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Message started by Tony on 07/23/07 at 15:54:02

Title: Polydeuces
Post by Tony on 07/23/07 at 15:54:02

Polydeuces is a newly-discovered moon of Saturn. It traces tadpole orbits around Dione's L5 point. Helene occupies Dione's L4 point. Polydeuces wanders further from its Lagrange point than any other known moon in the Saturn system.

Here's the simulation so you can try it yourself: http://orbitsimulator.com/gravity/simulations/polydeuces.gsim

Here's a simulation of the Saturnian system that includes many of Saturn's newly-discovered moons: http://orbitsimulator.com/gravity/simulations/saturiansystem.gsim

Here's a screenshot in a rotating frame with the period of Dione. Saturn is the yellow circle in the middle. Dione traces the white stationary orbit. Helene traces the purple orbit from the L4 point. Polydeuces traces the green orbit from the L5 point.

http://orbitsimulator.com/gravity/images/polydeuces.GIF

Title: Re: Polydeuces
Post by frankuitaalst on 07/26/07 at 06:42:15

Any idea whats the meaning of the "curl" in the orbit of Polydeuces ? Seems as it orbits twice another orbit .

Title: Re: Polydeuces
Post by Tony on 07/26/07 at 11:22:17


frankuitaalst wrote:
Any idea whats the meaning of the "curl" in the orbit of Polydeuces ? Seems as it orbits twice another orbit .

That's an artifact of the viewing angle. The view is looking down on the ecliptic plane, but Saturn's moons do not orbit in this plane. Consider the following picture of Pluto and its moons:
http://www.orbitsimulator.com/gravity/plutosystem2.GIF
Although these moons are in circular orbits, their orbits appear oval because of the viewing angle. Twice per orbit they seemingly have a close encounter with Pluto. When you rotate the frame, this produces some interesting effects. In the Polydeuces image, notice how Dione traces a nice round circle. This means that Dione is in a circular orbit around Saturn. It traces two of these circles for every 1 orbit, but they are on top of each other, so you only see one circle. Objects such as Polydeuces, whose orbits are elliptical, have their virtual close encounters twice per orbit too, but they hapen at different distances from the planet, so they trace a double loop patterns.

Try this yourself:
File > New
Objects > Create Objects, sma=0.1, leave all other values at their defaults
Objects > Create Objects, sma=0.1, ecc=0.1, give it a different color, leave all other values at their defaults
You end up with:
http://orbitsimulator.com/gravity/images/loop1.GIF

Now rotate the frame with the period of either object:
View > Rotating Frame Adjustment, choose the 2nd or 3rd object in the list, and choose the "Rotating Frame" option. You end up with:
http://orbitsimulator.com/gravity/images/loop2.GIF

Turn off the rotating frame and use the scroll bar on the right to change the viewing angle:
http://orbitsimulator.com/gravity/images/loop3.GIF

Turn the rotating frame on again:
http://orbitsimulator.com/gravity/images/loop4.GIF

Title: Re: Polydeuces and Helene
Post by frankuitaalst on 09/10/15 at 06:01:51

(Time flows when I see the date of the Original post ) .
I discovered this animation I made once , which shows Polydeuces in green and Helene ( in red) from an observer at Saturn looking at Dione ( in the middle of the screen) . View angle of the screen is 160.
Both Helene and Polydeuces librate around their Lagrange point .
The period of libration seems to be about 2 years .
Animation starts at 2009/01/01.

Title: Re: Polydeuces
Post by frankuitaalst on 09/11/15 at 11:28:38

This animation can also be seen in the simulation Tony  provided here :

http://orbitsimulator.com/gravitySimulatorCloud/simulations/1434245783786_Polydeuces.html

Then select Menu "Display"
Select Menuitem "Frame A"
In the listboxes one enters :
in Listbox "Target Object A" : select Dione
in Listbox "Camera Object A" : select Saturn
in Box "Zoom " : reduce zoom to about 125.

Title: Re: Polydeuces
Post by Tony on 09/11/15 at 16:51:57

Wow, that makes the exact same animation as yours.  No rotating frame needed.

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