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Ceres and Gefion (Read 8663 times)
ScottM
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Ceres and Gefion
05/03/14 at 21:09:55
 
Just for the fun of it (and because I'm an astronomy nerd), I've been studying Ceres a bit as of late. In the course of my research, I found references to Ceres have quasi satellites, and about its interesting orbital relationship with the asteroid Gefion. Ceres was once thought be a member of the asteroid family that is now named after Gefion, and so, I decided to plug the ephemeris data from Horizons into the simulator and observe the relationship myself. Personally, I found the results to be very interesting.
 
I centered the simulation around Ceres and started it. In the beginning, Gefion was in a quasi-orbit around Ceres which had a very large radius. However, as time progressed, the quasi orbit spiraled in closer and closer to Ceres, until Gefion ceased to be a quasi-satellite. Finally, the orbit began to sprial out again, and the quasi-orbit around Ceres resumed.
 
I thought it was pretty interesting how the simulator demonstrated Gefion's moving in and out of the quasi-satellite with Ceres every few years.
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frankuitaalst
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Re: Ceres and Gefion
Reply #1 - 05/04/14 at 09:44:38
 
Hello Scott ,  
 
I just started a sim of Ceres-  Gefion , in rotating frame with Ceres centered .  
As I see both are "coorbitals " .  
At present Gefion approaches Ceres and will overtake it in ca. 70 years from now .  
They  wil seem to be in orbit for a while , but Gefion will continue its orbital .  
The will come close every 350 -400 years about .  
I wonder if you have the same result ?  
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frankuitaalst
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Re: Ceres and Gefion
Reply #2 - 05/04/14 at 10:12:08
 
Here's a screenshot of my simulation , after ca. 100 years from now .  
Gefion's orbit is shown as seen from an observer on the "sun" with Ceres centered in the middle .  
The angle of view is 60°.  
Gefion will seem to be in a large orbit around Ceres but will leave its host ....
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PicN65_KM_Grefion__01012009_dat_1013.jpg
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ScottM
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Re: Ceres and Gefion
Reply #3 - 05/04/14 at 11:07:53
 
Ceres was once thought to be a part of the asteroid family now named after Gefion, and there are quite a few asteroids that are co-orbital, both members of the family, like Gefion, and interlopers, like Ceres and Minerva.
 
I didn't run the simulation for long enough last night to make the observations that you did, but when I have more time to do it (maybe tonight), I'll see what I come up with. I want to expand my simulation to include others of the group of co-orbital asteroids and see what else I find. I'm really glad I stumbled across that reference to the orbital relationship. I think this is going to be fun!
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Re: Ceres and Gefion
Reply #4 - 05/04/14 at 11:14:11
 
yes , I see what you mean . Perhaps some members of the family will show up as beeing in some resonance to each other , this is a possibility .  
This means horseshoe type orbits for instance .... Maybe  
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Re: Ceres and Gefion
Reply #5 - 05/04/14 at 11:48:54
 
I'm not sure which asteroids they are, but from some of what I've read, both Ceres and Vesta currently have quasi-satellites. I'm hoping if I add more of the Gefion family or its interlopers to the simulation I can learn more about it. I'll be sure to share anything I find.
 
When I'm through with my research on Ceres, I plan to do Vesta next, so I'll eventually do a simulation for that, too.
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Re: Ceres and Gefion
Reply #6 - 05/04/14 at 12:11:31
 
For your infomation Scott : I'm running a short simulation with some of the members of the Gefion family : Minerva , Oppavia , Burgundia .  
All of them are "coorbitals " to Ceres , but none of them seem to come in an orbit or horse-shoe orbit . Maybe some smaller members will .
If you have some idea's please post ....
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Re: Ceres and Gefion
Reply #7 - 05/04/14 at 12:30:35
 
Aah : in  a paper P. Wiegert seems to have found some librating asteroids around Ceres and also Vesta :  
http://arxiv.org/abs/1110.4810
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Re: Ceres and Gefion
Reply #8 - 05/04/14 at 12:33:48
 
