Gravity Simulator http://www.orbitsimulator.com/cgi-bin/yabb/YaBB.pl General >> Discussion >> Binary Eccentricity Test - volunteers needed! http://www.orbitsimulator.com/cgi-bin/yabb/YaBB.pl?num=1161743701 Message started by Mal on 10/24/06 at 19:35:00

 Title: Binary Eccentricity Test - volunteers needed! Post by Mal on 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 ;) 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 = 0.000Simulation 3) As (1) but planet SMA = 0.5 AUSimulation 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! :)

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by Mal on 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.  :POK, set it to 5,000 samples, every 10,000 years. That seems to work.

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by Mal on 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 (http://www.evildrganymede.net/temp/simulation1.gsim)

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by Mal on 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... http://www.evildrganymede.net/temp/sim1.gifSo 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 ;) ) 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 :).

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by Mal on 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 ;). I've still got to see if we can even see this cycle in the program...!

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by Mal on 10/25/06 at 07:29:38 Something's definitely wrong here. http://www.evildrganymede.net/temp/sim1b.jpgAfter 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?

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by Mal on 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.

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by 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]"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.

Title: Re: Binary Eccentricity Test - volunteers needed!
Post by Mal on 10/25/06 at 11:31:53

Tony wrote:
 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?

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by Tony on 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.

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by Mal on 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.

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by Tony on 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.

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by Mal on 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.

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by Mal on 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.

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by Tony on 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:http://orbitsimulator.com/gravity/kz99.GIFSo in this quick example, it seems right on the money.Here's the sim:http://orbitsimulator.com/gravity/simulations/kz99.gsim

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by Mal on 10/25/06 at 21:17:52 So you reckon it's all down to the timestep? That'd be annoying if it is, it means we can't do test runs that can last tens or hundreds of mlilions of years without leaving them running for weeks! How low does the timestep have to be to notice this effect?I guess I should stop the run I'm doing now now anyway... at 36 million years the planet inclination is at about 95° and eccentricity is still wobbling around 0.0017. It's just silly to carry on with this one now, it's clearly not going anywhere.

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by Tony on 10/25/06 at 21:38:14 I don't think 65K is too large of a time step for this sim.  I'm running another similar one, this time, 80 inc, 100 AU, .8 ecc.  I'm doing it at 32K time step.In this particular instance, the time step may be too fast because the Ecc Max brings the planet close to the Sun, requiring a slower time step.  But stay tuned for a few minutes.  If the results appear at all usable, I'll post them.

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by Tony on 10/25/06 at 21:48:04 The time step definately ruined this one.  Using formula 2, I computed its Kozai period at 61000 years.  And the first half-cycle does appear to take about 30000 years.  But with its ecc approaching 1 (not quite this time since I used inc=80 instead of 90), its perihelion was too close to the Sun for a 32K time step.  This introduced error which is obvious from this point onward.http://www.orbitsimulator.com/gravity/kz96.GIFI'll play with this some more.  We'll get to the bottom of this  8)

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by Mal on 10/25/06 at 22:13:59 Hm, a 65k timestep couldn't possibly have screwed things up in my run that much - even though the companion orbit has eccentricity of 0.8 it doesn't get closer than 150 AU and has a period of about 20,000 years, so a timestep of less than a day shouldn't affect it.  And the orbital period of the planet is nearly four years so it can't be significantly affected either. Most odd...I'll start again from the gsim file with a 16k timestep this time, and see what happens. BTW, what's happening with the inclination in your runs, Tony?

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by Mal on 10/26/06 at 07:19:57 OK, starting again with a 16k timestep we're seeing something interesting - the planet eccentricity is now increasing over time! It's still varying by +/-0.0002, but the value around which it's varying has increased from 0 to about 0.0025 in 3 million years, which isn't what happened before. Inclination of the planet is still increasing monotonically over time though, it's at 8 degrees after 3 million years. The other interesting thing is that the argument of pericentre of the planet seems to be converging to around 90 degrees - that didn't happen with the 65k timestep (the arg. of peri. for the companion is 39 degrees though).

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by frankuitaalst on 10/26/06 at 08:59:28 Hi Tony , I run the 5-planet sim and got it as output to a Wpad file and converted it to excel . However the meaning of the rows were lost . Where can I find the description of the values ? Kind RegardsFrank

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by Tony on 10/26/06 at 09:07:26 That's interesting, I wouldn't have thought time step would be that critical in this case.  But that's still a very small ecc gain compared to the maxEcc it needs to achieve halfway through the cycle at 12M years.Frank, it should be outputting as a .txt file.  Send me an e-mail and attach what you have.  Are you running 2.0 or the beta version?

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by Mal on 10/26/06 at 11:42:06 Tony, what was happening with the planet inclination in the runs you were doing? I think it's definitely wacky that in the 65k run the planet inclination was increasing to beyond the companion's - again, that could be down to the timestep though.

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by Tony on 10/26/06 at 15:46:53 I can't find the file now to make an inc graph.  I remember it fluxuated, but not like ecc.  And I discovered a error in the inclination output.  Under some conditions, its off by 180 degrees.  It's easy to spot though,  If your inclination all of a sudden instantly jumps 180 degrees, that a bug.  I'll try to find the file later and post an inc graph.

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by Mal on 10/26/06 at 18:15:42 At nearly 7 million years, things are still looking interesting... Planet:Inclination is around 18 degrees, still rising monotonically.Eccentricity is now varying around 0.0065, but the rate of increase of eccentricity is itself slightly increasing. Argument of Pericentre is converging to around 95 degrees - it started off going all around the orbit, but it's converged over time towards this value. No idea why!Companion:Inclination stable, varying slightly around 74 degrees. Eccentricity stable, varying around 0.792 +/- 0.01. Argument of Pericentre stable, varying slightly around 39 degrees.

