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Binary Eccentricity Test - volunteers needed! (Read 30260 times)
EDG
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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!
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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.
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« Last Edit: 10/28/06 at 08:34:27 by EDG »  

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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...  undecided
 
(at the actual halfway point of the cycle, the inclination is 34.4 degrees, which is well below half of 75 degrees)
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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 ?  
 
 
 
 
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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?!
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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).
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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...
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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.
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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.
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Re: Binary Eccentricity Test - volunteers needed!
Reply #54 - 10/28/06 at 16:25:01
 
Quote from Mal   on 10/28/06 at 14:45:41:

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).
 

 
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.
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Re: Binary Eccentricity Test - volunteers needed!
Reply #55 - 10/28/06 at 18:14:44
 
Quote from Tony   on 10/28/06 at 16:25:01:


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 Smiley.  
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.
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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!
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« Last Edit: 10/28/06 at 19:40:10 by EDG »  

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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!
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Re: Binary Eccentricity Test - volunteers needed!
Reply #58 - 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.
 

 
Probably 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.
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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.
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