That's the paper I stumbled upon. I was looking for papers on arxiv dealing with Ceres, and I came across that one. I'm glad you found it. I couldn't remember exactly where I had come across it.
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Re: Ceres and 1372 Haremari and 8877 Rentaro
Reply #9 - 05/04/14 at 12:55:20
 
In the paper above two asteroids are mentionned to be in relation with Ceres :  
1372 Haremari and 8877 Rentaro,
A quick sim in rotating frame to Ceres gives a rather unexepected behaviour of both :  
both seem to be quite stable at around 180° from where Ceres resides in rotating frame.  
If correct ( to be confirmed by others )  , as far as I remember I have never seen this before .
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Re: Ceres and Gefion
Reply #10 - 05/04/14 at 13:04:43
 
Here's a picture in rotating frame of both mentionned asteroids .  
Both seem to reside quite stable in their location relative to Ceres for the next couple of hundred years , only showing some small libration aroud their depicted orbit .  
As I said , never have seen this .  
 
I'm curious to see how other candidates behave . As far as I read the paper only these two were mentionned . The other identified members can be retrieved on demand from the authors ....
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PicN65_KM_Gefion__01012009_dat_1002.jpg
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Re: Ceres and Gefion
Reply #11 - 05/04/14 at 13:24:49
 
I only had time to skim the paper after I found it yesterday. Now that you've reminded me where I found it, I'll read it more carefully when I get a chance. I did see the part about the full list being available on request. I think I'd rather play around with it myself, though, than make the request. I have a feeling that playing around with other Gefion family members could lead to some interesting discoveries.
 
Btw, Wikipedia has a list of quite a few members of the family, if you want to check that out.
 
http://en.wikipedia.org/wiki/Gefion_family
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Re: Ceres and Gefion
Reply #12 - 05/05/14 at 08:59:18
 
In the paper above some asteroids are mentionned , which are worth  some simulation:  
138245  
 
166529
 
71210
 
81522
 
65313 and 129109 persist as L5 Trojans of Ceres,
 
76146 is a Quasi-Satellite of Ceres until .....yr.
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Re: Ceres and Gefion
Reply #13 - 05/05/14 at 12:54:30
 
I'm running a sim with the following asteroids mentionned in the paper above  
 
"138245","yellow",
"166529","red"
"71210","white"
"81522 ","green"
"Haremari","red"
"Rentaro","green"
"65313","white"
" 129109 ","green"
" 76146 ","yellow"
 
Here's a screenshot of the sim , in rotating frame to Ceres ( the red line at ca. 10 'o clock) , in about hundred years from now.  
It seems Ceres has 3 quasi -moons at this time , one red and two yellow .  
If I've some time later this week a probably can make an animation out of these ....
 
Correction : in another view the lower yellow asteroid seems not to circle "around" Ceres but is in a tadpole orbit . It actually seems to be "under " Ceres , therfor not circuling "around" .
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PicN65_KM_Ceres_Coorb_01012009_dat_1020.jpg
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Re: Ceres and Gefion
Reply #14 - 05/05/14 at 17:29:13
 
I'm getting ready to try to play around with this more, but I apparently have a lot to learn about how to use the program.
 
How do I set one object at the center and the rotating frame to another object?
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Re: Ceres and Gefion
Reply #15 - 05/05/14 at 18:56:10
 
Make sure you have the latest version of this program: http://orbitsimulator.com/gravity/beta/GravitySimulatorAlpha2013July24_3.0.exe  
 
Here is a link where quasi-satellites are discussed: http://www.orbitsimulator.com/cgi-bin/yabb/YaBB.pl?num=1194407194/7#7
 
Here is a simulation of Ceres and the 3 asteroids you have been discussing: http://orbitsimulator.com/gravity/simulations/ceres_resonance.gsim
 
To center one object and rotate on another, choose the center object as the Focus Object in the Focus Object dialog box.
Under View, choose "Rotating Frame Adjustment".  Choose Ceres from the dropdown list.  If Ceres drifts a bit, use the "Calibrate" button to fix.  Click this button, click on Ceres' orbit.  Wait a while, and click on Ceres' orbit again.  This tells the program the rate of drift so it can compensate.  The reason for the drift is it initially calculates Ceres' Period using Keplerian formulas that don't account for perturbations from other planets such as Jupiter.
 