Title: Re: Binary Eccentricity Test - volunteers needed!
Post by Tony on 10/26/06 at 18:47:39

This is identical to your sim #1, except the secondary is at 200 AU instead of 750 AU.  All other values are the same.

The formulas give:
Pkoz=486265 years
emax = .94

http://orbitsimulator.com/gravity/kz101.GIF

Again, the simulation is right on the money.  But I tried your sim at secondary sma=750 AU and got the same results you got... Insignificant delta eccentricity, and a linear inclination advancment.  It almost seems as if the Kozai Mechanism turns off at a certain distance.  Maybe that makes sense.  It turns off completely at inclinations <~35 degrees.

I ran this at time step 16K, which was too fast once the planet's ecc approached 0.94, so I don't trust the graph beyond what's shown.

So at what point between 200 AU and 750 AU does the Kozai Mechanism simply stop working as advertised?

Mal wrote:
 ...No idea why!...

Me too.  Despite all the forumlas in all the papers, I think there's still stuff to discover about the Kozai Mechanism.

I'll try a 400 AU run and see what happens.

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by Mal on 10/26/06 at 20:08:52 But that's the thing though - the values I'm using are from the paper, which shows a 28 million year cycle if the companion is at 750 AU. So I don't think the Kozai mechanism is cutting off before then, because the paper seems to think it's still going! I wonder if there's something in gravity simulator itself that's causing it to cut off?

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by frankuitaalst on 10/26/06 at 22:04:58 Hi Tony , Mal , out of my simulation of the 5 earths I got the following result : the time to get a noticible influence decreases rapidly with distance ... so the sim with 750 might run longer . Also , as distance increases the frequency of the mechanism decreases with time . And further a noticed that the maximum eccentricity decreases with distance . F.i. in the 3AU earth simulation the moon didn't get to an ecc of 1. This makes sense to me , intuitionally ... In one of the articles a also read that time step should be reduced if eccentrity gets high . I guess especcially in the points were the planet is close to the mother .

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by Mal on 10/26/06 at 22:16:44 I don't think this will be much use, but here's the Ford et al (2000) paper referenced in the Takeda and Rasio papers:http://www.astro.northwestern.edu/rasio/Papers/59.pdf

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by Mal on 10/26/06 at 23:15:38 Here's a graph of the state of affairs for the planet at 8.493 million years.http://www.evildrganymede.net/temp/sim1_16k.gifBlue is Arg of Pericentre, you can see how that's converging to about 96 degrees. That uses the left y-axis. I have absolutely no idea why this is converging to 96 - the only thing that could possibly be related is the Longitude of Ascending Node of the companion, which is about 179 degrees, and 96 is almost half of that. But it's a really tenuous link. Red is inclination. This uses the left y-axis too, and it's at 22 degrees so far. Pink is eccentricity. This uses the right y-axis. You can see that its rate of increase is accelerating with time. It may yet increase very steeply - I guess we'll know for sure if it's going to be like the graph in the paper at around the 15 to 20 million year mark (which will be tomorrow evening, I guess).(1000 on the x-axis is about 1 million years)

Title: Re: Binary Eccentricity Test - volunteers needed!
Post by Tony on 10/26/06 at 23:29:04

I got tired of punching the formulas into my calculator so...

http://orbitsimulator.com/gravity/KozaiCalc.GIF
http://orbitsimulator.com/gravity/KozaiCalc.exe

Code:
 Private Sub Command1_Click()Dim M0 As Double, M1 As Double, M2 As Double, A1 As Double, A2 As Double, E2 As Double, Pkoz As Double, P1 As DoubleDim pi As DoubleDim i As Double, eMax As Double, pi2 As DoubleOn Error Resume Nextpi2 = Atn(1) * 4 * 2i = Val(txi.Text) / 360 * pi2eMax = Sqr(1 - (5 / 3) * (Cos(i)) ^ 2)txEmax.Text = eMaxpi = Atn(1) * 4M0 = Val(txM0.Text)If optMsun(0).Value Then M0 = M0 * 1.989E+30If optMjupiter(0).Value Then M0 = M0 * 1.899E+27If optMearth(0).Value Then M0 = M0 * 5.97E+24M1 = Val(txM1.Text)If optMsun(1).Value Then M1 = M1 * 1.989E+30If optMjupiter(1).Value Then M1 = M1 * 1.899E+27If optMearth(1).Value Then M1 = M1 * 5.97E+24M2 = Val(txM2.Text)If optMsun(2).Value Then M2 = M2 * 1.989E+30If optMjupiter(2).Value Then M2 = M2 * 1.899E+27If optMearth(2).Value Then M2 = M2 * 5.97E+24A1 = Val(txA1.Text)If Option1(1).Value Then A1 = A1 * 149597870691#If Option2(1).Value Then A1 = A1 * 1000A2 = Val(txA2.Text)If Option1(2).Value Then A2 = A2 * 149597870691#If Option2(2).Value Then A2 = A2 * 1000E2 = Val(txe2.Text)P1 = 2 * pi * Sqr(A1 ^ 3 / (0.0000000000667 * M0))Pkoz = P1 * ((M0 + M1) / M2) * (A2 / A1) ^ 3 * (1 - E2 ^ 2) ^ (3 / 2)txPkoz.Text = Pkoz / 86400 / 365.25End Sub

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by Tony on 10/26/06 at 23:35:47 How do you put scales on both axes in Excel  ???  (we need a smily face with question marks too!)

