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Gravitational capture by Europa? (Read 8113 times)
RGClark
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Gravitational capture by Europa?
08/05/15 at 12:44:06
 
Suppose we put a spacecraft in elliptical orbit around Jupiter at the same periapsis distance as Europa. We arrange it so it makes a very close flyby, say less than 10 km, to Europa. How long would it take to be captured by Europa?
 Note this is known as ballistic capture or low energy transfer to save on the fuel requirements.
 
  Bob Clark
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« Last Edit: 08/06/15 at 05:51:08 by RGClark »  
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frankuitaalst
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Re: Gravitational capture by Europa?
Reply #1 - 08/05/15 at 13:14:39
 
Interesting question .  
Didn't even know it was even possible to have a capture in this configuration ( ie. a system of only one planet , one moon and one not propelled spacecraft ) .  
Always thought one would need another body to which energy is exchanged ( dissipated ) , in such a way the second body is not captured but "escapes" the capture.  
 
Edit : Oh , I forgot the sun , which is the fourth body . So capture might be possible .  
Will take some simulations to calculate the odds of such a succesful capture .
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Re: Gravitational capture by Europa?
Reply #2 - 08/05/15 at 14:12:39
 
Hi Bob,
Welcome to the forum!
It's not necessary to pass within 10 km.  Objects captured through ballistic capture will enter orbit through Europa's L1 or L2 points.  The captures are only temporary.  The object will also escape through L1 or L2.
Here's a simulation.  
 
http://orbitsimulator.com/gravitySimulatorCloud/simulations/1438807842185_Europa _capture.html
 
This simulation is in a rotating frame that matches Europa's period.  This makes it easy to visualize Europa's L1 and L2 points.  They are both along the Europa/Jupiter line, with L1 being in between Europa and Jupiter, and L2 being external to Europa's orbit.
If you can't see Jupiter, zoom out.  Once you're familiar with Jupiter's location, and the location of L1 and L2, zoom in for a more detailed view of the captures and escapes.  Refresh the page if you want to start over.
 
I made this simulation by realizing that a capture is simply an escape in reverse.  I created 20 objects in orbit around Europa at about 1/2 of a Hill Sphere distance, and ran it in reverse until some escaped.  I then deleted the ones that didn't escape.  I then ran time forwards and saved the Sim.
The ones that rapidly escape without going through L1 or L2 simply passed too close to Europa, where 16 s is too high of a time step for that close of a passage.  So those results should not be considered.  Refresh the sim and slow to timestep 8 s for better results.
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Re: Gravitational capture by Europa?
Reply #3 - 08/05/15 at 14:21:15
 
In 2007, Earth captured asteroid 2007 RH120 using ballistic capture.  It escaped about 1 year later.
http://orbitsimulator.com/gravitySimulatorCloud/simulations/1433806156068_2006%2 0RH120.html
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Re: Gravitational capture by Europa?
Reply #4 - 08/06/15 at 08:33:32
 
Thanks for those. On the Kerbal forum it was said Kerbal couldn't do "ballistic capture" because it only uses patched conics. Does GravitySimulator use an n-body approximation.
 
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Re: Gravitational capture by Europa?
Reply #5 - 08/06/15 at 10:00:32
 
I assume the pink colored ones are the moons, with Europa the one in the center and the blues are the spacecraft trajectories?
About the spacecraft trajectories some are odd looking in that sometimes as they approach Europa, they suddenly move off in right angles to the original path away from Europa. I can see why they might make a sharp turn towards Europa but not away.
 
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« Last Edit: 08/06/15 at 18:55:01 by RGClark »  
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Re: Gravitational capture by Europa?
Reply #6 - 08/06/15 at 11:30:19
 
Thanks Tony for the nice simulation . Smart way and strategy to get to the set-up !  
I tried to work on this sim and tried to create a bunch of bodies around Europa .  
Seemed to work , but the bodies don't show up in the sim , athough they are generated in the list of bodies .  
 Tried some colors , up to white , but no succes ...
Is this feature ( new...) already operational ?
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Re: Gravitational capture by Europa?
Reply #7 - 08/06/15 at 20:14:04
 
Quote from RGClark on 08/06/15 at 10:00:32:
I assume the pink colored ones are the moons, with Europa the one in the center and the blues are the spacecraft trajectories?
About the spacecraft trajectories some are odd looking in that sometimes as they approach Europa, they suddenly move off in right angles to the original path away from Europa. I can see why they might make a sharp turn towards Europa but not away.

 Bob Clark

This is why orbital dynamics is often counter-intuitive, especially in a rotational frame where "fictitious" forces are introduced.  In the dropdown list, change "Eurpoa" to "Stationary", and watch what this looks like in an inertial frame.
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Re: Gravitational capture by Europa?
Reply #8 - 08/06/15 at 20:17:03
 
Quote from frankuitaalst on 08/06/15 at 11:30:19:
Thanks Tony for the nice simulation . Smart way and strategy to get to the set-up !
I tried to work on this sim and tried to create a bunch of bodies around Europa .
Seemed to work , but the bodies don't show up in the sim , athough they are generated in the list of bodies .
Tried some colors , up to white , but no succes ...
Is this feature ( new...) already operational ?

