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Moon formation sims (Read 13628 times)
EDG
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Moon formation sims
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?
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« Last Edit: 03/15/09 at 21:00:57 by EDG »  

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EDG
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Re: Moon formation sims
Reply #1 - 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.
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« Last Edit: 03/16/09 at 00:30:39 by EDG »  

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Re: Moon formation sims
Reply #2 - 03/15/09 at 23:36:59
 
initial gsim for Run #1
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Re: Moon formation sims
Reply #3 - 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?
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Re: Moon formation sims
Reply #4 - 03/16/09 at 00:26:05
 
initial gsim for run #2
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Re: Moon formation sims
Reply #5 - 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 ?
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Re: Moon formation sims
Reply #6 - 03/16/09 at 10:48:33
 
Quote from 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 .

 
I was still expecting to see some significant eccentricity in the final moons... but I guess that expectation was wrong Smiley.  
 
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.
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Re: Moon formation sims
Reply #7 - 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! Smiley
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.
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Re: Moon formation sims
Reply #8 - 03/17/09 at 00:16:31
 
Quote from Mal on 03/16/09 at 20:01:26:
- 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 !  
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Re: Moon formation sims
Reply #9 - 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.
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Re: Moon formation sims
Reply #10 - 03/17/09 at 01:38:30
 
Almost forgot - here's the initial gsim for run #3
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Re: Moon formation sims
Reply #11 - 03/17/09 at 01:38:51
 
And here's the one for run #4
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Re: Moon formation sims
Reply #12 - 03/17/09 at 01:47:10
 
Quote from frankuitaalst on 03/17/09 at 00:16:31:
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?  
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Re: Moon formation sims
Reply #13 - 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?).
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Re: Moon formation sims
Reply #14 - 03/17/09 at 11:48:19
 
Quote from 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?).

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.  
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