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Message started by Mal on 03/15/09 at 17:40:15

Title: Moon formation sims
Post by Mal on 03/15/09 at 17:40:15

Ok, here's what I propose. For myself, frank, and anyone else who wants to give it a go - if you want to post gsim files for moon formation simulations then let's post them on this thread.

The rules are to:

(1): List the starting conditions as exactly as you can in the following format:

Timestep: 128
Primary Mass: 1.176 Jupiter Masses
Primary Radius: 73568.5 km
Number of bodies: 605
Mass: 1e21 kg +/- 0 km each
Radius: 430 km +/- 0 km each
Eccentricity: 0.025 +/- 100%
Inclination: 0 +/- 0°
Longitude/perifocus arg/Mean Anomaly: 180 +/- 100% (random)
SMA: 300,000 to 600,000 km

(2) Post the gsim file in its initial state (before the run begins)

(3) Allow the simulation to run for a minimum of 3,000 years.

(4) If you want to post supplementary graphs or excel sheets or screenshots then feel free, but it's probably best to do it all in one go for each gsim.

(5) At the end, post the mass, diameter, sma and eccentricity of each of the final moons that are the result.

Shall we give this a go and see what happens?

Title: Re: Moon formation sims
Post by Mal on 03/15/09 at 20:10:25

Run #1:

Timestep: 128
Primary Mass: 1.176 Jupiter Masses
Primary Radius: 73568.5 km  
Number of bodies: 605  
Mass: 1e21 kg +/- 0 km each
Radius: 430 km +/- 0 km each
Eccentricity: 0.025 +/- 100%
Inclination: 0 +/- 0°
Longitude/perifocus arg/Mean Anomaly: 180 +/- 100% (random)
SMA: 300,000 to 900,000 km


RESULTS: (3004 years)

3 moons

1: 1.56e23 kg, 4629.56 km diameter, 354625.997 km SMA, 0.07786564 ecc
2: 2.98e23 kg, 5744.3 km diameter, 596360.5779 km SMA, 0.043890744 ecc
3: 1.51e23 kg, 4579.56 km diameter, 866242.1891 km SMA, 0.027720794 ecc


COMMENTS:
- System had 3 moons after 147 years of sim time.
- Interestingly, the total mass of the moons exactly adds up to the total mass of all 605 initial moonlets - so why weren't any of the moonlets ejected from the system?
- The three moons are similar in radius and mass.

Title: Re: Moon formation sims
Post by Mal on 03/15/09 at 23:36:59

initial gsim for Run #1

Title: Re: Moon formation sims
Post by Mal on 03/16/09 at 00:25:46

Run #2:

Timestep: 128
Primary Mass: 1.176 Jupiter Masses
Primary Radius: 73568.5 km  
Number of bodies: 605  
Mass: 1e21 kg +/- 0 km each
Radius: 430 km +/- 0 km each
Eccentricity: 0.25 +/- 100%            <----------- higher initial eccentricity
Inclination: 0 +/- 0°
Longitude/perifocus arg/Mean Anomaly: 180 +/- 100% (random)
SMA: 300,000 to 900,000 km  


RESULTS (3083 years):

3 moons:
1: 2.06e23 kg, 5079.11 km diameter, 371436.3047 km SMA, 0.038925995 ecc
2: 3.87e23 kg, 6267.13 km diameter, 637621.7792 km SMA, 0.016626004 ecc
3: 1.00e21 kg,  860.00 km diameter, 1035171.484 km SMA, 0.05293083 ecc

COMMENTS:
- System has 3 moons after 47 years of sim time.
- Curiously we now have LESS mass than we started - a total of 5.94e23 kg. So 11 moonlets (1e21 kg each) worth of mass has been ejected from the system. Does having a higher eccentricity make it easier to eject moonlets?
- moons are more widely spaced than run #1. Would have to do more runs to see if this was typical of higher eccentricity runs.
- The outermost moon is an unmodified original moonlet! Its orbit seems stable but this is certainly the most vulnerable to being ejected from the system or colliding with another moon in the future.
- the final orbits are remarkably circular given the initial eccentricity range (0.00-0.50 ecc) - I thought that the resulting eccentricity would average out to 0.25, but it's actually close to zero! It may be interesting to see what happens if we use a range of say 0.2 +/- 50% (to get 0.10 to 0.30) - would the eccentricities still average out to near-zero, or would they average out to 0.1 or higher?

