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Cancri 55 now has 5 known planets (Read 9516 times)
Tony
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Cancri 55 now has 5 known planets
11/06/07 at 19:46:34
 
Here's a link to the paper describing the find:  http://www.oklo.org/wp-content/images/debra.pdf
 
Here's a new Gravity Simulator file of the lastest version of the 55 Cancri system.
http://orbitsimulator.com/gravity/simulations/Cancri55.gsim
 
Here's a screenshot of the system

 
Planet b, perhaps nearly as massive as Jupiter, is the most massive planet in the inner Cancri 55 system.  Holding it still in a rotating frame exposes what appear to be resonances with planets c and e.  However, as the simulation is run for a longer period of time, it becomes obvious that there is no libration.  Hence, c and e are not in a mean motion resonance with b.
 


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EDG
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Re: Cancri 55 now has 5 known planets
Reply #1 - 11/06/07 at 21:55:20
 
The discoverers mentioned the possibility of rocky planets in that gap between planets d and f.  
 
The big jovian (planet d) looks like it'll keep a good part of that gap cleared of rockies. If, like in our system, the extreme inner edge of any asteroid belt is defined by the 5:1 resonance with "Jupiter", that lands at 1.97 AU. The "main belt" between the 4:1 and 2:1 resonances would be between 2.29 and 3.63 AU. The "reach" of planet d (as defined by Underwood/Sleep/Jones, 2005) is between 3.11 and 7.80 AU - within this range, any bodies would get tossed out or destroyed (which would curtail our asteroid belt).  
 
I can get a 0.144 jupiter mass planet assuming a radius of 40,000 km and density of 1020 kg/m3 - I'll assume that's the new "planet f". Its "reach" turns out to be between 0.51 and 1.02 AU, and it's belt (as defined by 4:1 and 2:1 resonances ) would be between 0.31 and 0.49 AU .
 
All of which fits the system observed, which is promising. So I'm going to predict that (if/when we get the technology to observe them) we might find one rocky planet between 1 and 2 AU, and probably an asteroid belt between 2.3 and 3.1 AU. Smiley
 
(I used Table 2 from the paper to figure this out)
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Re: Cancri 55 now has 5 known planets
Reply #2 - 11/07/07 at 12:45:28
 
I think the system shows a resonance between the c and b planets .  
In annex a screenshot in rotating frame to c .
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Cancri55_cb_Reson.jpg
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Tony
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Re: Cancri 55 now has 5 known planets
Reply #3 - 11/07/07 at 17:31:31
 
Quote from frankuitaalst on 11/07/07 at 12:45:28:
I think the system shows a resonance between the c and b planets .
In annex a screenshot in rotating frame to c .

 
What appears as a resonance is really just because you are in floating mode, which centers the image on the system barycenter rather than on the star.  Since the orbits of these planets are quite round, the rotating frame would have a hard time exposing any resonance that might exist.  But graphing the data can expose the resonances.  In this case Planets B and C do not seem like they are locked into any resonance.  They're close to 3:1, so you would expect the ratios of their periods to oscillate around 3, rather than simply near it.  But that is not the case, so there is no resonance.  Here's the graph:
 

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Tony
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Re: Cancri 55 now has 5 known planets
Reply #4 - 11/07/07 at 17:49:06
 
Re: Mal's post
 
I get similar results of 3.76 to 7.73 using the formulas from Jones et. al (2006).  I made some javascript calculators for these formulas available here:  http://orbitsimulator.com/formulas
 
But keep in mind that the masses of the planets are not known.  They're dependent of the inclination of the system (hence Msin(i)*Jupiter rather than just Mjupiter), so that would put some ranges on the possibilities.
 
Have you tried yet to simulate your proposed planet and corresponding asteroid belt?
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Re: Cancri 55 now has 5 known planets
Reply #5 - 11/07/07 at 23:21:56
 
Quote from Tony on 11/07/07 at 17:49:06:
Have you tried yet to simulate your proposed planet and corresponding asteroid belt?

 
Nope, I just did a quick mathematical sketch of the system Smiley. I don't really have time right now to do any proper gravsim simulations (too busy with other stuff right now!)
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frankuitaalst
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Re: Cancri 55 now has 5 known planets
Reply #6 - 11/08/07 at 12:32:47
 
embarrassed I wasn't aware that floating mode was standard on . Changing to absolute mode gives indeed another picture as the eccentricity of b is small , and the planet orbits in a circle.  
But .... if we take the rotating frame to b (instead as to c) and observe the c orbit the c makes a nice figure . Picture in annex . Simulation was run for 1 year .  
Can we say that b and c are almost in or in "near" resonance ?
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Cancri_bc_reson.jpg
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Tony
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Re: Cancri 55 now has 5 known planets
Reply #7 - 11/08/07 at 13:07:57
 
Quote from frankuitaalst on 11/08/07 at 12:32:47:
embarrassed I wasn't aware that floating mode was standard on . Changing to absolute mode gives indeed another picture as the eccentricity of b is small , and the planet orbits in a circle.
But .... if we take the rotating frame to b (instead as to c) and observe the c orbit the c makes a nice figure . Picture in annex . Simulation was run for 1 year .  
Can we say that b and c are almost in or in "near" resonance ?

There really is no "standard".  Which ever mode is used when I save the simulation is the mode the simulation opens with.  I choose Floating for this simulation only because the star is noticably seperated from the system barycenter.
 
Although it appears at first glance that resonance exists, you must check for libration.
 
Here's 2 animations illustrating libration.  Notice in the top one, Mercury traces a resonant pattern when Earth is held still, but this resonant pattern continuously drifts in one direction.  Hence, there is no libration.  Nothing is locking this resonance in place, so it's nothing more than a near-resonance. The green object around Earth is an asteroid in a quasi-orbit 1:1 resonance with Earth.  It is librating.  It only drifts so far before it is sheparded back, ensuring that over long periods of time it averages to exactly 1:1 (actually, quasis are only temporarily stable but this animation still serves to illustrate the difference between librating and non-librating.)
 
In the bottom animation you can see the asteroid Toutatis in a librating resonance with Jupiter.  It only drifts so far before being sheparded back, ensuring that it stays locked in its 3:1 resonance.

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