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moon capture question (Read 3820 times)
frankuitaalst
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moon capture question
03/02/08 at 02:39:03
 
Someone here has experience with the gravitational moon capture by a planet ?  undecided
Reason to ask : I want to simulate some initital parameters for an asteroid so that it will be captured by Earth after some time ( fi . 1/2 a revolution ) . seems the be awfully difficult to set an initial set so that the body is captured .  
I already get very close fly-bys , resulting in very weird orbital pattern ( espescially in rotating frame) , but the asteroids alawys tend to get into a near Earth orbit . Maybe this is even impossible ....
I read somewhere that in a three body problem it is impossible to have a capture ....
If this is true the old theory about the origin of our moon as being a single captured body may be ruled out
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Re: moon capture question
Reply #1 - 03/02/08 at 08:32:05
 
I think you need another body to be involved for capture to work - not just the Earth and the Asteroid. e.g. the asteroid has to be binary - then its companion ends up being tossed out of the system and the main asteroid gets captured.
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frankuitaalst
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Re: moon capture question
Reply #2 - 03/02/08 at 08:57:49
 
I think you're right Mal . Is it an opinion you have or is there some underlying theory ?
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frankuitaalst
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Re: moon capture question
Reply #3 - 03/02/08 at 11:16:28
 
I guess Mal is right . After running tens of simulations in an asteroid , sun earth configuration so that the asteroid comes close to earth , I didn't find any configuration leading to a capture .  
Increasing the mass of the asteroid up to the size of earth didn't result in a capture either ...
Herunder is an animation where a second earth sized body was injected into Earths orbit using the initial conditions herunder :  
"Earth",-1.3498607e+11,-6.4257389e+10,0,1.2806106e+4,-2.6901901e+4,0
"Ast",-1.200454e+11,0,0,0,-3.5017131e+4,0
The Earth sized body ( bright red) is initially inside Earths orbit and makes a close encounter to earth . From then on both bodies interchange energy from numerous close encounters resulting in changing orbits . After some years both planets even switch orbits for a couple of orbits ... but no capture....
Animation was run for 400 years .

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2Earthsanim.gif
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Re: moon capture question
Reply #4 - 03/02/08 at 11:22:46
 
Capture is possible, even in a 3-body configuration.  However, the resultant orbit is very unstable, hence a future ejection will likely occur.
 
Keep in mind that ejections are simply the time reversal of captures.  This makes creating them easy:
 
File > New
Pause the simulation.
Objects > Edit Objects.  Change name to Sun.
Objects > Create Objects.  Place an Earth-massed and size object in a SMA of 1 AU.
Make this object the focus object and zoom so it is a little larger than a pixel.
Objects > Create Objects.
  Choose your planet as the reference object
  number of objects: 100
  semi-major axis: 1000000 +-50% km
  Leave all other numbers at their defaults.
  Press Create.
menu Time > Time Backwards
Unpause the simulation.
 
Some objects will be in permanent orbits.
Some objects will immediately escape the planet as they venture beyond the planet's stability zone (related to the Hill Sphere)
Others will complete several orbits before escaping.  These are the interesting ones.  Identify one, wait for it to get a good distance from the Planet. Then pause the simulation.
menu Objects > Delete Objects.  Delete all objects except the Sun, the planet, and this object.  Then menu Time > Time Forward.  Save the simulation.  Unpause it and watch as the object approaches the planet and gets captured..
 
You can also try creating retrograde captures by setting inclination to 180 +- 0% in the above procedure.  These tend to be more stable.
 
Then there's the possibility that Mal mentioned, a binary being stripped of its partner during a close pass to Earth, with one member being ejected and the other being captured.  Some theorize that this explains Triton's orbit around Neptune.  I haven't tried this yet, but I'd also do the time-reverse method.  Set it up exactly as before, but this time, after you've deleted all objects but one, edit that object, give it some mass, and create an object orbiting it.  Play around with the distances.  The wider, the easier a split capture will be.  Also, give this pair a 100:1 mass ratio, or you'll significantly change its trajectory.
 
Other types of capture are possible as well that can not be modeled by Gravity Simulator.  A planet may have a thin extended atmosphere that helps brake the asteroid into orbit, robbing it of energy at each periapsis, so its orbit becomes stable.  Then after the extended atmosphere disipates, the object remains in a stable orbit, and tidal forces can circularize its orbit.
 
Keep in mind, most scientists dismiss the theory of capture as the origin of Earth's moon.
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frankuitaalst
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Re: moon capture question
Reply #5 - 03/02/08 at 11:41:42
 
thanks for the hint Tony , using the reverse method . I was using the forward method , making use of the conservation of energy . This is the hard way . I'll give your approach a try ...
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« Last Edit: 03/02/08 at 14:03:23 by frankuitaalst »  
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frankuitaalst
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Re: moon capture question
Reply #6 - 03/05/08 at 13:42:02
 
Just want to report that I wasn't succesfull in creating a capture using the "reverse" time method .  
Starting with 100 planets I selected about 20 of them beeing moderately ejected .  
However , running the sim forward again with this bodies , all of them were also ejected from Earth again , going into orbit around the sun ....
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Re: moon capture question
Reply #7 - 03/05/08 at 16:56:12
 
You should have temporarily captured some of them.  But an ejection is to be expected since you captured them into unstable orbits.
 
This is the biggest problem with the capture theory.  It's hard to make it work.
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frankuitaalst
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Re: moon capture question
Reply #8 - 03/09/08 at 05:11:19
 
Yes indeed it's very hard to make it work , but Eureka ... Smiley I managed to capture one for about 20 years .  
Hereunder is the capture in rotating frame of a moon of 1/10 Earth mass.  
The moon originally has an orbit close to Earths ( inside Earhts orbit ) and is captured in an orbit with highly varying eccentricity .  
I don't believe capture is possible if the orbits are widely separated ( ie . the angle of approach in the direction of motion must be small ) .  
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capturemoonanimRot.gif
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frankuitaalst
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Re: moon capture question
Reply #9 - 03/09/08 at 05:37:59
 
Above simulation was done with the following initial parameters :  
"EarthMass",5.9736e+24
"AstMass",5.9736e+23"
"Earth",1.4950e+11,0,0,0,2.9794e+4,0
"Ast",1.5020e+11,0,0,-145,30595,0
Please note the capture is in the past  
 
Hereunder is an animation of the capture . Screenshot was made every 0.25 years .  
Simulation was run for 6 years .  
Screenwidth is 0.05 AU .
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Mooncapturedetail.gif
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frankuitaalst
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Re: moon capture question
Reply #10 - 03/09/08 at 06:01:35
 
In rotating frame to Earth , and centered to Earth the capture looks like this :
Each screenshot represents 1/10 years .
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animDetailcaptureRot.gif
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frankuitaalst
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Re: moon capture question
Reply #11 - 03/09/08 at 12:51:41
 
Playing aroud with the same sim as above , but changing masses and distances gives me the strong feeling that capture is easier when the second body is bigger . Small masses are more difficult to capture then bigger ones .  
Herunder is a sim where a second Earth is captured by Earth for a couple of years .  
Screenwidth is 0.05 Au . Screenshots are taken every 0.2 years.  
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AnimCaptureEarth.gif
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