Title: Re: Binary Eccentricity Test - volunteers needed!
Post by Tony on 10/26/06 at 23:40:40

frankuitaalst wrote:
 Hi Tony , Mal , out of my simulation of the 5 earths I got the following result : the time to get a noticible influence decreases rapidly with distance ... so the sim with 750 might run longer . Also , as distance increases the frequency of the mechanism decreases with time . And further a noticed that the maximum eccentricity decreases with distance . F.i. in the 3AU earth simulation the moon didn't get to an ecc of 1. This makes sense to me , intuitionally ... In one of the articles a also read that time step should be reduced if eccentrity gets high . I guess especcially in the points were the planet is close to the mother .

I never ran it long enough to see the 3AU complete a cycle, but I'm surprised it didn't approach 1.  Can you give us details, such as time step used and a graph, or the .txt file so Mal or I can make a graph from it?

Check your e-mail.  I sent you a link to the beta copy.  You should have a copy if you're doing these types of sims.

Title: Re: Binary Eccentricity Test - volunteers needed!
Post by Mal on 10/26/06 at 23:48:42

Tony wrote:
 How do you put scales on both axes in Excel  ???  (we need a smily face with question marks too!)

Select the data line in the graph that you want on the secondary axis, rightclick on it, select "Format Data Series", go to the Axis tab, tick the "secondary axis" checkbox. Then you can adjust the values on the new secondary axis on the right and they'll change independently of any changes on the primary axis on the left.

If you're clever about it you can show one graph above another graph if you manipulate the max and min values of their axes accordingly.

Title: Re: Binary Eccentricity Test - volunteers needed!
Post by Mal on 10/26/06 at 23:57:19

Tony wrote:
 This is identical to your sim #1, except the secondary is at 200 AU instead of 750 AU.  All other values are the same.The formulas give:Pkoz=486265 yearsemax = .94

I notice the graph for inclination seems to be flattening out at 90 degrees...

Quote:
 It almost seems as if the Kozai Mechanism turns off at a certain distance.  Maybe that makes sense.  It turns off completely at inclinations <~35 degrees.

Well this is the thing - if it does turn off around the 40 degree mark, then that means that if the starting inclination is 75°, when the planet's inclination increases to above 35°, the effect should cease. This is because the companion inclination isn't changing - so as soon as the planet inclination hits (companion inclination - 40), it should behave as if it's coplanar. So how the heck does the effect continue after that?!

Could this be why the effect stops working at a certain distance? Because if you run the simulation long enough, the relative inclinations will become lower than the critical one at which the Kozai effect stops?

It's bugging me enough that I may email Takeda and ask him what the inclination is doing in his graph. I wonder if he's just assuming it doesn't change (i.e. so that the relative inclinations are always above the critical angle, so Kozai continues).

Quote:
 I ran this at time step 16K, which was too fast once the planet's ecc approached 0.94, so I don't trust the graph beyond what's shown.

What would be ideal is some kind of automatic, dynamic adjustment by the program, so it notices that the velocity of the object is getting too fast for the stated timestep, and adjusts the timestep accordingly to compensate.

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by Tony on 10/27/06 at 00:00:06 On your graph, if the slope of the ecc line keeps increasing, it'll be close to vertical soon and will quickly climb to the 0.94 value it's predicted to have.The curve at this point looks like it can be approximated as an exponential.  In reality its sinusoidal.  Can you get Excel to draw you an exponential trend line and display the equation? Then use that equation to extrapolate to 25 million years.

Title: Re: Binary Eccentricity Test - volunteers needed!
Post by Tony on 10/27/06 at 00:09:51

Mal wrote:
 ...It's bugging me enough that I may email Takeda and ask him what the inclination is doing in his graph. I wonder if he's just assuming it doesn't change (i.e. so that the relative inclinations are always above the critical angle, so Kozai continues). ...What would be ideal is some kind of automatic, dynamic adjustment by the program, so it notices that the velocity of the object is getting too fast for the stated timestep, and adjusts the timestep accordingly to compensate.

Let me ponder this for a day.  It might have to do with a combination of inc and ecc.  But you will notice that if you plug values under ~35 degrees into the formula for eMax that you end up with a negative sign under the radical which generates an error (or in the case of the above mentioned calculator generates a 0 as the program is told to ignore errors.)

You can use Autopilot to adjust the time step, providing you know when you want the time step to change.  In simulations such as this, it will work since you know from the formulas when ecc will peak (1/2 the period), so you can compute this time, add and subtract 20% and adjust the timestep accordingly using Autopilot.

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by Tony on 10/27/06 at 01:27:02 I'm 1 million years into a sim with secondary sma=400, and unlike my sma=200 sim, its behaving a lot like the sma=750 sim.  The ecc is averaging a value without picking up steam.  4 million years is the predicted Kozai period.  So it only has 1 million more years to reach its peak at the half-cycle.  It better pick up the pace and fast...Results tommorow morning  ;D

Title: Re: Binary Eccentricity Test - volunteers needed!
Post by Mal on 10/27/06 at 07:24:31

Tony wrote:
 On your graph, if the slope of the ecc line keeps increasing, it'll be close to vertical soon and will quickly climb to the 0.94 value it's predicted to have.The curve at this point looks like it can be approximated as an exponential.  In reality its sinusoidal.  Can you get Excel to draw you an exponential trend line and display the equation? Then use that equation to extrapolate to 25 million years.

I can't get an exponential one that fits, but a 3rd order polynomial claims that it'll be 0.125 at 25 million years.

