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Message started by RGClark on 08/05/15 at 12:44:06

Title: Gravitational capture by Europa?
Post by RGClark on 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

Title: Re: Gravitational capture by Europa?
Post by frankuitaalst on 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 .

Title: Re: Gravitational capture by Europa?
Post by Tony on 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.

Title: Re: Gravitational capture by Europa?
Post by Tony on 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%20RH120.html

Title: Re: Gravitational capture by Europa?
Post by 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

Title: Re: Gravitational capture by Europa?
Post by 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

Title: Re: Gravitational capture by Europa?
Post by 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 ?

Title: Re: Gravitational capture by Europa?
Post by Tony on 08/06/15 at 20:14:04


RGClark wrote:
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.

Title: Re: Gravitational capture by Europa?
Post by Tony on 08/06/15 at 20:17:03


frankuitaalst wrote:
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.

Title: Re: Gravitational capture by Europa?
Post by Tony on 08/06/15 at 20:18:38


RGClark wrote:
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.

Title: Re: Gravitational capture by Europa?
Post by RGClark on 08/07/15 at 11:14:48


Tony wrote:
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

Title: Re: Gravitational capture by Europa?
Post by frankuitaalst on 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 .

Title: Re: Gravitational capture by Europa?
Post by frankuitaalst on 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...



Title: Re: Gravitational capture by Europa?
Post by RGClark on 08/08/15 at 04:31:51

Thanks for that info.

 Bob Clark

Title: Re: Gravitational capture by Europa?
Post by Tony on 08/08/15 at 21:49:04


frankuitaalst wrote:
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 :)

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

Title: Re: Gravitational capture by Europa?
Post by frankuitaalst on 08/09/15 at 03:21:16

excellent explanation Tony in the video !

Title: Re: Gravitational capture by Europa?
Post by frankuitaalst on 08/09/15 at 11:16:25

Question to Tony .
I seem to have problems creating a new body .
In the Original sim ( Europa capture ) I proceed as following :

(with sim pauzed)
press m in order to get the menu
select the menu objects
select the submenu create
change the reference object to "Europa " as I want to create a body around Europa
input data for the new body  : objectnew, mass 1 , ...Sma [b]40000 km
[/b]press apply
unpauze the sim .

Result : I don't see the new body , which should be around Europa , but zooming much much  further out the body is there, far beyound all planets .
Looking at the elements of the orbit I observe Sma -3000 Au , sometimes +1000 Au .
( I repeated the setup several times ...) .
The orbit of this body also is weird . In case of an elliptical orbit the body seems to go around the sun at perihelium very slow , at aphelion very quick.
I guess I'm doing someting wrong at setup , but don't know what .

Title: Re: Gravitational capture by Europa?
Post by Tony on 08/09/15 at 12:19:40

When I save a simulation, it retains most of the settings of the parent simulation.  In the case of the Europa Capture simulation, the distribution button is set to "Start, End" because that's how I used it to create multiple objects.  So in the field where you are typing 40000, it is expecting 2 values.  Just press "Start, End" until it turns back into "+/- %" and it should work fine.

As an example of how to create 3 objects with sma of 30000, 40000, and 50000 km do the following.
Leave this at Start, End.  Change the number of Objects to 3.  Type 30000, 50000.  Press Create.

You don't need to give the particle a mass of 1 kg.  1 kg will not be significant to the simulation, but it will make the RK4 routine do extra math and slow down the sim.  It handles 0 mass particles differently, not doing hundreds of calculations that will ultimately result in 0.  For just one object you won't see the difference, but if you add many objects it will slow you down.

Title: Re: Gravitational capture by Europa?
Post by frankuitaalst on 08/09/15 at 13:07:41

Thx Tony , I'm aware of the start/end feature.
Repaeted the new body , called it frank and gave it 40000 , 50000 km from Europa .
Simultion was pauzed , then saved it and shared it , so that you can load it .
The asteroid frank seems to be far out of the solar system .
No idea what happens . Can you run it ?
(and delete it after you've checked it ?)

Title: Re: Gravitational capture by Europa?
Post by Tony on 08/09/15 at 13:42:45

If you give it 40000, 50000, you must create more than one object.  I just tried it and I get the same result you do if I try to create 1 object and give it a range rather than a +/-%
Either change number of objects > 1, or press Start, End until it reads +/-%.

I deleted it at your request, but you don't need to check "share on orbitsimulator".  With "create temporary link" you can copy the link and paste it here.  Then it never appears on the simulations page.

Title: Re: Gravitational capture by Europa?
Post by frankuitaalst on 08/09/15 at 13:56:40

Thx Tony .
Applying +/- for Sma succeeds for 1 body . Fine !
However if I try >1 bodies and apply Start / end with ValStart<ValEnd then the bdoies are created far far away .
Looking at the Objects Elements I read "NAN" when I look a second time.

Title: Re: Gravitational capture by Europa?
Post by Tony on 08/09/15 at 23:32:46

You'll have to send me a screen shot of the Create Objects interface.  I get good results with the method you describe.

When I was first getting used to the interface, I would sometimes get the results you describe.  When creating objects around the Sun, I often forgot to change km to AU, and created the objects inside the Sun.  With "collisions" turned off, the object was ejected at faster than light speed until its distance was greater than Javascript can count.  At that point you get NaN (not a number) errors.

Title: Re: Gravitational capture by Europa?
Post by RGClark on 08/12/15 at 01:00:12

Thanks for that simulation, Tony. How long after the spacecraft enters elliptical orbit around Jupiter does it enter circular orbit around Europa? What was the delta-v for the circularization burn?

 Bob Clark

Title: Re: Gravitational capture by Europa?
Post by Tony on 08/12/15 at 14:14:02


RGClark wrote:
Thanks for that simulation, Tony. How long after the spacecraft enters elliptical orbit around Jupiter does it enter circular orbit around Europa? What was the delta-v for the circularization burn?

 Bob Clark

It will happen the first time the spacecraft ventures into Europa's Hill Sphere through L1 or L2.  It could take as few as 1 orbit, or as many as thousands of orbits.

I posted a YouTube a few posts back showing how to make the capture sim.  The vid shows that the circularization burn had a delta v of 336 m/s.  If you weren't interested in a close circular orbit, you could make your orbit permanent with a lower delta-v.

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