I'm surprised that Ceres can have quasi-satellites, assuming that quasi-satellites are defined as being locked in resonance and librating about the 1:1 resonance.  Ceres doesn't have much mass.  An NBA basketball player could jump onto the roof of the arena if it were on Ceres.
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Re: Ceres and Gefion
Reply #16 - 05/06/14 at 14:29:13
 
Did we inspire the creation of a new simulation?
 
From the reading I've done, Ceres, Vesta, and Pluto all have quasi-satellites, but in each of their cases, the orbital relationships are just coincidental, because of the low mass and gravity that they each have. Personally, I think that makes it more interesting. There's no reason it should be there, but yet, there it is.
 
Thanks for the help on the rotating frame. I'll try that out when I get a chance this evening.
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Re: Ceres and Gefion
Reply #17 - 05/06/14 at 19:16:46
 
Yes, you inspired a new sim!  They're easy to make.  With a little practice, you'll get good at making them.  In the meantime, if there are any other asteroids (perhaps you'll email Wiegert et. al.), let me know and I'll make the sim for you, or teach you how to make them with their data.  In the past, Wiegert has been very approachable and happy to answer emails.
 
A true quasi-satellite uses the planet's (in this case Ceres) gravity to stay locked in quasi-orbit for at least a few quasi orbits.  This requires either a strong gravity or a VERY slow longitudinal approach.  Ceres doesn't have strong gravity.  Gefion has a very speedy longitudinal approach (apparent speed in the rotating frame).  From everything I've seen, there's not a chance Ceres can capture Gefion.  Haremari and Rentaro are amazingly still in the rotating frame, as Frank pointed out.  That means they have almost the same semi-major axis, and hence orbital period as Ceres.  But they will slowly drift. After centuries of approaching Ceres, Ceres might be able to influence their orbits.  In the rotating frame, it can repel them.  That would be a horseshoe or tadpole orbit.  In a tadpole orbit, the object will also be seemingly repelled by Ceres' L3, while in a horseshoe orbit it will pass the L3 and centuries later approach Ceres from the other side.  Ceres can also capture them into quasi-orbits.  Or they can simply drift past Ceres after making a series of what seem like quasi-orbits.  Only a simulation will tell.
 
Any object can have an "accidental" quasi satellite, even a massless object.  It simply requires two objects very close to each other with the exact same semi-major axis and slightly different eccentricities.  Imagine an astronaut untethered outside the ISS who fires a short blast of his thruster towards Earth.  This does not change his semi-major axis.  So he will still orbit the Earth with the exact same period as the space station.  But the thrust introduced some eccentricity.  He will drop closer to Earth, where he will speed up in orbit, allowing the ISS to get above and ahead of him in orbit.  After he reaches perihelion, he'll climb again, this time slowing down in his orbit, allowing him to catch up to and surpass the ISS as he passes over it.  To the astronaut, he is seemingly orbiting the ISS, yet it has nothing to do with the ISS's gravity.
 
A feature in the program that is useful for these types of sims is the "Auto Save" feature in the File menu.  Set it to automatically save a copy of the sim every 100 years or so.  That way when you wake in the morning to find that the asteroid in question has migrated past Ceres, you can "rewind" by opening the sim closest to the event.
 
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frankuitaalst
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Re: Ceres and Gefion
Reply #18 - 05/07/14 at 09:04:46
 
Here is an animation of the above mentionned asteroids in rotating frame to Ceres , for the next 500 years .  
Each frame covers 4.6 years which is the orbital period of Ceres .  
It is remarkable how stable most orbits are , except for the apparental "breathing " which is probably due to disturbances from the nearby mighty Jupiter .  
 