At 11.34 Ma, planet eccentricity is now at 0.019 (de/dt still increasing), inclination is 30 degrees, and arg of pericentre is converging to about 98.5 degrees.

(companion inclination is still at 75 degrees)

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by Tony on 10/27/06 at 10:05:36 My 400 AU sim ultimately gained lots of eccentricity.  But it peaked at ~0.8 instead of ~0.9 as predicted by the formula, and it peaked a little late.  The formula had it peaking (assuming peak to be 1/2 period) at just under 2 million years.http://www.orbitsimulator.com/gravity/kz104.GIF

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by Mal on 10/27/06 at 11:18:56 It's interesting that the inclination is still increasing after the eccentricity peaks - plus, it's well within the critical relative inclination. I emailed Dr Takeda to ask about what he thinks the inclination should be doing, and pointed him to this thread too.

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by Mal on 10/27/06 at 17:22:09 14.89 million year update:Planet eccentricity still rising, but it's still only at about 0.044 - has a long way to go to reach 0.8ish!Planet inclination still rising, it's nearly 40° now.Planet argument of pericentre is still converging, looks like it's actually going to converge on 100°.No real change in companion properties. Hrm.

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by Tony on 10/27/06 at 18:09:52 14.89 million years seems too long.  With a Kozai Period of 25 million years it should have peaked at around 12 million years.

Title: Re: Binary Eccentricity Test - volunteers needed!
Post by Mal on 10/27/06 at 20:12:46

Tony wrote:
 14.89 million years seems too long.  With a Kozai Period of 25 million years it should have peaked at around 12 million years.

The graph looks like it peaks around 19 Ma. But even at 15.9 Ma, the eccentricity is only about 0.054, and I suspect that it's not going to get much higher than 0.1 in the end.

Have you tried the run I'm doing, Tony? I'm sure I entered everything in properly, but verification that someone else is getting the same results as I am would reassure me somewhat...

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by Tony on 10/27/06 at 20:39:48 I started, but when my results were the same as yours I gave up in favor of a smaller semi-major axes for the secondary just to see if a trend develops.But I can try yours again.  Just to verify:primary: 1 Msunplanet: 2.5 AU, 0 ecc, 0 incsecondary: 750 AU, .8 ecc, 75 inc.What time step are you using?

Title: Re: Binary Eccentricity Test - volunteers needed!
Post by Mal on 10/27/06 at 20:52:27

Tony wrote:
 I started, but when my results were the same as yours I gave up in favor of a smaller semi-major axes for the secondary just to see if a trend develops.But I can try yours again.  Just to verify:primary: 1 Msunplanet: 2.5 AU, 0 ecc, 0 incsecondary: 750 AU, .8 ecc, 75 inc.What time step are you using?

That's right - also, the planet is 1 jupiter mass, companion is 0.9 solar masses, and I'm using 16k timestep now. And make sure you start it with planet and companion having the arg of pericentre, longitude of ascending node and mean anomaly specified in the first post here.

I don't expect you to run it as long as I've done, just long enough to see if it's the same or not.

Thanks!

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by Mal on 10/27/06 at 23:07:37 16.86 million years:Eccentricity at 0.06834 and still rising.Arg of Peri is converging further to 99.5°.Inclination at 45.18°Plotting an exponential trendline to the eccentricity matches it when it's below about 0.02, but diverges badly at higher value, so probably isn't much good to use for extrapolation.

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by Mal on 10/27/06 at 23:20:08 Hm.The companion inclination is 75 degrees. Half of that is 37.5 - and the inclination of the planet hits 37.5° at 13.998 million years. I had thought the Kozai cycle was about 28 million years for this, so I thought this was suspicious that the planet inclination was halfway there at the halfway point of the cycle. But apparently the cycle is actually supposed to be 25.6 million years long, so that makes this possible connection more tenuous than I thought it was...  :-/(at the actual halfway point of the cycle, the inclination is 34.4 degrees, which is well below half of 75 degrees)

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by frankuitaalst on 10/28/06 at 05:07:32 Hallo , Here are the results so far for the 5 Earths sim . Time step was 128 sec. I ran the sim for about 400 years . The moons of 1,2,3,4 were ejected after some time  :-[, the 5th was still there . As expected it took longer to get at max ecc with ascending AU . This function is exponentially with AU . Help : i can't insert the graphs .  :-[ how does it works ?

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by Mal on 10/28/06 at 08:45:45 20.1 million years:http://www.evildrganymede.net/temp/sim1_16k_b.gifSomething interesting is going on...Eccentricity is rising faster, now at 0.1438.Inclination still rising, now at 53.78°.Arg of Peri is now actually starting to decrease! It's now at 97.5° - the peak was around 13.93 million years at 100.5°Longitude of Ascending Node (which I haven't mentioned or shown before) has been decreasing steadily. In the first few thousand years it shot up to 270 degrees, and since about 10,000 years it's been decreasing with time - at 20.1 million years it's at 259.5° and still dropping.Maybe this is going to work after all?!

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by Tony on 10/28/06 at 11:14:43 It will be interesting to see if the argument of perigee expands out again after your ecc maxes and returns to 0.Keep in mind, argument of perigee is degrees from the longitude of the ascending node, so they're tied together.It's possible that the recent dip in argument of perigee is related to the time step.  As your ecc increases, your planet's periastron decreases, making it more sensitive to the timestep.The drift of Longitude of Periapsis, which you can compute from Longitude of the Ascending Node + Argument of Periapsis, is time step sensitive.See the results I posted in the thread http://www.orbitsimulator.com/cgi-bin/yabb/YaBB.pl?board=news;action=display;num=1158230793 to see how only a time step of 128 and lower converged on Mercury's true precession of perihelion (excluding GR).

