10/17/19 at 02:14:29 News: Registration for new users has been disabled to discourage spam. If you would like to join the forum please send me an email with your desired screen name to tony at gravitysimulator dot com.

 Pages: 1 2 3 4 5 6
 Binary Eccentricity Test - volunteers needed! (Read 53541 times)
 Tony YaBB Administrator Posts: 1060 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: 1060 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: 1060 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: 1060 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