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Binary Eccentricity Test - volunteers needed! (Read 30324 times)
EDG
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Binary Eccentricity Test - volunteers needed!
10/24/06 at 19:35:00
 
So let's try something here - Tony was wanting some structured test runs so let's try a little bit of low-tech distributed computing here Wink  
 
 
I'm going to run a simulation of Figure 1 of the paper with the following initial parameters:
 
-------------
Simulation (1)
 
Primary Star: 1 solar mass, 1 solar radius (yellow)
 
Planet: SMA = 2.5 AU, mass = 1 Jupiter mass, radius = 69,911 km , e=0.000, i=0.000, long of asc. node = 54, arg of perifocus = 146, mean anomaly = 16. (purple)
 
Companion: SMA = 750 AU, mass = 0.9 solar masses, radius = 626400 km (0.9 solar), e = 0.800, i = 75, long of asc. node = 179, arg of perifocus = 39, mean anomaly = 140. (red)
 
Timestep = 65536 secs.
Start time = year 1 1 0 , time 0 0 0
------------------
 
Now, what I need are some people to run this simulation with a few changes (these are all to be run in separate runs), so we can see how the different variables affect everything:
 
Simulation 2) As (1), but companion eccentricity = 0.000
 
Simulation 3) As (1) but planet SMA = 0.5 AU
 
Simulation 4) As (1), but companion mass = 0.08 solar masses, companion radius = 65,000 km  
 
 
So everything else remains the same in each run. Make sure you specify the values of the longitude of ascending node etc in all the runs to those shown above - the only things we want to change in each run are what's specified above, otherwise different starting positions/orbit orientations might make things wildly different (I just generated some random numbers for those). Also make sure that all the +/- cells are set to zero - we want no variability in the parameters here!  
 
Leave that running for at least 50 million years. You'll need the latest beta (14Oct) of Gravity Simluator for this though, because we need to output data to a text file to plot it. Set that to print output data (a, e, i, little omega, and big omega) for the planet and companion every 1000 years, and we want 50,000 samples (excel can only handle up to 65536 rows, so 50k is a good number).  
 
Then post results on this board (might be worth starting new threads for each run?), and also graphs if you can.  
 
Let's see how tihs goes! Smiley
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Re: Binary Eccentricity Test - volunteers needed!
Reply #1 - 10/24/06 at 20:49:49
 
Interesting. Apparently 50,000 samples every 1000 years is too much for the program - I got an overflow error and it crashed.  Tongue
 
OK, set it to 5,000 samples, every 10,000 years. That seems to work.
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Re: Binary Eccentricity Test - volunteers needed!
Reply #2 - 10/24/06 at 20:54:03
 
Here's a link to the Simulation (1) gsim file at the start. You'll need to speed it up to 65536.  
 
simulation1.gsim
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Re: Binary Eccentricity Test - volunteers needed!
Reply #3 - 10/24/06 at 23:07:24
 
Hrm.  
 
After 2.8 million years, it's not doing much. And it doesn't look like it's doing what it's supposed to yet...  
 

 
 
So far the eccentricity of the planet (pink line) is wobbling around 0.017 with a period of 170,000 years. The eccentricity of the companion (blue line) is wobbling around 0.795-ish with a period of about 210,000 years. (100 units on the x-axis is 980,000 years). Planet inclination is increasing monotonically from 0.0, it's at abut 7 degrees now.  
 
Looking at the graph, it's still early days yet - we're still in the bottom left corner. I'll give it til I wake up... that should be at least 10 million years (I'm a long sleeper Wink ) it should have climbed up to about 0.2 by then. Though I wonder what timestep they used to make their graph. Of course, if it stays like this and doesn't increase then something's wrong - either the time step is too large, or gravity simulator isn't accurate enough somehow, or they're wrong Smiley.  
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Re: Binary Eccentricity Test - volunteers needed!
Reply #4 - 10/25/06 at 00:02:02
 
See this paper: http://arxiv.org/abs/astro-ph/0502404 for how to calculate the period of the eccentricity cycles!  
 
According to eqn (2) there, the period of the Kozai cycle for this run (Simulation #1) should be about 25.6 million years.
 
For Simulation #2, it should be 118.7 million years - the circular inclined orbit makes a difference!  
 
For Simulation #3, it should be 3.2 billion years. So being close to the star makes a big difference!
 
For Simulation #4, it should be 288 million years.  
 
 
So er, don't let that put anyone off trying to simulate this anyway Wink. I've still got to see if we can even see this cycle in the program...!
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Reply #5 - 10/25/06 at 07:29:38
 
Something's definitely wrong here.  
 

 
After 15 million years, the eccentricity of the planet hasn't increased at all - it's still cycling around 0.0017 (for some reason there was a data recording hiccup around 2.8 million years - it stopped recording for a while, which is why the envelope looks wider there. I think it might be because I opened the txt file with excel, maybe it can't write to it while it's being used). That and the period of the cycle is wrong too (compared to the equation in the paper), it's far too short.  
 
