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General >> Discussion >> Inner and Outer Reaches
http://www.orbitsimulator.com/cgi-bin/yabb/YaBB.pl?num=1226290391

Message started by Mal on 11/09/08 at 20:13:10

Title: Inner and Outer Reaches
Post by Mal on 11/09/08 at 20:13:10

Note: This thread references this paper by Jones, Underwood and Sleep (http://www.journals.uchicago.edu/doi/abs/10.1086/428108) (referred to as JUS) that defines inner and outer "reaches" for jovians. This defines the band around a jovian within which a rocky planet will be ejected from the system within 1000 My, due to the jovian's gravitational influence. I'm also assuming that if a potential planet is located between a jovian's 4:1 and 3:2 distances then its formation is disrupted by the jovian's gravity and it forms an asteroid belt instead.


I noticed something interesting about Jupiter - its 3:2 distance is at 3.97 AU, but its Inner Reach distance (determined using the formula in JUS) is 3.88 AU - these regions therefore overlap, which may explain this graph from the New System (http://www.orbitsimulator.com/cgi-bin/yabb/YaBB.pl?num=1223246512/30#30) thread - there's just no orbit beyond the 3:2 where asteroid orbits can be stable:

http://www.orbitsimulator.com/yabbfiles/Attachments/solsysbelt1.gif


Now, here's one of the systems I generated (the one from the New System thread):


Code:
  Num Star      Age    ZMass   Mass        ZLum           Lum         Rad   Met Pha
 2840 G2 V     4.736   0.992   0.992     0.7072248     1.0207404     0.997   2   1
 
ZAMS Inner Zone =    0.704   Current Inner Zone =    0.833
ZAMS Hab Zone   =    1.407   Current Hab Zone   =    1.668
ZAMS Earth Equiv=    0.841   Current Earth Equiv=    1.010
ZAMS Outer Zone =    2.132   Current Outer Zone =    2.562

Num    AU        ecc       type      mass     den       rad        peri       aph      hill     inner     outer      4:1       2:1      migrate
1     0.300     0.044     4.000     0.000  5000.000  3200.000     0.287     0.313     0.001     0.282     0.319     0.119     0.189     0.671
2     0.570     0.094     4.000     0.000  3500.000  2400.000     0.516     0.624     0.002     0.511     0.633     0.226     0.359     0.671
3     0.969     0.000     5.000      Planetoid Belt
4     2.291     0.030     2.000     0.379  1246.700 51658.500     2.223     2.358     0.113     1.882     2.812     0.909     1.443     0.671
5     4.123     0.063     2.000     0.350   993.500 54227.500     3.863     4.383     0.199     3.266     5.377     1.636     2.597     0.671
6     7.834     0.036     3.000     2.123  2340.200 74357.000     7.554     8.113     0.689     5.487    10.870     3.109     4.935     0.671
7    16.451     0.044     1.000     0.236  1700.280 39746.000    15.726    17.175     0.696    13.640    19.957     6.528    10.363     0.671
8    24.676     0.025     1.000     0.196  1706.880 37318.000    24.048    25.304     0.981    21.105    29.227     9.792    15.545     0.671


The planet in orbit 4 (2.291 AU) is a Jupiter-class gas giant, between Jupiter and Saturn in size. The rocky planet that was in Orbit 3 (0.969 AU) is an asteroid belt because its semimajor axis is between the 4:1 and 2:1 orbits of the jovian in orbit 4. However, this jovian's Inner Reach extends to 1.882 AU, but it's 3:2 orbit (not shown on the table) is at 1.75 AU - thus there's a gap between the Inner Reach and the 3:2 resonance.

One thing to point out is that the values used to determined the JUS Reaches are determined experimentally - basically they ran a souped up version of Gravity Simulator and found out where a planet with a mass equal to the Earth+Moon survived for 1000 My and where it was ejected before that time. The resonance values are however determined theoretically by calculating them from the jovian's orbital period. It's possible that the JUS values should actually correspond roughly to resonances... or maybe they're unrelated.

So the question is... are the orbits in this gap actually stable? To try to test this, I set up a reduced version of the 2840 system in gravsim, with just the sun and the jovian at 2.291 AU. I then put 20 asteroids between 1.62 and 1.74 AU (red, within the 3:2), 20 asteroids between 1.75 and 1.88 AU (yellow, between the 3:2 and the Inner Reach), 20 asteroids between 1.89 and 2.01 AU (green, beyond the Inner Reach distance). I hoped that the yellow ones would be most stable since they're beyond 3:2 and also beyond the Inner Reach...

I've uploaded the gsim file if you want to play around with it yourselves.

Title: Re: Inner and Outer Reaches
Post by Mal on 11/09/08 at 20:37:00

Well I can't show the animation, because it's too big... but I can show a still of the end result of SMA vs Ecc, and it's a bit surprising. It looks as if actually the asteroids between the two zones aren't actually much more stable than the ones within the resonance zone, but they definitely are more stable than the ones within the Reach zone (which are flung into wildly different orbits pretty quickly in the simulation - that's the line sloping toward the star from the 2 AU region).

So for this system at least I'd say that any planets that want to form between the 3:2 and the Inner Reach are probably going to still be disrupted by the jovian and become belts instead, but they probably won't be ejected completely from the system. The squat slab-like peak beneath that is the 3:2 resonance (skewed to the left here, for reasons unclear to me).

Title: Re: Inner and Outer Reaches
Post by frankuitaalst on 11/11/08 at 13:46:19

Hi Mal , what's the steep disruption around 1.7 AU ?

Title: Re: Inner and Outer Reaches
Post by Mal on 11/11/08 at 14:47:23

I'm not sure. I think it's to do with the angle that the 3:2 peak is skewed at, but maybe it's something different. It doesn't seem to correspond to a resonance itself though - here are all the resonances for the jovian that I can think of:


Code:
res      AU
8:1     0.57
7:1     0.63
6:1     0.69
5:1     0.78
4:1     0.91
7:2     0.99
3:1     1.10
8:3     1.19
5:2     1.24
7:3     1.30
2:1     1.44
7:4     1.58
5:3     1.63
8:5     1.67
3:2     1.75
7:5     1.83
4:3     1.89
5:4     1.97
6:5     2.03
7:6     2.07
8:7     2.10
1:1     2.29 <<<<<< Jovian
7:8     2.50
6:7     2.54
5:6     2.59
4:5     2.66
3:4     2.78
5:7     2.87
2:3     3.00
5:8     3.13
3:5     3.22
1:2     3.64
3:7     4.03
2:5     4.22
3:8     4.41
1:3     4.77
2:7     5.28
1:4     5.77
1:5     6.70
1:6     7.56
1:7     8.38
1:8     9.16

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