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Plot/Don't Plot - It's Not Just For Reading E-mail (Read 4417 times)
Michael_C._Emmert
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Plot/Don't Plot - It's Not Just For Reading E-mail
10/11/05 at 22:40:56
 
Howdy;
 
Having gotten some hands-on experience with GravitySimulator, I decided to re-read the instructions.  I figured I'd missed something.  I was right.  embarrassed
 
Gravity Simulator is the greatest video game I have ever played.   8)  It' better than Defender, with eight scanners instead of one.  There is also a kind of chess-like quality to it; in something like Defender, you can't pause the game and figure out some kind of plot against the Evil Green Landers.   Grin  But there are times when the excitement factor is down.   Sad
 
My simulations involve flying a binary (Xena/Triton) past Neptune, and I am using a time step of 64 seconds, which is awfully slow.  (I have to slow down even more during the actual flyby, both for accuracy and because there are a lot of things to do and data to copy when this happens).  So I used Don't Plot and read one e-mail and made one message board post, a short one.  By the time I got back, the binary had flown past Neptune!
 
Since everybody's simulation is different, to see how long to wait on Don't Plot, run it for one minute, then double click the plot button on the graphics option.  This will make a dot.  Wait another minute and make another dot.  This will give you some idea.  Remember that things happen faster when an object approaches another that has significant gravity.  I had my second simulation after coming up with this technique overshoot because I underestimated this effect.
 
The machine really does run a lot faster if it doesn't have to create a graphics display several times every second and remember where the trails are and such.   undecided  This allows a lot more simulations, so you can adjust them to make them more realistic and see if your idea is true or just a figment of your imagination.   Wink
 
Plus, you can read e-mails, participate in message boards, look up facts about astronomical objects and even read the links Tony has provided.   Smiley
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Tony
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Re: Plot/Don't Plot - It's Not Just For Reading E-
Reply #1 - 10/11/05 at 23:08:54
 
Hey Mike,
Glad to see you're having a good time with the program.
 
A few other features that might help with the kinds of things you're doing:
 
Auto Pilot : Pause
This way, you can use the don't plot mode, but have the program automatically pause at a specified time so you don't miss your flybys.  The way I use this is to save the simulation I'm working on, then run it at a very fast time step, observing the date and time that the flyby occurs.  Then I re-open the saved simulation and run it at an acceptable time step, adding an Autopilot Pause command slightly before the scheduled flyby.  Then put it in Don't Plot mode, and you can come back a few minutes later to a paused program right before the flyby.  Unpause it, choose plot mode and watch your flyby.
 
Another feature you might like is Auto Save in the File Menu.  If you use this feature, I suggest you create a new folder for your simulation and save it there.  Then using Auto Save, you have it save the simulation at a given interval.  That way, if you come back to your simulation and something got flung to a weird orbit, but you don't know how, you can open the auto-saved simulations to look for the event that caused this.
 
For example, if you choose Auto Save and choose to save the simulation every 1 day, then you run the simulation for 1 year, when you come back to the computer, you'll have 365 saved simulations.  Open the one that occured halfway between the beginning and the end of your run, and see if the behavior you're looking for has occured yet.  If not, choose the halfway point between that point and the end of your run, etc, until you find the autosaved simulation that contains the event you're looking for.
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Michael_C._Emmert
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Re: Plot/Don't Plot - It's Not Just For Reading E-
Reply #2 - 10/12/05 at 15:30:24
 
Thanks, Tony  Smiley.  This will be useful information in future simulations where I will be populating the Lagrange stability zones with low mass objects and waiting to see if they coalecse into one object, a few binaries, or whatever happens.  This might involve running a Don't Plot program for days!
 
With the 65536 sec. time step, I have noticed that Mercury's orbit starts looking a little funny after about a half a million years, so I don't follow flyby escapees much longer than that.  At what time step is the inner solar system reasonably stable over, say, 10 million years?  I feel an answer to this has general interest, since I don't know what the other GravitySimulators are doing, but would guess that a lot of them are doing projects in the solar system.
 
Since extremely close flybys introduce mathematical errors, I was thinking of making my Lagrange population's diameters artificially large; thus they would have a density of a few millibars of air, like giant soap bubbles.  Could I return realism to that demonstration by calculating how much faster this simulation occurs than with normal ice/rock densities?  Even with Don't Plot and Autosave, such a simulation might take a very long time, since individual flybys and collisions would have to be supervised at a low time step.  Neptune's Lagrange stability zone is more than a billion kilometers across in it's shortest dimension, and two Triton's worth of mass isn't a lot in something that size.
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Tony
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Re: Plot/Don't Plot - It's Not Just For Reading E-
Reply #3 - 10/12/05 at 16:31:47
 
Quote:
With the 65536 sec. time step, I have noticed that Mercury's orbit starts looking a little funny after about a half a million years...