The inclination of the planet is now 40 degrees though. I'm half wondering if the inclination is going to be what ends up on a big cycle. Will it increase to a maximum of around 90 and then start coming down again?
 
 
The eccentricity of the companion is still cycling around 0.795, and it's inclination is generally stable, cycling by a few degrees around 74.  
 
 
This is nothing like what the paper says should be happening here - the planet eccentricity should be increasing to well above 0.2 by now. So what's going wrong here? Have I entered something incorrectly? Is there a bug in the program?
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« Last Edit: 10/25/06 at 10:29:29 by EDG »  

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Re: Binary Eccentricity Test - volunteers needed!
Reply #6 - 10/25/06 at 11:01:35
 
Actually, it makes more sense for the planet's inclination to be increasing so that it becomes equal to the companion's inclination. Of course, once it gets below the critical value there'll be no more Kozai effects... but I suspect what will happen is that the planet's inclination will end up being the same as the companion's so that everything becomes coplanar, and that'll be that.
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Re: Binary Eccentricity Test - volunteers needed!
Reply #7 - 10/25/06 at 11:24:40
 
If you have it opened in Excel, Gravity Simulator can't write to the file.  Maybe I should add a warning box, something like "Error: can not open abcd.txt.  Please make sure the file is not opened in another application.  [Retry], [Cancel Output File]"
 
I found the period formula in your lastest link to be quite accurate in my 5-Earth simulation.  In the formula I used 0=Earth, 1 = Moon, 2 = Sun.
 
I'll look at this thread in more detail tommorow.
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Re: Binary Eccentricity Test - volunteers needed!
Reply #8 - 10/25/06 at 11:31:53
 
Quote from Tony   on 10/25/06 at 11:24:40:
If you have it opened in Excel, Gravity Simulator can't write to the file. Maybe I should add a warning box, something like "Error: can not open abcd.txt. Please make sure the file is not opened in another application. [Retry], [Cancel Output File]"

 
While you're at it, can you fix the overflow error too so it can do 50,000 samples at 1000 year intervals?
 
 
I should be able to see what happens with the inclination by this evening. Got any ideas on what could be going on so far?
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Re: Binary Eccentricity Test - volunteers needed!
Reply #9 - 10/25/06 at 11:44:17
 
at what point did the overflow occur?  When you tried to set it up, or during the middle of your simulation?  If during the middle, how many times did it output before crashing?
 
As far as commenting on the sim, I'll have more time later tonight to look at it in enough detail.
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Re: Binary Eccentricity Test - volunteers needed!
Reply #10 - 10/25/06 at 12:28:56
 
I got the overflow as soon as I tried pressed "OK" after I'd set it to record a,e,i,w,W at 1000 year intervals and 50,000 samples. So it didn't even start, it just borked out as soon as I tried to set it.  
 
But setting it to 10,000 year intervals and 5000 samples worked fine.
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Re: Binary Eccentricity Test - volunteers needed!
Reply #11 - 10/25/06 at 12:40:22
 
I'll fix that for you and upload a new beta later tonight.  I'm storing the values in integer variables which can't count beyond 32k.  I'll just just long integers or double variables.
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Re: Binary Eccentricity Test - volunteers needed!
Reply #12 - 10/25/06 at 12:43:12
 
OK, though we don't really need it to go above 65,000 rows, since that's Excel's limit. But I guess you want to assume that it's going to hold all of the possible data (i.e. about 20 checkboxes?) for say 10 bodies, and up to 65,000 rows.
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Re: Binary Eccentricity Test - volunteers needed!
Reply #13 - 10/25/06 at 17:20:33
 
OK, back home now, and it's totally not what the paper is predicting.
 
The planet's inclination has now overshot the companion's - at 29.9 million years the planet inclination is at 79.7 degrees and still increasing monotonically, whereas the companion is still stable and varying slightly around 75 degrees. I have no idea why this would happen.  
 
The planet eccentricity remains as it was - varying by about +/- 0.0005 around 0.0017. Companion eccentricity remains as it was before too.  
 
I think we can officially call this a blow-out. I've inputted the parameters exactly as described in the caption for Figure 1 in the 2006 paper and it's turned out to be absolutely nothing like what the graph says (at this stage, the planet eccentricity should be coming down from around 0.8, and it's not budged rfom around 0.0017 here) .  
 
So either I've entered something incorrectly here, or gravity simulator is doing something wrong in its calculations, or the paper is wrong.
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Re: Binary Eccentricity Test - volunteers needed!
Reply #14 - 10/25/06 at 20:57:12
 
I ran this at time step 4096.
 
I created a simulation exactly like yours, except the secondary object was 10 AU instead of 750, 0 eccentricity and 90 inclination.
 
Using formula 2, I computed the Kozai Period to be 289 years.
 
I ran it and I got:
 

 
So in this quick example, it seems right on the money.
 
Here's the sim:
http://orbitsimulator.com/gravity/simulations/kz99.gsim
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