Title: Re: Moon formation sims
Post by Mal on 03/16/09 at 00:26:05

initial gsim for run #2

Title: Re: Moon formation sims
Post by frankuitaalst on 03/16/09 at 10:01:32

My guess is that the original eccentricities will average out going to almost zero as the system ages .
Eccentricity is not a property which is conserved .

BTW : why do you start with eccentric orbits ?

Title: Re: Moon formation sims
Post by Mal on 03/16/09 at 10:48:33


frankuitaalst wrote:
My guess is that the original eccentricities will average out going to almost zero as the system ages . Eccentricity is not a property which is conserved .


I was still expecting to see some significant eccentricity in the final moons... but I guess that expectation was wrong :).


Quote:
BTW : why do you start with eccentric orbits ?


It's more realistic that way. I can do a run with perfectly circular orbits too though.

Title: Re: Moon formation sims
Post by Mal on 03/16/09 at 20:01:26

Run #3:

Timestep: 128
Primary Mass: 1.176 Jupiter Masses
Primary Radius: 73568.5 km  
Number of bodies: 605  
Mass: 1e21 kg +/- 0 km each
Radius: 430 km +/- 0 km each
Eccentricity: 0 +/- 0%              <-------------- no eccentricity, by popular demand! :)
Inclination: 0 +/- 0°
Longitude/perifocus arg/Mean Anomaly: 180 +/- 100% (random)
SMA: 300,000 to 900,000 km  


RESULTS: (3039 years)

3 moons

1: 7.80e22 kg, 3674.49 km diameter, 325557.6814 km SMA, 0.058567295 ecc
2: 2.96e23 kg, 5731.42 km diameter, 476325.9648 km SMA, 0.054341125 ecc
3: 2.27e23 kg, 5246.15 km diameter, 877642.5021 km SMA, 0.11714745 ecc


COMMENTS:
- final three moons formed 96 years after formation
- their orbits are pretty eccentric, considering that none of the particles had any to start with!
- total mass of moons is 6.01e23 kg, so we have still lost some mass. Maybe it was coincidental that the first run didn't lose any?
- we're still ending up with three big moons though... I guess that the scale of the disc is small enough for the big moons to suck everything in? I just wonder why we don't end up with say, five or six smaller moons.

Title: Re: Moon formation sims
Post by frankuitaalst on 03/17/09 at 00:16:31


Mal wrote:
- we're still ending up with three big moons though... I guess that the scale of the disc is small enough for the big moons to suck everything in? I just wonder why we don't end up with say, five or six smaller moons.

I think the fact you don't have 6 moons is due to the gravitational interactions , the system getting "full" .
I've run three sims now with range 300.000-2.000.000 km and I always end up with 6,7,7 moons .
Nice job Mal !

Title: Re: Moon formation sims
Post by Mal on 03/17/09 at 01:35:45

Run #4:

Timestep: 128
Primary Mass: 1.176 Jupiter Masses
Primary Radius: 73568.5 km  
Number of bodies: 605  
Mass: 1e21 kg +/- 0 km each
Radius: 430 km +/- 0 km each
Eccentricity: 0.025 +/- 100%              
Inclination: 0 +/- 0°
Longitude/perifocus arg/Mean Anomaly: 180 +/- 100% (random)
SMA: 300,000 to 1,500,000 km  <-------------- double the width of the disk from previous runs


RESULTS: (3018 years)

4 moons

1: 9.70e22 kg, 3951.44 km diameter, 382436.5155 km SMA, 0.054825793 ecc
2: 1.7E+23 kg, 4764.11 km diameter, 648907.2813 km SMA, 0.03962017 ecc
3: 2.53E+23 kg, 5439.25 km diameter, 1031941.169 km SMA, 0.032185083 ecc
4: 8.5E+22 kg, 3781.27 km diameter, 1645691.395 km SMA, 0.050202389 ecc


COMMENTS:
- four moons formed after 245 years.
- A wider disk (with the same total mass as before) produced four large moons (again, comparable in size and mass). No mass ejected from the system this time though (interestingly this is the same as run #1 - which also had no ejections - but with a wider disk).
- The orbits are similar in scale to (but not the same as) the Galilean Satellites, with the  "europa" and "ganymede" equivalents being the largest moons.

