APOD: The Kepler-90 Planetary System (2020 Apr 28)

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neufer
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Re: APOD: The Kepler-90 Planetary System (2020 Apr 28)

Post by neufer » Wed Apr 29, 2020 4:17 pm

isoparix wrote:
Wed Apr 29, 2020 9:34 am

I still want to know how you pack eight Jupiters stably, in between Earth and Mercury....
First: there are only 2 Saturn/Jupiters (on the outside).

And it probably helps that none of the planets lies in the
dreaded 3:1 or 2:1 resonant "Kirkwood Gaps" of any other (larger) outer planet:

Code: Select all

                       The Kepler-90 planetary system
                       
         (AU) 	        Orbital period (days) 	  Radius
...............................................................................
b 	0.074 ± 0.016  	     7.008151 day 	 1.31 R⊕
...............................................................................
                       2:1   7.22 day i resonant "Kirkwood Gap"
...............................................................................
c 	0.089 ± 0.012 	     8.719375 day 	 1.18 R⊕
i 	0.107 ± 0.03 	    14.44912 day 	 1.32 R⊕
...............................................................................
                       3:1  19.91 day d resonant "Kirkwood Gap"
                       2:1  29.87 day d resonant "Kirkwood Gap"
                       3:1  30.65 day e resonant "Kirkwood Gap"
                       3:1  41.64 day f resonant "Kirkwood Gap"
                       2:1  45.57 day e resonant "Kirkwood Gap"
...............................................................................
d 	0.32 ± 0.05 	    59.73667 day 	 2.88 R⊕
...............................................................................
                       2:1  62.46 day f resonant "Kirkwood Gap"
                       3:1  70.20 day g resonant "Kirkwood Gap"
...............................................................................
e 	0.42 ± 0.06 	    91.93913 day 	 2.67 R⊕
...............................................................................
                       2:1 105.30 day g resonant "Kirkwood Gap"
                       3:1 110.53 day h resonant "Kirkwood Gap"
...............................................................................
f 	0.48 ± 0.09 	   124.9144 day	         2.89 R⊕
...............................................................................
                       2:1 165.80 day h resonant "Kirkwood Gap"
...............................................................................
g 	0.71 ± 0.08 	   210.6070 day 	 8.13 R⊕
h 	1.01 ± 0.11 	   331.6006 day 	11.32 R⊕ 
But primarily the relative stability of the system has been tested:
https://arxiv.org/abs/1310.5912 wrote:
A Hill stability test and an orbital integration of the system shows that the system is stable.
Art Neuendorffer

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Ann
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Re: APOD: The Kepler-90 Planetary System (2020 Apr 28)

Post by Ann » Wed Apr 29, 2020 4:59 pm

neufer wrote:
Wed Apr 29, 2020 4:17 pm
isoparix wrote:
Wed Apr 29, 2020 9:34 am

I still want to know how you pack eight Jupiters stably, in between Earth and Mercury....
First: there are only 2 Saturn/Jupiters (on the outside).

And it probably helps that none of the planets lies in the
dreaded 3:1 resonant "Kirkwood Gap" of any other (larger) outer planet:

Code: Select all

                       The Kepler-90 planetary system
                       
         (AU) 	        Orbital period (days) 	  Radius
...............................................................................
b 	0.074 ± 0.016  	     7.008151 day 	 1.31 R⊕
c 	0.089 ± 0.012 	     8.719375 day 	 1.18 R⊕
i 	0.107 ± 0.03 	    14.44912 day 	 1.32 R⊕
...............................................................................
                       3:1  19.91 day d resonant "Kirkwood Gap"
                       3:1  30.65 day e resonant "Kirkwood Gap"
                       3:1  41.64 day f resonant "Kirkwood Gap"
...............................................................................
d 	0.32 ± 0.05 	    59.73667 day 	 2.88 R⊕
...............................................................................
                       3:1  70.20 day g resonant "Kirkwood Gap"
...............................................................................
e 	0.42 ± 0.06 	    91.93913 day 	 2.67 R⊕
...............................................................................
                       3:1 110.53 day h resonant "Kirkwood Gap"
...............................................................................
f 	0.48 ± 0.09 	   124.9144 day	         2.89 R⊕
...............................................................................
g 	0.71 ± 0.08 	   210.6070 day 	 8.13 R⊕
h 	1.01 ± 0.11 	   331.6006 day 	11.32 R⊕ 
But primarily the relative stability of the system has been tested:
https://arxiv.org/abs/1310.5912 wrote:
A Hill stability test and an orbital integration of the system shows that the system is stable.
So what would happen and why would it happen if any of the planets lay in the dreaded resonant Kirkwood gap? Bear with us who can't draw the obvious conclusions from an equation or a list, the way smart people can!

