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Hill Sphere period - another formula (Read 22944 times)
EDG
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Re: Hill Sphere period - another formula
Reply #15 - 09/10/08 at 08:27:42
 
What would that look like with prograde orbits? (a mess, I'd imagine, since apparently those aren't stable near the hill sphere!).  
 
I do like the spiral arms effect there...
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Re: Hill Sphere period - another formula
Reply #16 - 09/10/08 at 08:58:11
 
Quote from Mal on 09/10/08 at 08:27:42:
What would that look like with prograde orbits? (a mess, I'd imagine, since apparently those aren't stable near the hill sphere!).

I do like the spiral arms effect there...

Right ! that's why I haven't posted them . Visuals should be kept somehow attractive  Wink
Well concerning the effect of the arms : it's even nicer to see how they form at simulation. The frames taken 1 year apart cover a lot .  
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Re: Hill Sphere period - another formula
Reply #17 - 09/11/08 at 16:02:08
 
An interesting thing about the objects that are right at the edge of stability, is that they can complete several orbits before being stripped away by the sun.  When they escape the planet, they always do so through the L1 or L2 points.  Then after orbiting the sun a few times, they get re-captured through the L1 or L2 point, complete a few orbits and then get ejected again.  It's fun to watch in the rotating frame as the positions of L1 and L2 are easy to spot.  Try this yourself:
 
File > New
Objects > Create -- Create a 1 Jupiter-mass object at SMA 1 AU.  Name it Jupiter.  Leave all inputs at their default.
 
Zoom out so you can see both objects.
View > Rotating Frame Adjustment.  Set it to the period of Jupiter.
Choose Rotating Frame.
 
Choose Jupiter as your focus object.
 
Create objects around it near the edge of stability:
 
Objects > Create Objects
With Jupiter set as the reference object, choose 0.31 AU as the SMA.  Change its color.  Leave all other inputs at their default.  Press Create.
Repeat, creating objects with sma's of 0.32, 0.33, 0.34, 0.35.  Play around with other values too.
 
Under Preferences, choose a graphics update interval of 50.
 
Set the time step to 512.
 
Sit back and watch as these objects escape Jupiter through the L1 and L2 points, orbit the Sun for a while, and get recaptured through the L1 and L2 points.
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Re: Hill Sphere period - another formula
Reply #18 - 09/11/08 at 16:14:43
 
Nice remark ! I'll give it a try . How do you know this ?
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Re: Hill Sphere period - another formula
Reply #19 - 09/11/08 at 18:16:15
 
Quote from frankuitaalst on 09/11/08 at 16:14:43:
...How do you know this ?

Because I know everything  Grin
 
Or just from trying different things.  Here's a screen shot of a system with a planet of 10 Jupiter masses orbiting at 1 AU.  A test particle is randomly placed in an orbit around the planet with an SMA of 0.8 AU.  It orbits a bit, escapes through L1, gets captured again through L1, over and over again.  This is very chaotic.  Any small change will ensure that you will not get the same results twice.
 
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Re: Hill Sphere period - another formula
Reply #20 - 09/11/08 at 18:18:44
 
Quote from Tony on 09/11/08 at 18:16:15:
Quote from frankuitaalst on 09/11/08 at 16:14:43:
...How do you know this ?

Because I know everything  Grin
http://orbitsimulator.com/gravity/images/L1capture.GIF

That's what I thought  Smiley
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Re: Hill Sphere period - What is this?
Reply #21 - 09/12/08 at 03:02:38
 
Applying the input above as you mention Tony ( but instead of 1 Jovian - 10 Jovian masses ) at 1Au and 0.31 AU for the moon I got this amazing .gsim simulation .  
My first reaction was " what the hell..." .  
Thought first a had done something wrong . Simulation starts in rotating frame .  
Till now my question is open .... Smiley.  
I'll post an animation later on .
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Re: Hill Sphere period
Reply #22 - 09/12/08 at 03:19:06
 
Here's the animation of the above gsim .  
Screenshots every 0.1 years .  
The body seems to travel between sun and Jupiter continiously .  
I must have been lucky , because when I created the body it was exactly on the line between sun and jupiter .  
Still don't know whats happening exactly , but I guess I must have created "by accident" a 0.5 resonance with appropriate eccentricity .  
 
Edit : in order to investigate the parameters of the object I started the above simulation again, as I had saved it . Timestep 64 s.  
To my surprise the object didn't have the linear orbit anymore but performed (also nice to see) a flowerlike orbit around the sun. Don't know whats happening or happens . Any idea Tony ?  I guess you other guys have the same result .  
 
Animation:
http://www.orbitsimulator.com/yabbfiles/Attachments/Whatthehellzeropointoneyears Anim.gif
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« Last Edit: 09/14/08 at 03:34:14 by frankuitaalst »  

WhatthehellzeropointoneyearsAnim.gif
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Hill Sphere period - Jupiter
Reply #23 - 09/12/08 at 12:22:05
 
I've tried to reproduce the simulation above , but no succes . I can't understand what happened and why opening the same sim afterwards gives a normal situation ...
Nevertheless , I performed the simulation Tony suggested , but this time with te real solarsystem . Put 100 bodies around Jupiter at 0.283 AU and let run .  
Animation hereunder .  
( actually I was anxious to see how the inner solar system would be affected ) .  
One can see the bodies escape over the L1 , other over the L2 point .  
Note : I think the 0.283 AU setting was to much as the bodies escape rather quickly .  
 