No new features in the last few days.  Make sure you choose Europa for the reference object, and that you use the correct units for SMA.  Otherwise, they are created inside Jupiter, and get unrealistically ejected at high speeds.  If you like, tomorrow I'll post some detailed instructions.
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Re: Gravitational capture by Europa?
Reply #9 - 08/06/15 at 20:18:38
 
Quote from RGClark on 08/06/15 at 08:33:32:
Thanks for those. On the Kerbal forum it was said Kerbal couldn't do "ballistic capture" because it only uses patched conics. Does GravitySimulator use an n-body approximation.

 Bob Clark

Yes, Kerbal can't do this because it is not an n-body simulator.  Gravity Simulator does n-body with Runge Kutta 4th order method.
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Re: Gravitational capture by Europa?
Reply #10 - 08/07/15 at 11:14:48
 
Quote from Tony on 08/06/15 at 20:18:38:

Yes, Kerbal can't do this because it is not an n-body simulator.  Gravity Simulator does n-body with Runge Kutta 4th order method.

 
 Thanks. Pretty cool. I noticed that though some bodies did orbit Europa for a few orbits, after awhile they were all ejected. Is it possible to focus in on those bodies that go into orbit to see their distances from Europa, periods etc.?
 
 In case you're interested I want to find low delta-v trajectories to Europa to allow a landing there. That the spacecraft in orbit would at some point be ejected is alright if the landing already took place. And even for the orbital spacecraft case, it might be possible to just do a small delta-v burn to put it in permanent orbit.
 
Low cost Europa lander missions.
http://exoscientist.blogspot.com/2015/02/low-cost-europa-lander-missions.html
 
   Bob Clark
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Re: Gravitational capture by Europa?
Reply #11 - 08/07/15 at 13:57:59
 

Maybe some tricks to try wiith the simulation,  Bob .
Press "m" and you will see a menu show up .  
This allows for further control of the simulation .  
Fi : Choose preferences , and change "Do events " to 10.  
The sim wil show more smoother and more realistic .  
You can also try out the "object" menu .  
This will give you access to a lot of info about the objects .
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Re: Gravitational capture by Europa?
Reply #12 - 08/07/15 at 14:16:36
 

Quote:
Thanks. Pretty cool. I noticed that though some bodies did orbit Europa for a few orbits, after awhile they were all ejected. Is it possible to focus in on those bodies that go into orbit to see their distances from Europa, periods etc.?

In case you're interested I want to find low delta-v trajectories to Europa to allow a landing there. That the spacecraft in orbit would at some point be ejected is alright if the landing already took place. And even for the orbital spacecraft case, it might be possible to just do a small delta-v burn to put it in permanent orbit.


In case you want to experiment with trajectory design you might consider to download the Gravity Simulator as  executable from this forum .  
This application allows to give thrust to your spacecraft at various points of your mission . Might be interesting .  
I guess Tony can guide here here...
 
 
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Re: Gravitational capture by Europa?
Reply #13 - 08/08/15 at 04:31:51
 
Thanks for that info.
 
  Bob Clark
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Re: Gravitational capture by Europa?
Reply #14 - 08/08/15 at 21:49:04
 
Quote from frankuitaalst on 08/07/15 at 14:16:36:

In case you want to experiment with trajectory design you might consider to download the Gravity Simulator as  executable from this forum .
This application allows to give thrust to your spacecraft at various points of your mission . Might be interesting .
I guess Tony can guide here here...

You can do this in the new version, but the procedure is much different.  All autopilot features require you do a small amount of Javascript programming.  The disadvantage is that the learning curve is steeper.  The advantage is that you can "autopilot" almost anything, whether or not I thought to add it to the program, such as Yarkofsky Effect.  And the Javascript is very easy.  You use Power Basic.  The four biggest differences are that you use square brackets for arrays, you use the word "var" instead of "dim", blocks of code are enclosed in curly braces, and every line ends with a semicolon.
 
I put together a YouTube video showing how to take one of the objects from the capture simulation, and cause it to brake into circular orbit around Europa after the ballistic capture.  I wanted to add voice, but I'm having microphone trouble after my upgrade to Windows 10.  So sorry, this is a silent movie Smiley
 
The strategy in the video is this:
1. Pick one object and delete the others.  I chose Object 10.
2. Run the sim and after ballistic capture, determine the time of closest Europa approach, and the speed and distance relative to Europa at that time.
3. Calculate the speed it would need for circular orbit at that distance, and how much you need to change its existing velocity.
4. Set up Autopilot to perform the "burn" at that time.
 
https://www.youtube.com/watch?v=3Eu0b3UvhPA
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