Title: Re: Moon formation sims
Post by Mal on 03/17/09 at 01:38:30

Almost forgot - here's the initial gsim for run #3

Title: Re: Moon formation sims
Post by Mal on 03/17/09 at 01:38:51

And here's the one for run #4

Title: Re: Moon formation sims
Post by Mal on 03/17/09 at 01:47:10


frankuitaalst wrote:
I think the fact you don't have 6 moons is due to the gravitational interactions , the system getting "full" . I've run three sims now with range 300.000-2.000.000 km and I always end up with 6,7,7 moons .
Nice job Mal !


Thanks! Are you going to post your sims too?

Title: Re: Moon formation sims
Post by Mal on 03/17/09 at 01:52:31

I have an ulterior motive here... I want to see if it's possible to make a system like Saturn's satellite system. It recently struck me as being really weird that Jupiter's and Uranus' satellites are roughly similar in size and mass (within each system), but Saturn's is really skewed in favour of Titan, which contains almost all of the mass of the satellite system.

And so far it's looking as if Jupiter's and Uranus' systems are more "normal"... if you take out Titan and look at Saturn's then you get seven major satellites that are roughly similar in size too, so I'm wondering if Titan was somehow an interloper that formed elsewhere and was captured by Saturn (and possibly disrupted some of the satellites in the system, e.g. Hyperion)

Right now the only way I can think of that might form Titan naturally in the system is if there's a really densely packed band of material with a lot of mass at a fixed distance from Saturn within the rest of the disk, so when that forms a moon it forms more quickly and pulls in more stuff from around it before anything else does. But that's not very likely to happen (is it?).

Title: Re: Moon formation sims
Post by frankuitaalst on 03/17/09 at 11:48:19


Mal wrote:
I have an ulterior motive here... I want to see if it's possible to make a system like Saturn's satellite system. It recently struck me as being really weird that Jupiter's and Uranus' satellites are roughly similar in size and mass (within each system), but Saturn's is really skewed in favour of Titan, which contains almost all of the mass of the satellite system.

And so far it's looking as if Jupiter's and Uranus' systems are more "normal"... if you take out Titan and look at Saturn's then you get seven major satellites that are roughly similar in size too, so I'm wondering if Titan was somehow an interloper that formed elsewhere and was captured by Saturn (and possibly disrupted some of the satellites in the system, e.g. Hyperion)

Right now the only way I can think of that might form Titan naturally in the system is if there's a really densely packed band of material with a lot of mass at a fixed distance from Saturn within the rest of the disk, so when that forms a moon it forms more quickly and pulls in more stuff from around it before anything else does. But that's not very likely to happen (is it?).

I think it's very difficult to get a system with a Titan Mass at the outside if one starts from a constant distribution . Most systems will tend to put the larger bodies in the center of the distribution . This may be one of the reasons some scientists think Titan may be captured during the planet formation .
Here's an animation of my 3 results , always started at Ecc=0 and distribution from 300.000 to 2.000.000 kms , except for one sim where the upper limit was 2300.000 kms.

Title: Re: Moon formation sims
Post by frankuitaalst on 03/17/09 at 11:52:46

What I said about the tendency of a system to put the larger bodies at the center may become clear here :
The plot gives the results of the above sims .
X-axis represents the Sma in 1000 kms.
Y-axis is the % Mass distribution of each moon .
Smaller moons tend to be near the planet , while the bigger ones are found near the middle ...
Curious what the distribution will be if more simulations are run .

Title: Re: Moon formation sims
Post by Mal on 03/17/09 at 16:18:52

The thing we have to keep in mind is that this isn't the whole story - there's things like gas drag within the protosatellite disk, and more material coming in from the protoplanetary disk as well. Plus of course the lack of tidal interactions (which will be important for the innermost objects).