Animation:
http://www.orbitsimulator.com/yabbfiles/Attachments/100HillObjFromJupiter.gif
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« Last Edit: 09/14/08 at 03:34:54 by frankuitaalst »  

100HillObjFromJupiter.gif
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Re: Hill Sphere period - What is this?
Reply #24 - 09/12/08 at 14:26:55
 
Concerning the mysterious linear motion above : I've been lucky to recover some more screenshots I made running this sim .
Screenshots start with Rotating frame to Jupiter , then I went to normal view , where the result is a elliptical orbit ( 1: 4 resonance to Jupiter I think) .  
I can't understand how this elliptical orbit results in a straight line in rotating frame ...
( for the confort and "debugging" I made the animation extra slow)  
 
Animation:
http://www.orbitsimulator.com/yabbfiles/Attachments/DetailLinear_motion.gif
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« Last Edit: 09/14/08 at 03:35:28 by frankuitaalst »  

DetailLinear_motion.gif
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Re: Hill Sphere period - at the edge of stability
Reply #25 - 09/13/08 at 03:48:16
 
For the solarsystem a Hill radius of 0.155Au to Jupiter seems to be a configuration at the edge of stabilty ( in this orbital configuration starting at 2037) .  
100 bodies were given 0.155 SMA around Jupiter  
The simulation covers almost 100 years and consists of 400 individual frames.  
One can see the system "wind up" for several tens of years , then some bodies escape to the inner solar system over the L1 point  one after another .  
Watch how Jupiter seems to shoot every time it is near  aphelion . Only a few escape over L2 , leaving their orbit towards the outer solar system .  
The animation appears to be of "poor" resolution or quality . This is due to the scaling and the reduction of colors and compression in order to fit the 1MB upload limit . The original amount of data before compression was about 1GB in bmp.  
 
Animation:
http://www.orbitsimulator.com/yabbfiles/Attachments/100HillBodies0p155AU.gif
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« Last Edit: 09/14/08 at 03:35:59 by frankuitaalst »  

100HillBodies0p155AU.gif
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Re: Hill Sphere period - Saturns stability
Reply #26 - 09/13/08 at 10:46:31
 
For comparison : Saturn allows about distance of 0.185 AU as stable region .  
This  simulation shows Saturn from the point where it releases its first moons .  
The orbits of the released moons seem to show less dynmices compared to these of jupiters moons.  
Also the rate at which Saturn spews out the bodies is less compared to jupiter .  
 
Animation:
http://www.orbitsimulator.com/yabbfiles/Attachments/Saturn100bodies0p185AU.gif
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« Last Edit: 09/14/08 at 03:36:52 by frankuitaalst »  

Saturn100bodies0p185AU.gif
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Re: Hill Sphere period - Saturn
Reply #27 - 09/13/08 at 10:51:05
 
Prior to the release of the moons by Saturn ("wind up ") the system evolves from its initial configuration at 0.185 AU from saturn as shown hereunder .  
Watch how the end of the animation a couple of moons escape at the left corner above over the L1 point .  
 
Animation:
http://www.orbitsimulator.com/gravity/images/users/frankuitaalst/Saturn0p185Deta il.gif
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« Last Edit: 09/13/08 at 13:19:53 by Tony »  
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Re: Hill Sphere period - another formula
Reply #28 - 09/13/08 at 12:04:01
 
Very neat animations!  As Jupiter gets closer to the sun, its Hill Sphere shrinks.
 
I edited the thread because having several large animated GIFs on one page causes the page to load too slowly, and makes the animations run slow as well.  So instead of seeing the animations, you see links to the animations which allow you to open them one at a time.
 
Saturn gets hidden off the bottom of the screen in one of the animations.  You can prevent this if you rotate the rotating frame with the > and < buttons.
 
There's a new feature in the latest beta (probably the one you're running now) in the view menu called Pointer.  So if you're zoomed in enough that you can't see the sun, you can at least have a pointer showing you the direction of the sun.  But there's a bug in this feature.  Sometimes the pointer's starting position is off the screen, which means you can't see it or drag it to a convienent place.  Try it anyway, as it might work for you.
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Re: Hill Sphere period
Reply #29 - 09/13/08 at 13:05:10
 
Quote from Tony on 09/13/08 at 12:04:01:
I edited the thread because having several large animated GIFs on one page causes the page to load too slowly, and makes the animations run slow as well.  So instead of seeing the animations, you see links to the animations which allow you to open them one at a time.

Well done so ...you're right , that was my point some time ago .  
Can we as users also add some command to hide the annexe ?  
 
BTW ; do you have any idea what was happening in the sim were there was a straight line in the rotating frame ?  
Seems so weird , looks as if SMA and velocity are coupled in a strange ...way . Body must orbit a spiralling ellipse but I don't understand the physics , or might it be some bug ?  
 
EDIT : if I try to open one of the attachments I don't get them . I get the message :" page not found" .  
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