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 Binary Eccentricity Test - volunteers needed! (Read 42544 times)
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: 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       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! Back to top (formerly known as Mal)   IP Logged
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: 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.     OK, set it to 5,000 samples, every 10,000 years. That seems to work. Back to top (formerly known as Mal)   IP Logged
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: 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 Back to top (formerly known as Mal)   IP Logged
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: 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 ) 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 . Back to top (formerly known as Mal)   IP Logged
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: 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 . I've still got to see if we can even see this cycle in the program...! Back to top (formerly known as Mal)   IP Logged
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: Re: Binary Eccentricity Test - volunteers needed! 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? Back to top « Last Edit: 10/25/06 at 10:29:29 by EDG »   (formerly known as Mal)   IP Logged
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: 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. Back to top (formerly known as Mal)   IP Logged
 Tony YaBB Administrator Posts: 1058 Gender: 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. Back to top IP Logged
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: 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? Back to top (formerly known as Mal)   IP Logged
 Tony YaBB Administrator Posts: 1058 Gender: 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. Back to top IP Logged
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: 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. Back to top (formerly known as Mal)   IP Logged
 Tony YaBB Administrator Posts: 1058 Gender: 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. Back to top IP Logged
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: 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. Back to top (formerly known as Mal)   IP Logged
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: 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. Back to top (formerly known as Mal)   IP Logged
 Tony YaBB Administrator Posts: 1058 Gender: 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 Back to top IP Logged
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #15 - 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. Back to top (formerly known as Mal)   IP Logged
 Tony YaBB Administrator Posts: 1058 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #16 - 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. Back to top IP Logged
 Tony YaBB Administrator Posts: 1058 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #17 - 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.   I'll play with this some more.  We'll get to the bottom of this  8) Back to top IP Logged
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #18 - 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? Back to top (formerly known as Mal)   IP Logged
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #19 - 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). Back to top (formerly known as Mal)   IP Logged
 frankuitaalst Ultimate Member Great site Posts: 1510 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #20 - 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 Regards Frank Back to top IP Logged
 Tony YaBB Administrator Posts: 1058 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #21 - 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? Back to top IP Logged
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #22 - 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. Back to top (formerly known as Mal)   IP Logged
 Tony YaBB Administrator Posts: 1058 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #23 - 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. Back to top IP Logged
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #24 - 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. Back to top (formerly known as Mal)   IP Logged
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #26 - 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? Back to top (formerly known as Mal)   IP Logged
 frankuitaalst Ultimate Member Great site Posts: 1510 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #27 - 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 . Back to top IP Logged
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #28 - 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 Back to top (formerly known as Mal)   IP Logged
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #29 - 10/26/06 at 23:15:38   Here's a graph of the state of affairs for the planet at 8.493 million years.     Blue 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) Back to top (formerly known as Mal)   IP Logged
 Tony YaBB Administrator Posts: 1058 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #30 - 10/26/06 at 23:29:04   I got tired of punching the formulas into my calculator so...   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 Double Dim pi As Double Dim i As Double, eMax As Double, pi2 As Double On Error Resume Next pi2 = Atn(1) * 4 * 2 i = Val(txi.Text) / 360 * pi2 eMax = Sqr(1 - (5 / 3) * (Cos(i)) ^ 2) txEmax.Text = eMax pi = Atn(1) * 4 M0 = Val(txM0.Text) If optMsun(0).Value Then M0 = M0 * 1.989E+30 If optMjupiter(0).Value Then M0 = M0 * 1.899E+27 If optMearth(0).Value Then M0 = M0 * 5.97E+24 M1 = Val(txM1.Text) If optMsun(1).Value Then M1 = M1 * 1.989E+30 If optMjupiter(1).Value Then M1 = M1 * 1.899E+27 If optMearth(1).Value Then M1 = M1 * 5.97E+24 M2 = Val(txM2.Text) If optMsun(2).Value Then M2 = M2 * 1.989E+30 If optMjupiter(2).Value Then M2 = M2 * 1.899E+27 If optMearth(2).Value Then M2 = M2 * 5.97E+24 A1 = Val(txA1.Text) If Option1(1).Value Then A1 = A1 * 149597870691# If Option2(1).Value Then A1 = A1 * 1000 A2 = Val(txA2.Text) If Option1(2).Value Then A2 = A2 * 149597870691# If Option2(2).Value Then A2 = A2 * 1000 E2 = 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 / 365.25 End Sub ``` Back to top IP Logged
 Tony YaBB Administrator Posts: 1058 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #31 - 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!) Back to top IP Logged
 Tony YaBB Administrator Posts: 1058 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #32 - 10/26/06 at 23:40:40   Quote from 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 . 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. Back to top IP Logged
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #33 - 10/26/06 at 23:48:42   Quote from 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!)   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. Back to top (formerly known as Mal)   IP Logged
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #34 - 10/26/06 at 23:57:19   Quote from 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   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. Back to top (formerly known as Mal)   IP Logged
 Tony YaBB Administrator Posts: 1058 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #35 - 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. Back to top IP Logged