But I think this is still useful to give the right kind of idea for how regular satellite systems can form.

Title: Re: Moon formation sims
Post by Mal on 03/19/09 at 22:15:12

Run #5:

600 bodies (blue, tiny)
5e20 mass each
341km  radius each
0 ecc?
0 inc
random orbits
300,000 to 900,000

305 bodies (purple, moonlet) <-------------dense second ring of material at fixed distance within main disk.
1e21 mass each
430km  radius each
0.025 +/- 100% ecc
0 inc
random orbits
600,000 to 650,000

RESULTS (4403 years)

4 moons:
1: 3.45e22 kg, 2797.27 km diameter, 336699.8338 km SMA, 0.071377976 ecc, tiny 318
2: 9.90e22 kg, 3975.64 km diameter, 438558.2045 km SMA, 0.040308547 ecc, tiny 401
3: 3.90e23 kg, 6281.56 km diameter, 627899.5448 km SMA, 0.020376947 ecc, moonlet 63
4: 8.30e22 kg, 3749.10 km diameter, 869612.6261 km SMA, 0.0575289 ecc, moonlet 135


COMMENTS:
- I made two belts - a main "tiny" belt containing 600 bodies at 5e20kg, from 300k-900k (I think I accidentally set their ecc to 0), and a denser "moonlet" belt within the main belt containing 305 bodies at 1e21 kg from 600k to 650k with ecc 0.00-0.05.
- it only took 17 years to form the four satellites.
- However, the moons are listed in gravsim in a strange order - the two outer moons are listed first, then the two inner moons. I have no idea why.
- Bizarrely there is MORE mass here than there was to start with?! I have no idea how that happened, I seem to have sprouted an extra 3 "tinies" worth of mass (6.065e23 kg total instead of 6.05e23 kg. I was sure that I had 600 tinies (3e23kg total) and 305 (3.05e23 kg total) moonlets...! I guess I must be wrong about that but... weird! :o
- I did however end up with a larger moon around the 600k distance, with the other three moons being about the same sort of size as in the other sims. I'm not sure if the largest moon formed first though (my collision.dat file for some reason didn't record this gsim?) - as far as I can see the last body in its neighbourhood that might have been in its neighbourhood was moonlet 97 which disappeared at year 3 (it hit either 63 or 135), then 317 and 318 merged closest to the planet at year 17 and there were four moons after that.
- Very strange. Maybe someone else could regenerate the run from scratch and see what they get?

Title: Re: Moon formation sims
Post by Mal on 03/19/09 at 22:19:11

initial gsim for run #5.

Title: Re: Moon formation sims
Post by frankuitaalst on 03/20/09 at 09:26:32


Mal wrote:
- Bizarrely there is MORE mass here than there was to start with?! I have no idea how that happened, I seem to have sprouted an extra 3 "tinies" worth of mass (6.065e23 kg total instead of 6.05e23 kg. I was sure that I had 600 tinies (3e23kg total) and 305 (3.05e23 kg total) moonlets...! I guess I must be wrong about that but... weird! :o

I had the same experience with missing or added mass . In my 5 runs with 400 bodies each there was a loss or gain of maximum 5 body masses (395...403 ) . I didn't pay much attention to it .

Title: Re: Moon formation sims
Post by Mal on 03/20/09 at 10:32:33


frankuitaalst wrote:
I had the same experience with missing or added mass . In my 5 runs with 400 bodies each there was a loss or gain of maximum 5 body masses (395...403 ) . I didn't pay much attention to it .


Missing mass could just be mass ejected from the system (it'd be nice if there was a flag for that). But if mass is being added then there must be a bug there somewhere... Tony, any ideas?

Title: Re: Moon formation sims
Post by Tony on 03/20/09 at 11:54:45

Mass should be conserved.  It could be a bug.  Can you send me before and after sims?

Title: Re: Moon formation sims
Post by Mal on 03/20/09 at 12:40:15


Tony wrote:
Mass should be conserved.  It could be a bug.  Can you send me before and after sims?


The "before" sim is attached to the previous post, it's the AccraMoonFormation0000r5.gsim file.

Can you see what's going on with the moon sizes as well? They don't seem to increase in radius as shown in the gravsim window, though they are increasing in radius in the file itself.