Title: Re: Binary Eccentricity Test - volunteers needed!
Post by Mal on 10/28/06 at 14:35:49

Tony wrote:
 It will be interesting to see if the argument of perigee expands out again after your ecc maxes and returns to 0.

If I keep it running that long... I was just intending to run it til it passed the eccentricity peak and the inclination passed or hit 75 degrees.

Quote:
 Keep in mind, argument of perigee is degrees from the longitude of the ascending node, so they're tied together.It's possible that the recent dip in argument of perigee is related to the time step.  As your ecc increases, your planet's periastron decreases, making it more sensitive to the timestep.

Well, 16k seconds is a 4.5 hour timestep. Even if the planet eccentricity reached 0.900, the perihelion would be 0.25 AU - would it really be moving so fast at that point that even a 4.5 hour timestep is too low resolution to keep up with it?

Hm. Is there a way to make a timelapse picture of the position of a planet on its orbit using a given timestep?

BTW, at 22.273 Ma, things are hotting up for the planet:

eccentricity: 0.223
inclination: 59.44°
Arg of Peri: 94.7°
Long of AN: 258.1°

One more interesting thing - looking at the companion inclination, it's actually starting to decrease ever so slightly - it's about 73.7° now. The *planet's* inclination is a linear increase, so extrapolating from a trendline, I think it should hit 75° at about 27.756 million years, or 73.7 at about 27.284 million years.

So I reckon the really interesting stuff is going to happen between 25 and 30 million years...

Title: Re: Binary Eccentricity Test - volunteers needed!
Post by Tony on 10/28/06 at 14:39:37

Mal wrote:
 Hm. Is there a way to make a timelapse picture of the position of a planet on its orbit using a given timestep?

You mean similar to the one I posted on the "5 planets" sim?  Probably.  Let me know what you have in mind and I'll figure out how to do it.

Title: Re: Binary Eccentricity Test - volunteers needed!
Post by Mal on 10/28/06 at 14:45:41

Tony wrote:
 You mean similar to the one I posted on the "5 planets" sim?  Probably.  Let me know what you have in mind and I'll figure out how to do it.

Well, just to see how fast a 1 Jupiter mass planet with an orbit with 2.5 AU semimajor axis and 0.9 eccentricity is moving. So at each timestep (e.g. 16k), you plot the position of the planet on its orbit. That way you end up with a bunch of dots that follow the orbit showing the planet's location at that time. They should be spread furthest apart at perihelion, and closest together at aphelion.

Basically I'm after a plot of one orbit's worth of points - how the orbit moves in space isn't relevant to this.

Title: Re: Binary Eccentricity Test - volunteers needed!
Post by Tony on 10/28/06 at 16:25:01

Mal wrote:
 So at each timestep (e.g. 16k), you plot the position of the planet on its orbit. That way you end up with a bunch of dots that follow the orbit showing the planet's location at that time. They should be spread furthest apart at perihelion, and closest together at aphelion.Basically I'm after a plot of one orbit's worth of points - how the orbit moves in space isn't relevant to this.

That's what the T (trails) button does.  It appears that it is tracing the orbit, but it is only plotting points.  The spacing between the points it plots are usually less than a pixek, giving the appearance it is drawing a continuous curve.

Here's the inner solar system at 16K time step zoomed in enough to see the pixels representing each planet's position at each time step.  You can even follow the moon as it orbits the Earth (blue).

http://orbitsimulator.com/gravity/pixels.GIF

In regards to the argument of perapsis converging on a value, I think I know why.  Consider that a perfectly circular will have no periapsis.  If it's a circle, there is no close point.

Now consider the longitude of the ascending node.  In an orbit whose inclination is 0, there is no ascending node.  Ascending node is the point where it passes from below the ecliptic to above the ecliptic.  In an orbit with 0 inc, the planet rides on the ecliptic, never going above or below.  So the node is undefined.

You're starting out with a round orbit with 0 inclination.  Imagine standing on the North Magnetic Pole of Earth with a compass.  The needle is spinning all over the place.  It doesn't know which way to point.  Same thing with Gravity Simulator's periapsisometer and ascendingnodometer (I just made up those words).  You're asking it for the derivative of a non-differentialble point.  It doesn't know which way to point, and its "needle" is swinging all over the place.  But once small amounts of eccentricity and inclination are introduced into the orbit, the periapsis and ascending nodes become more clearly defined.  You need enough eccentricity and inclination that these values rise above the background noise of the simulator, and the pertabutions generated on the planet by the secondary.  (remember, the secondary also tugs on the Sun, complicating things and ensuring that your average eccentricity per orbit is not necessarily your instantaneous eccentricity at all points).  The more ecc and inc, the better the number is defined, and your graph starts to converge on a value.

Title: Re: Binary Eccentricity Test - volunteers needed!
Post by Mal on 10/28/06 at 18:14:44

Tony wrote:
 That's what the T (trails) button does.  It appears that it is tracing the orbit, but it is only plotting points.  The spacing between the points it plots are usually less than a pixek, giving the appearance it is drawing a continuous curve.

Oh yeah, I forgot about that :).
So can we tell if 16k really is going to be too fast if the eccentricity hits 0.9?