 Tony YaBB Administrator Posts: 1058 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #37 - 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 Back to top IP Logged
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #38 - 10/27/06 at 07:24:31   Quote from 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.   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) Back to top (formerly known as Mal)   IP Logged
 Tony YaBB Administrator Posts: 1058 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #39 - 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. Back to top IP Logged
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #40 - 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. Back to top (formerly known as Mal)   IP Logged
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #41 - 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. Back to top (formerly known as Mal)   IP Logged
 Tony YaBB Administrator Posts: 1058 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #42 - 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. Back to top IP Logged
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #43 - 10/27/06 at 20:12:46   Quote from 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.   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... Back to top (formerly known as Mal)   IP Logged
 Tony YaBB Administrator Posts: 1058 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #44 - 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 Msun planet: 2.5 AU, 0 ecc, 0 inc secondary: 750 AU, .8 ecc, 75 inc.   What time step are you using? Back to top IP Logged
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #45 - 10/27/06 at 20:52:27   Quote from 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 Msun planet: 2.5 AU, 0 ecc, 0 inc secondary: 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! Back to top (formerly known as Mal)   IP Logged
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #46 - 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. Back to top « Last Edit: 10/28/06 at 08:34:27 by EDG »   (formerly known as Mal)   IP Logged
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #47 - 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) Back to top (formerly known as Mal)   IP Logged
 frankuitaalst Ultimate Member Great site Posts: 1510 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #48 - 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 ? Back to top IP Logged
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #49 - 10/28/06 at 08:45:45   20.1 million years:     Something 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?! Back to top (formerly known as Mal)   IP Logged
 Tony YaBB Administrator Posts: 1058 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #50 - 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). Back to top IP Logged
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #51 - 10/28/06 at 14:35:49   Quote from 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.   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... Back to top (formerly known as Mal)   IP Logged
 Tony YaBB Administrator Posts: 1058 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #52 - 10/28/06 at 14:39:37   Quote from Mal   on 10/28/06 at 14:35:49: 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. Back to top IP Logged
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #53 - 10/28/06 at 14:45:41   Quote from Tony   on 10/28/06 at 14:39:37: 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. Back to top (formerly known as Mal)   IP Logged
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #56 - 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! Back to top « Last Edit: 10/28/06 at 19:40:10 by EDG »   (formerly known as Mal)   IP Logged
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #57 - 10/28/06 at 18:47:23   EDIT: Simulation still going from restarted version. Nothin' to see here! Back to top (formerly known as Mal)   IP Logged
 Tony YaBB Administrator Posts: 1058 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #59 - 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. Back to top IP Logged
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #60 - 10/28/06 at 19:03:20   Quote from 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.   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. Back to top (formerly known as Mal)   IP Logged
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #61 - 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! Back to top (formerly known as Mal)   IP Logged
 Tony YaBB Administrator Posts: 1058 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #62 - 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. Back to top IP Logged
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #63 - 10/28/06 at 19:32:41   Quote from 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".   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? ) Back to top (formerly known as Mal)   IP Logged
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #64 - 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°... Back to top (formerly known as Mal)   IP Logged
 Tony YaBB Administrator Posts: 1058 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #65 - 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. Back to top IP Logged
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #66 - 10/28/06 at 22:50:15   Quote from 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.   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 . Back to top (formerly known as Mal)   IP Logged
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #67 - 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. Back to top « Last Edit: 10/29/06 at 09:58:52 by EDG »   (formerly known as Mal)   IP Logged
 frankuitaalst Ultimate Member Great site Posts: 1510 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #68 - 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 . Back to top IP Logged
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #69 - 10/29/06 at 07:28:54   27.857 million years:     Well, 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.           I'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. Back to top (formerly known as Mal)   IP Logged
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #70 - 10/29/06 at 07:36:44   Quote from 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 .   Hm, that shouldn't be happening - the relative inclination is supposed to be going between the starting value and 40 degrees. Back to top (formerly known as Mal)   IP Logged
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #71 - 10/29/06 at 09:58:25   OK, that's it, I've given up .       Final time: 28.561 million years.   Eccentricity dropping Inclination 76° and still increasing Arg of Peri and LAN still decreasing   So 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. Back to top (formerly known as Mal)   IP Logged
 frankuitaalst Ultimate Member Great site Posts: 1510 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #72 - 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 !!!           ** modified by Tony -- added img tags. Back to top « Last Edit: 10/29/06 at 12:35:56 by Tony »     IP Logged
 Tony YaBB Administrator Posts: 1058 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #73 - 10/29/06 at 13:29:23   The 3rd one is surprising.  It looks like eccentricity has a double peak. Back to top IP Logged
 frankuitaalst Ultimate Member Great site Posts: 1510 Gender: Re: Binary Eccentricity Test - volunteers needed! Reply #74 - 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 Back to top IP Logged