"138245","yellow",  
 "166529","red"  
 "71210","white"  
 "81522 ","white"  
 "Haremari","red"  
 "Rentaro","green"  
 "65313","white"  
 " 129109 ","green"  
 " 76146 ","green"
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Ceres_coorbitals.gif
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frankuitaalst
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Re: Ceres and Vesta
Reply #19 - 05/07/14 at 12:56:11
 
I took a look at the paper which was mentionned above ( Apostolos A. Christou, P. Wiegert  ) . In this paper some asteroids are said to be in coorbital motion with Vesta :
"22668","98231""156810","121118 ","134633"
 
Maybe they are also  worth to run a simulation on them ?
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Re: Ceres and Gefion
Reply #20 - 05/07/14 at 17:41:14
 
The yellow one looks like it might actually be librating in a 1:1 with Ceres.  The others seem to 'breathe' with the same period as each other, whether they're near Ceres or not, suggesting the Jupiter influence.
 
This suggests two more sims and animations:  
1. Set Ceres mass to 0 and see if anything changes.
2. Set Jupiter's mass to 0 and see what changes.
 
Here's 2 more sims with all the asteroids you mentioned in your last 2 posts, so you or Scott can play around with them:
 
http://orbitsimulator.com/gravity/simulations/ceres_and_vesta_resonances.gsim  
http://orbitsimulator.com/gravity/simulations/vesta_resonances.gsim
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Ceres and Gefion- coorbitals of Ceres
Reply #21 - 05/08/14 at 09:33:49
 
Here's an animation for 500 years of some of the asteroids , as an observer on the sun , looking at Ceres,  would observe the coorbitals.  
Each frame covers 1 Ceres year .  
It is clear that the yellow asteroid does not "orbit" Ceres as is stays "under" the dwarf planet .
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CeresCoorb2FromSun.gif
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Re: Ceres and Gefion- coorbitals of Ceres
Reply #22 - 05/08/14 at 09:39:53
 

 
Thanks Tony , I'll give it a try to set Jupiter at minimum mass .  
Almost sure that the asteroids will stop "breathing" .  
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« Last Edit: 05/09/14 at 08:02:42 by frankuitaalst »  
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Re: Ceres and Gefion
Reply #23 - 05/08/14 at 10:02:57
 
Setting Jupiter Mass to almost zero gives the following result :  
 
1. Breathing stops .  
2. Ceres looses quickly some coorbitals
3. But may gain some others  
 
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CoorbitalsCeresFromSunJup0Mass500y.gif
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Re: Ceres and Gefion
Reply #24 - 05/09/14 at 01:52:42
 
Quote from frankuitaalst on 05/07/14 at 09:04:46:
Here is an animation of the above mentioned asteroids in rotating frame to Ceres , for the next 500 years .
Each frame covers 4.6 years which is the orbital period of Ceres .
(...)

 
Frankuitaalst, how do create these animations ? Is there an automated way to output such pictures, or you have done it by hand ?
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Re: Ceres and Gefion
Reply #25 - 05/09/14 at 08:06:36
 
GravSim lets you output the screen under "File / Screenshots " .
You then get a series of .bmp files , which can be converted by a gif animator program to an animated gif .  
This is done with free downloadable gif animator program .
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Re: Ceres and Gefion
Reply #26 - 05/09/14 at 08:45:20
 
The simulation hereunder extends the previous simulations.  
I could extend the number of coorbitals to 11 ( various sources ) .  
Further , the sim herunder covers 6000 years from now.  
It is amazing how different the orbits of each coorbital behave .
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CeresCoorbiatls6000y11AstRotFrameCeres.gif
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Ceres coorbitals
Reply #27 - 05/09/14 at 09:04:24
 
Is there something special to be a Ceres coorbital ?  
 
I wouldn't think so , see the animation hereunder which spans 6000 years .  
The orbits of each coorbital show at first sight no real correlation, except for the SMA which is close to Ceres" SMA.  
 
Ceres is represented in blue . The coorbitals are represented in different colors .  
Remarkable is the strong precession of the orbits ( due to the overall precession of of solar system , for whick Jupiter and Saturn are responsable ..among others )
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