Quote:
 You're starting out with a round orbit with 0 inclination.  Imagine standing on the North Magnetic Pole of Earth with a compass.  The needle is spinning all over the place.  It doesn't know which way to point.  Same thing with Gravity Simulator's periapsisometer and ascendingnodometer (I just made up those words).  You're asking it for the derivative of a non-differentialble point.  It doesn't know which way to point, and its "needle" is swinging all over the place.  But once small amounts of eccentricity and inclination are introduced into the orbit, the periapsis and ascending nodes become more clearly defined.  You need enough eccentricity and inclination that these values rise above the background noise of the simulator, and the pertabutions generated on the planet by the secondary.  (remember, the secondary also tugs on the Sun, complicating things and ensuring that your average eccentricity per orbit is not necessarily your instantaneous eccentricity at all points).  The more ecc and inc, the better the number is defined, and your graph starts to converge on a value.

That's what I figured was happening with the Arg of Pericentre - like you said, it starts off with zero eccentricity and then the orbit locks into a specific orientation as it gets more eccentric. What I'm wondering about is why is headed toward 95-100 degrees - what's so special about that?

Same for the LAN - it shot up to 270 degrees from 54 degrees, and then slowly crept downwards over time (though there was some variation at the start as it was trying to find its way, but I guess since the inclination is increasing faster than the eccentricity, the variation in LAN got damped more quickly). But why 270 degrees in the first place?

At the end of this simulation I'll post a link to the full text file output so others can play around with it and plot it to see what's going on.

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by Mal on 10/28/06 at 18:32:24 EDIT: Disaster averted. Computer crashed, but I was able to restart the sim from the last saved values. Phew!

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by Mal on 10/28/06 at 18:47:23 EDIT: Simulation still going from restarted version. Nothin' to see here!

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by Tony on 10/28/06 at 18:56:55 It's easy enough to just make a new sim to see the spacing.  Here's 2 objects at 2.5 AU, the purple one at .9 ecc and the green one at .94 ecc.  This is run at 16K time step.http://orbitsimulator.com/gravity/pixels2.GIFProbably the best way to determine if the time step is influencing your results is to do a sim.  While your long sim is still running, you can turn on Auto Save for a single save.  This will make a copy of your simulation without affecting the currently-running sim.Then take your Auto-Saved sim, run it for a few minutes at a slower time step, plot your data and see if there's any difference.  If so, try it again at an even slower time step.  At some point, your graphs are going to converge on a value.  At that point, you can trust your time step.  This is what I did in the "precession of Mercury" graph I mentioned in the other thread.

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by Tony on 10/28/06 at 18:59:57 Aren't you going to continue until you reach max ecc?  It looks like you're getting close.Why weep?  It's possible you've found a problem with their formulas.  Maybe they break down at certain values.  If so, that would be very important to the study of exo-solar planets.Or its possible that Gravity Simulator is the culprit.  In any case, you've certainly proven the case that more study needs to be done in this area.

Title: Re: Binary Eccentricity Test - volunteers needed!
Post by Mal on 10/28/06 at 19:03:20

Tony wrote:
 Aren't you going to continue until you reach max ecc?  It looks like you're getting close.Why weep?  It's possible you've found a problem with their formulas.  Maybe they break down at certain values.  If so, that would be very important to the study of exo-solar planets.Or its possible that Gravity Simulator is the culprit.  In any case, you've certainly proven the case that more study needs to be done in this area.

EDIT: I managed to restart the simulation using the final values from the saved output file from the crashed sim. I'll use the Mean Anomalies that I started with - hopefully that won't make too much of a difference. I should be able to add the output to the existing text file.

I guess the resume.gsim didn't save because the program wasn't closed down manually - since it crashed, all it had to go on were the initial parameters.

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by Mal on 10/28/06 at 19:19:45 Hm, doesn't look like it's going to be too bad after all - after the first 40,000 years the values are still doing what they were doing before (inc and ecc are still increasing, AoP and LAN still decreasing). Phew. Looks like the show is still on! :)

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by Tony on 10/28/06 at 19:27:12 oops, I missed your "crash post".  Tough way to learn to autosave.  Hmmm, I could make Gravity Simulator create a backup sim every few minutes like Microsoft Word does:  "backup.gsim".I'm glad you could reconstrut it.  I doubt that the anomolies will affect your results since nothing is locked into resonance.

Title: Re: Binary Eccentricity Test - volunteers needed!
Post by Mal on 10/28/06 at 19:32:41

Tony wrote:
 oops, I missed your "crash post".  Tough way to learn to autosave.  Hmmm, I could make Gravity Simulator create a backup sim every few minutes like Microsoft Word does:  "backup.gsim".

Well, I'm autosaving every million years now, just in case! That said, an autosaved backup.gsim file wouldn't be a bad idea...!

Quote:
 I'm glad you could reconstrut it.  I doubt that the anomolies will affect your results since nothing is locked into resonance.

Yeah, it looks like it'll be OK. The only pain will be merging the text files into one file that I can plot a graph from, but it's no big problem. I've duly edited my "wailing and gnashing of teeth" posts accordingly :)

I'll remove the simulation1.zip file for now. It ain't over yet! :)

(and er, I guess this is now the longest thread ever on this forum? ;))

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by Mal on 10/28/06 at 20:30:58 Got a reply from Genya Takeda which was rather interesting. Apparently the inclination is also supposed to oscilate between the starting relative inclination and that critical value of about 40 degrees! This isn't happening in the GravSim simulation - the relative inclination is already well below the critical value. So something is still not right here in GravSim- either the algorithm used here isn't accurate enough or the timestep is still too large. More experiments are due, I guess!However, he also mentioned that the Arg of Peri is either going to be circling around 360° or it's going to be oscillating around 90°, and it does look like this might be happening here! Remember, the sim did vary wildly around 360° at first, and now it looks like it's partway through a long period oscillation around 90°...

