiter messes them up?

Title: Re: Kirkwood gaps?
Post by frankuitaalst on 10/05/08 at 14:26:12

In my opinion there  is not enough time in the simulation to get trojans . Some may evolve to this behaviour after much more time .
Trojans can be stable here ( fi . see the subject Mars Trojans ) .

Title: Re: Kirkwood gaps?
Post by Mal on 10/05/08 at 14:36:59

Well I'm doing a new run now, of a totally new system with a (200 asteroid) belt, just to see if the same sort of gaps are created in the belt.

Would it be possible for me to use your graph drawing program at all? Or would I have to send you the results again if I wanted to see the graphs/animations?

Title: Re: Kirkwood gaps?
Post by frankuitaalst on 10/05/08 at 22:07:38

I'll send you the program as an executable . Hope that it works on your computer also as I haven't tested it elsewhere.

Title: Re: Kirkwood gaps?
Post by Mal on 10/05/08 at 22:34:26

cool, thanks a lot!

Title: Re: Kirkwood gaps?
Post by frankuitaalst on 10/06/08 at 09:01:44

In annex you'll find the visualisation tool.
It represents the data from a .txt file from GravSim containing the SMA(a),e( eccentricity), i ( inclination) .
The program should be kept in a separate folder containing the .txt file of GravSim .
Instruction :
* (right click on the icon to copy it )
* First give the file an .exe extension (once )
* Run the program double clicking .
* It will ask for the file to represent : enter the filename + extension ( you can copy the filename and paste it )
* The program then reads the data
* It will then prompt you to enter :
** maximum eccentricity
** maximum SMA
** minimum SMA
** continious representation or adding each screen shot till the end
** cycle of representation ( 1 : all data to represent ; 2: every second to represent ....aso )
Please be aware that the program will write a sequence of screenshots in the folder you use .

In case of trouble you can contact me .



Title: Re: Kirkwood gaps?
Post by Mal on 10/06/08 at 13:36:49

thanks, I'll take a look at this later tonight and see if I can get some results posted for my new asteroid belt system.

Title: Re: Kirkwood gaps?
Post by frankuitaalst on 10/06/08 at 13:40:21

Mal , If the program works well on your PC you should get a picture looking as :

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