Title: Re: Moon formation sims
Post by frankuitaalst on 03/21/09 at 03:38:42

Mal , for some reason your above program terminates after some seconds without warning . I don't know why . I had this with some other simulations , I think when there are some bodies merging from the start , but this isn't the case in your simulation as I can see move the timer .

Hereunder is the result of 5 sims I've made with 300.000-2.000.000 km range around Jupiter ( 400 circular bodies ) .
Black circles are the real thing .
The distributions seem to match relatively well , except for the innermost Io which has about 3 times more mass .
If the smaller inner moons are merged into each other the situation might correspond better to reality .
Maybe Io really was created by merging some smaller protomoons orbiting close to Jupiter as a relict of Jupiters creation itself  ?

Title: Re: Moon formation sims
Post by Tony on 03/21/09 at 15:31:39

I get the same problem as Frank.  I'll have to debug this.  As far as size, your objects are 860 km and your screen scale is 16 million km.  So each pixel represents 10000 km.  So one has to be larger than this before it is bumped up to 2 pixels in size.

Title: Re: Moon formation sims
Post by Mal on 03/21/09 at 16:37:21

huh. let me recreate it here and upload a new version and you can try that (I'm using the latest beta too)

EDIT: here's the start. I recreated it exactly as shown above, but I gave the 600 'tinies' an eccentricity of 0.025 +/- 100% (which is what I wanted to give them initially). So it's:

Run #5b:

600 bodies (blue, tiny)
5e20 mass each
341km  radius each
0.025 +/- 100% ecc  
0 inc
random orbits
300,000 to 900,000 km

305 bodies (purple, moonlet) <-------------dense second ring of material at fixed distance within main disk.
1e21 mass each
430km  radius each
0.025 +/- 100% ecc  
0 inc
random orbits
600,000 to 650,000 km

Title: Re: Moon formation sims
Post by Mal on 03/21/09 at 22:46:36

OK, so here are the results for 5b (left it running for 15851 years though)


RESULTS (15851 years)

3 moons:
1: 8.25e22 kg, 3740.64 km diameter, 350288.8325 km SMA, 0.060213114 ecc, tiny 6
2: 2.025E+23 kg, 5048.12 diameter, 803979.2898 km SMA, 0.029265853 ecc, moonlet 663
3: 3.195E+23 kg, 5877.36 km diameter, 565369.4297 km SMA, 0.023163272 ecc, moonlet 673


COMMENTS:
- this time it took much longer to form three satellites - 1127 years. Before that, there were four moons since year 94.
- However, the moons are listed in gravsim in a strange order - the two outer moons are listed first, then the two inner moons. I have no idea why.  
- This time the total mass was 6.045e23, which is one "tiny" less than what we started with.
- Again, the largest moon is at the 600k distance, but it's not really that much bigger than the second moon...
- This time the masses were listed in the right order in gravsim.

Title: Re: Moon formation sims
Post by Mal on 03/21/09 at 22:47:28

And here's what the run was like at the end when I stopped it.

Title: Re: Moon formation sims
Post by frankuitaalst on 03/22/09 at 07:33:04

I did the following experiment :
Took a full develloped system with 7 moons
Added the same original system with 400 small bodies
---> 7 moons with a lot of bodies as start of a new sim .
Result : the 7 moons which were stable end up with 4 moons + ca. 20 original small bodies which sma increases with time .
The result in Mass as function of Sma is shown here :
The result is shown in red , whereas blue represents the original sim and black is the Jovian configuration .

Interpretation : adding smaller moonlets will reduce the number of big moons . The merging occurs very quickly in the inner region . The outer region needs more time to merge . Some moonlets will not be merged but will escape the system over longer timeperiods as their eccentricity builds up .

Title: Moon formation sims
Post by frankuitaalst on 03/22/09 at 07:37:01

The evolution of the individual moonlets' Sma can be seen here versus time .
The inner space is rather quickly cleared as the moonlets mere with the existing moons . Some inner moons also merge . The outer moons need more time to merge .
Result is that the system "ends" with 4 big moons and about 20 very tiny moonlets at high eccentricity .

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