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by Tony on 10/28/06 at 22:38:24 In measuring the inclination, you can't go by what Gravity Simulator tells you because that's inclination from the ecliptic.  I think what you want is inclination from the plane of the secondary.  And it's not as easy as subtracting one from the other.If you gave the planet 75 degrees of inclination and the secondary 0 degrees, then the inclination of the planet that Gravity Simulator gives you would be useful since the secondary orbits in the ecliptic plane.

Title: Re: Binary Eccentricity Test - volunteers needed!
Post by Mal on 10/28/06 at 22:50:15

Tony wrote:
 In measuring the inclination, you can't go by what Gravity Simulator tells you because that's inclination from the ecliptic.  I think what you want is inclination from the plane of the secondary.  And it's not as easy as subtracting one from the other.If you gave the planet 75 degrees of inclination and the secondary 0 degrees, then the inclination of the planet that Gravity Simulator gives you would be useful since the secondary orbits in the ecliptic plane.

Erm, wait a minute... the ecliptic can be anything you want if there's two bodies orbiting the star. You can set the planet at 0 degrees inclination and the companion at 75, and the planet's orbit will be the ecliptic. Or you can set the companion's orbit at 0 degrees and the planet's at 75 and the companion's orbit will be the ecliptic. It only gets fixed if you have a several bodies orbiting in roughly the same plane and one or two well outside it - in which case the plane that most of the bodies orbits in is the ecliptic. (technically, the Ecliptic in the solar system is the plane of Earth's orbit around the sun, but the other seven planets orbit roughly in that plane)

Of course the difference in orientation of the orbits is probably a problem, because I guess then you're talking about dog-leg angles when calculating the difference in inclinations. That I could understand being a problem.

Unless I've completely missed the point of what you're saying ;).

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by Mal on 10/28/06 at 23:02:09 25 million year update:Interesting, the eccentricity looks like it's starting to flatten out, and it's nowhere 0.900. I'm also not entirely sure that the Arg of Peri is going to oscillate around 90° here.... and inclination is still increasing.

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by frankuitaalst on 10/29/06 at 01:27:36 Hi Mal , inclination will grow rapîdly as e wil go to 1 . I have the same experience with the 5-earths sim . I'll try to upload the images .

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by Mal on 10/29/06 at 07:28:54 27.857 million years:http://www.evildrganymede.net/temp/sim1_16k_e.gifWell, something's definitely gone pear-shaped. Eccentricity peaked at 0.35 at 26.5 million years and is now falling. Inclination is now 74.8 degrees. Arg of Peri is now 71 degrees and falling dropping. This is not supposed to be happening.Oh, and here's what the companion orbit has been doing. Note that there's a kink where I restarted the graph after the crash. I don't know if this affected the outcome, I can't see a similar break in the planet  data. http://www.evildrganymede.net/temp/sim1_16k_comp.gifI'll let this run a little longer, but it looks like a bust - it's not doing anything like what it's supposed to be doing. I'll try another simulation after this - a 0.9 solar mass companion at 250 AU, with a 1MJ planet at 5 AU, everything else as before. Period should be about 300k years, which means I can run it at a slower timestep without dying of old age. I'll try at a 4k timestep and see what happens - that surely can't be too fast for this.

Title: Re: Binary Eccentricity Test - volunteers needed!
Post by Mal on 10/29/06 at 07:36:44

frankuitaalst wrote:
 Hi Mal , inclination will grow rapîdly as e wil go to 1 . I have the same experience with the 5-earths sim . I'll try to upload the images .

Hm, that shouldn't be happening - the relative inclination is supposed to be going between the starting value and 40 degrees.

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by Mal on 10/29/06 at 09:58:25 OK, that's it, I've given up :). http://www.evildrganymede.net/temp/sim1_16k_final.gifFinal time: 28.561 million years. Eccentricity droppingInclination 76° and still increasingArg of Peri and LAN still decreasingSo something's obviously not as it should be here. Gonna try the quicker one - I'll start a new thread. I think actually I'll make it simple by having the orbits starting off oriented in the same way (arg of peri and LAN both at 0) with the mean anomalies being different. See what happens then.

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by frankuitaalst on 10/29/06 at 11:26:42 here some results for the 5-earth sim . I ran them for about 400 years . Timestep = 128 sec . Tilmestep was perhaps too big for the 4 inner planets , as they lost their moons . The 5th earth kept his moon . Interesting is the following : 1. Time before the Kozai becomes "visible" rises about exponentially with AU ( see last Excel-graph ) . This means that the moons of the outer planets must be protected by "time" . 2. Inclination changes slowly in the beginning , but increases rapidly as the ecc. goes to 1. 3. After reaching the max ecc the system gets in a cycle with decreasing ecc and decreasing incl , rising again , a.s.o. It is further interesting to run the sim with a smaller time step in order to obtain the frequency of the fluctations of incl . ( avoiding the moons are lost ) . I tried to correlate the frequency of oscillation tothe time needed to obtain full ecc , but data are to few . Such a link must exist surely . Note : running the sim I observed that the moon of the first earth changed the orientation at ecc=1 , meaning she returned to the earth in the some direction as she come from , meaning rotating clockwise instead of anti-clockwise . Really surprising !!! http://http://www.orbitsimulator.com/gravity/images/users/frankuitaalst/f1.GIFhttp://www.orbitsimulator.com/gravity/images/users/frankuitaalst/f2.GIFhttp://www.orbitsimulator.com/gravity/images/users/frankuitaalst/f3.GIFhttp://www.orbitsimulator.com/gravity/images/users/frankuitaalst/f4.GIFhttp://www.orbitsimulator.com/gravity/images/users/frankuitaalst/f5.GIFhttp://www.orbitsimulator.com/gravity/images/users/frankuitaalst/f6.GIFhttp://www.orbitsimulator.com/gravity/images/users/frankuitaalst/f7.GIFhttp://www.orbitsimulator.com/gravity/images/users/frankuitaalst/f8.GIF** modified by Tony -- added img tags.