At that timestep, Mercury's orbit will unnaturally precess due to math error.  The best way to figure out how fast is too fast is to run a simulation at a given time step, then run it again at 1/2 that time step and compare your results.  As you get slower and slower, your results will begin to converge upon a value, and slowing the time step further will just waste time.
 
Mercury's orbit precesses naturally too.  The biggest factor is the pertabutions from the other planets, which Gravity Simulator accounts for.  And a much smaller factor is General Relativity, which Gravity Simulator does not take into account.
 
Quote:
At what time step is the inner solar system reasonably stable over, say, 10 million years?

65536 should keep the inner solar system stable (16384 if you include Earth's Moon), but the objects will not be in their correct positions after 10 million years.  There isn't a timestep slow enough to keep the planets in their correct positions for that long of a period of time.  This is because Gravity Simulator only models point mass gravity.  Since that is by far the most dominant force shaping the solar system, the results are very good.  However, lots of other forces that are insignificant in the short term add up to something significant in the long term.  Chaos had a lot to do with this.  There are no simulators or mathamatical models that can accurately predict where the planets will be in 10 million years.  But that's not to say that the system isn't stable.  In 10 million years, the planets will still have orbits with basically the same orbital elements, both in real life and in Gravity Simulator.  It's just where in those orbits the planets will be that causes the most uncertainty.
 
To give you an example of the accuracy, I started with the simulation Fullsystem, propogated it about 40 years into the future, then compared the position of Earth and the Moon to their positions as predicted by JPL Horizons.  The Earth was within 1 Earth diameter of its JPL-predicted position, and the Moon was within 1 Moon diameter of the JPL-predicted position.  So in the short term Gravity Simulator is almost accurate enough to predict eclipses.  The same type of experiment didn't fare quite as well for the moons of Saturn.  The closer ones were off by a few tens of thousands of km after only 2 years, while the further ones remained truer to their JPL-predicted positions.  Not horrible considering that some of these moons travelled a half a billion kilometers relative to Saturn during this time.  But in real life, Saturn bulges at the equator by a noticable amount and this will cause an error.
 
Quote:
Since extremely close flybys introduce mathematical errors, I was thinking of making my Lagrange population's diameters artificially large...

That's a good idea.  Sometimes you have to play tricks like this to make up for the fact that a simulator is not real life.  You could start with a given exxagerated size, count your collisions, do it again with an exaggerated size half the original, count your collisions, do it again half size... etc., then see if you can recognize a trend line.  Where would the trend line be when the objects approached heir real sizes?  Is it linear or polynomial or something else?
 
***
 
Another thing to consider when choosing a time step for simulations involving collisions is that if your time step is too large, objects destined to collide with each other can simply pass through each other unaffected.  If your moons are 100 km wide, but are advancing 1000 km / time step, they're not likely to occupy the same space at the same time.
 
The Lagrange points 4 and 5 are simply stable points with a 1:1 resonance.  The Lagrange points are not the only stable areas where objects can congregate and coalesce.  Consider Neptune's 3:2 resonant points.  Pluto is trapped in one of them, as well as other objects now refered to as "Plutinos".  Here's an animated GIF I made with Gravity Simulator of Pluto's orbit in a rotating frame.  The blue dot is Neptune, the purple path is Pluto's orbit.  Notice what happens to Pluto's orbit when its perihelion gets too close to Neptune.  Neptune seemingly repels it, preventing it from ever coming too close.

If you get a chance, post some of your simulations, or e-mail them to me and I'll post them for you.
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Michael_C._Emmert
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Re: Plot/Don't Plot - It's Not Just For Reading E-
Reply #4 - 10/19/05 at 10:20:03
 
[quote author=Tony  
 
The Lagrange points 4 and 5 are simply stable points with a 1:1 resonance.  The Lagrange points are not the only stable areas where objects can congregate and coalesce.  Consider Neptune's 3:2 resonant points.  Pluto is trapped in one of them, as well as other objects now refered to as "Plutinos".  
 
Hi, Tony;
 
I take the other resonances, 3:2, 5:3, 11:6, whatever, very seriously.  I am quite sure they do in fact create objects, just like the Lagrange points do.
 
The question is, how much material would you find in the Solar nebula which is at or near these resonances?  Would there be enough material at such inclinations in the face of the Kozai mechanism to form an object such as Pluto?
 
One way possibly to find out is to see how large the resonance is before it switches to some  other resonance or a non-resonance.  Unfortunately, I am extremely busy with aspects of my own model and will not have time to model this.  Sorry.  I would hope that somebody else, a naysayer perhaps, might step foreward to do this.  As I said, I think it is a serious scenario for forming objects.
 
Here is a simulation, which frankly I'm not very satisfied with, which tries to outline the size of the Sun/Neptune L4 stability zone:
 
http://orbitsimulator.com/gravity/simulations/XL%20full%201.0.gsim
 
I used the randomizing dispersion feature to create a ball of 80 objects with a SMA of 270 million kilometers + or - 49%, eccentricity 0.49 + or - 98 %, orbital inclinations of 180 degrees + or - 100 %, and all other dispersions + or - 100%.  The total mass of the objects were twice the mass of Triton.  Those were named "Beelzebub" after the lord of the flies.
 