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by Tony on 10/29/06 at 13:29:23 The 3rd one is surprising.  It looks like eccentricity has a double peak.

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by frankuitaalst on 10/29/06 at 14:14:03 In order to "save" the moons I started the sim with reduced timestep ( 32 instead of 128) . I lost already 3 moons ( also for 2Au , the one with the double peaks ) . I wonder how the results will be ... Keep you informed . BTW : the integration is done by Runge Kutta 4 or another method ? Frank

Title: Re: Binary Eccentricity Test - volunteers needed!
Post by frankuitaalst on 02/03/07 at 07:12:54

Remembering the Kozai ?

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

I ran this Kozai kz99 again with Picard and got the following amazing  :o result  ...
The calculated period of the oscillation also matches as can be seen from the picture herunder , but , whats interesting is that the inclination really jumps from lets say 20° to nearly 180° after about 150 years . What does an inclination of nearly 180° mean by the way ??
I noticed that the change took place when the planet was at the far point from the sun and turned his back , ie it returned clockwise and continued turning clockwise , where it was revolving anti-clockwise before ...

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by frankuitaalst on 02/03/07 at 07:49:02 Wondering how the system would evolve I ran the same sim as above for about 2200 years and got the weird result hereunder . It seems the system is not quite stable , changing , or seeking its "home" inclination about every 150 years . It also seems that once the initial condition is left the max. eccentricity always gets to about 1 , but  the 0 eccentricity is hardly achieved againThe frequency of the Kozai cycle  however is rather stable .

Title: Re: Binary Eccentricity Test - volunteers needed!
Post by abyssoft on 02/03/07 at 09:56:01

Quote:
 I ran this Kozai kz99 again with Picard and got the following amazing   result  ... The calculated period of the oscillation also matches as can be seen from the picture herunder , but , whats interesting is that the inclination really jumps from lets say 20° to nearly 180° after about 150 years . What does an inclination of nearly 180° mean by the way ??  I noticed that the change took place when the planet was at the far point from the sun and turned his back , ie it returned clockwise and continued turning clockwise , where it was revolving anti-clockwise before ...

If memory serves me correctly 180 deg and greater = retrograde motion.  Also, looking at the graphs I'd say that over geologic time of the system the planemo would be ejected.  I would be interested in seeing a longer run with [e, a, i] vs [P,S] of the planemo.

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by frankuitaalst on 02/03/07 at 10:34:17 ok , I will run it over a longer time ... In the meantime I created a screenshot at about 350 years of simaulation which shows that the planet comes almost as close as the radius of the sun , so a good chance of collision exists ...This also means that , while the system has a companion at 90° ,the system  is not stable at all and is due to a lot of ...chaos ...

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by frankuitaalst on 02/03/07 at 11:20:00 you're right ... the planet decided to evolve the other way several times ... and is ejected .... The system survived more than  20 close passes with the sun , but after about 3000 years the fun was over , and the planet is ejected . Hereunder the Excel-Graph of inclination and SMA ( in m, instead of AU ) vs. time .... At the last encounter with the sun the planet came as close as 420*10E-6 Au of the sun ...I cut the graph at ~3000 years , because the SMA was rising out of proportion...Am I right when I see that the Kozai frequency gets exited the closer time approaches 3000 years ?

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by abyssoft on 02/03/07 at 13:11:57 If you'll notice in your graph the kozai period is in a continual decrease with a distinct acceleration after  ~2500a.I'm currently working on a large project.  A recode of the "Stargen" program by Eldacur.  after I have it completed I will also add an option to export the system to Gsim format.  I'm hoping to have a beta ready by the end of march or earlier.

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by abyssoft on 02/03/07 at 13:17:51 oh one other question, What are the masses of [P, S] and what is the periapsis of the 2.One reason the planemo may have been ejected is it may have move into the binary zone of instability.I'll post more about this zone at a later time, when time permits.

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by frankuitaalst on 02/03/07 at 14:12:50 The data were taken from this sim :http://orbitsimulator.com/gravity/simulations/kz99.gsim The companion is rather "heavy" , almost the suns mass .

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by Tony on 02/03/07 at 14:13:30 Abysoft is right, 180 inclination is a retrograde orbit.  But I don't think that's what's happening in your graph.  I can't see the entire y-axis scale on the right, but it looks like inclination jumped to 1600?  I'm confused there, because Gravity Simulator shouldn't be outputting numbers this high for inclination.Usually, when I see a graph like that it is because some value crosses the 360 mark and jumps to 0, or crosses 0 to 360.  And sometimes, inclination and mean anomoly can give you 'off by 180' errors, but usually for orbits with 0 inclination as lots of orbital properties are measured from longitude of the ascending node, and an orbit with no inclination has no ascending node.

 Title: Re: Binary Eccentricity Test - volunteers needed! Post by frankuitaalst on 02/03/07 at 14:44:41 not to worry about GravitySimulator , it works perfect . :) To avoid decimals I got the output in integers , multiplying the inclination with 1000. This means 180000 on the scale = 180 degrees .  In the sim I saw the planet make retrograde orbits .