As I had suspected, most of the objects were not really in the Lagrange stability zone, so these were tracked down and deleted.  Then these were used as focus objects for creating more objects with 100 million kilometer SMA.  These were named for the "sons of Beelzebub".  (I don't believe in Beelzebub, those people were responsible for their own actions).
 
Tony, you know more about your program than I do.  How can I more realistically fill the Lagrange stability zone?
 
Anyway, the Lagrange stability zone is about a billion kilometers wide on the x - y axis and about the sam on the Z axis.  One object, Polpot 51, has moved in and out of the zone, sometimes in a horseshoe orbit and sometimes in a Lagrangian oscillation; it has the most extreme inclination.  When in the zone, it drifts from a little over a billion kilometers from Neptune to nearly the other side of it's orbit. all the time oscillating up and down by about a billion kilometers.
 
Thanks for your questions, some of them take some time to answer  Tongue  Have a nice day Smiley
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Re: Plot/Don't Plot - It's Not Just For Reading E-
Reply #5 - 10/20/05 at 11:33:14
 
Here's something fun to try:
 
Start with a new simulation
File > New
Give object a new name and color if desired.
 
Objects > Create Objects
Create 400 objects, each with a mass of 0.005 Earth masses.  So in total you will have 2 Earth masses worth of matter.
 
Size: 500,000 km.  This is unrealistic, but it will increase the collision rate.
 
Semi-major axis = 1AU +/- 0%
 
Press Create.
 
Turn trails off.
 
Zoom out to about 3 AU.
 
Save your simulation!  That way, if this run yields interesting results you can replay it.
 
Increase time step to 16384.
 
Sit back and watch!
 
As these planetesimals coalesce into planets, these planets can get trapped in each other's lagrange 4 & 5 points.
 
Use the "Don't Plot" feature to speed things up when you get bored watching.
 
Every time you try it, you get different results.  Once I got 1 planet that contained all the mass.  Another time I got 2 planets in horseshoe orbits similar to Janus and Epimetheus.  Another time I got 3 co-orbital planets is "psudo horsheshoe" orbits.
 
Next time I add simulation articles to the website I'll probably include a version of this.
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Michael_C._Emmert
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Re: Plot/Don't Plot - It's Not Just For Reading E-
Reply #6 - 10/21/05 at 23:57:31
 
Thanks.  This is a pretty good demonstration to watch.
 
It's interesting to watch the simulation speed up as more and more of the objects collide and coalesce.  Of course I slowed it down to watch it, but it's also interesting to watch the different patterns when the simulation starts moving really fast.  It's kind of like the wagon wheels on the old black & white western movies, where as the wagon goes faster, the wheel slows, appears to stop, then goes backwards.  It's an illusion, of course, caused by taking 24 frames/second.
 
In the case of the above simulation, the pattern alters suddenly in steps.  I would think this is happening when two objects approach each other.  Whether this is futher useful, I haven't figured out yet.
 
I'm getting mostly horseshoe orbits.
 
This simulation is of general interest, but it's helped me on my specific project.  I need to expand the diameters of my "soap bubbles" because they were too small to coalesce in a reasonable time.  I was thinking mathematical errors; from previous simulations I knew there would be a velocity dispersion of up to about 1 km/sec in the Sun/Neptune Lagrange stability zone and I was using a time step of 65536 sec., so the diameter worked out to 65536 km to avoid too-close approaches and artificially high velocities.
 
One of the posters on the Space.com message board commented that Lagrange points don't appear until there is an object massive compared to the total material in the belt of material orbiting at the future planets' distance.  It has occured to me that this Lagrange theory might be useful in solving the current debate about whether gas giants first formed a core which then accreted gas, or if they collapsed as a single blob of gas as stars do. undecided
 
I have noticed that if I give the mass a 99% dispersion, I wind up with a little less than one Earth mass.  I'm pretty sure this is an artifact of the random number generator.  Some mathematician once proved there is no such thing as a truly random number generator.  I assume you used a commericially available one in GravitySimulator (why reinvent the wheel?) and most are pretty good approximations.  Perhaps you could print some comments from the manufacturer's brochure.  In my dinky little computer, it takes about 20 or 30 seconds to apply mass dispersion to 400 objects, which is pretty reasonable.
 
I had a pretty humorous inversion of the roll of the dice in one of these.  I wound up with two objects that traded orbits like the two shepard moons in Saturn's rings.  The one that had less than a third of the total mass had over twice the diameter!
 
Or is it chance?  The lightweight had to have eaten over 8 times as many objects, since the objects were all the same size...
 
Now, if you apply dispersion both diameter and mass, does the program care about density?  Or do you wind up with a huge range of densities?  I suppose the lesson here is to only randomize one item at a time.  This makes it easier to interpret whatever result you get.
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