Ann
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Re: APOD: The Kepler-90 Planetary System (2020 Apr 28)

Post by Chris Peterson » Wed Apr 29, 2020 5:16 pm

Ann wrote:
Wed Apr 29, 2020 4:59 pm
So what would happen and why would it happen if any of the planets lay in the dreaded resonant Kirkwood gap?
Resonances in orbital systems can result in major shifts in planetary orbits.

Although the reference says the system is "stable", this isn't technically true. No naturally occurring system with more than two bodies is truly stable. All are metastable, all are chaotic. What the model demonstrates is that the system has a high degree of stability, like our own (although the Kepler-90 system is less than half the age of the Solar System).

Something like a passing star could disrupt the system (as it could our own). Another possibility is a weakly bound gas giant much farther out, which could be perturbed into the inner system by an encounter with another star passing less than a light year or so distant.
Chris

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Re: APOD: The Kepler-90 Planetary System (2020 Apr 28)

Post by neufer » Wed Apr 29, 2020 9:55 pm

Ann wrote:
Wed Apr 29, 2020 4:59 pm

So what would happen and why would it happen if any of the planets lay in the dreaded resonant Kirkwood gap?
Orbiting JUST INSIDE a 2:1 "Kirkwood Gap" resonance can prove useful in some cases:

Code: Select all

                      The Galilean moon system
...............................................................................              
Orbital radius (Gm)      Orbital period (days) 	 Mass (10 Yg)
...............................................................................
                       3:1  1.184 day Europa resonant "Kirkwood Gap"
...............................................................................
Io 	        0.4218      1.769 day 	 89.3
...............................................................................
                       2:1  1.776 day Europa resonant "Kirkwood Gap"
                       3:1  2.385 day Ganymede resonant "Kirkwood Gap"
...............................................................................
Europa  	0.6711 	    3.551 day 	 48.0
...............................................................................
                       2:1  3.577 day Ganymede resonant "Kirkwood Gap"
                       3:1  5.563 day Callisto resonant "Kirkwood Gap"
...............................................................................
Ganymede 	1.070 	    7.155 day 	 148. 
...............................................................................
                       2:1  8.345 day Callisto resonant "Kirkwood Gap"
...............................................................................
Callisto 	1.883 	    16.69 day 	 108. 
Art Neuendorffer

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Re: APOD: The Kepler-90 Planetary System (2020 Apr 28)

Post by Ann » Thu Apr 30, 2020 5:36 am

neufer wrote:
Wed Apr 29, 2020 9:55 pm
Ann wrote:
Wed Apr 29, 2020 4:59 pm

So what would happen and why would it happen if any of the planets lay in the dreaded resonant Kirkwood gap?
Orbiting JUST INSIDE a 2:1 "Kirkwood Gap" resonance can prove useful in some cases:
Art, I thank you for your nice little animation showing the orbits of Io, Europa and Ganymede.

Tell me, though. You said that a 2:1 Kirkwood resonance could be useful. (Or rather, you said that an orbit just inside a 2:1 Kirkwood resonance could be useful.) Useful in what way? Is it useful because the Galilean moons stay in their orbits thanks to their Kirkwood resonances? Or is it useful because Europa is subjected to the kind of tidal forces that might cause it to have an underground ocean?

Ann
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Re: APOD: The Kepler-90 Planetary System (2020 Apr 28)

Post by neufer » Thu Apr 30, 2020 3:01 pm

Ann wrote:
Thu Apr 30, 2020 5:36 am

You said that a 2:1 Kirkwood resonance could be useful. (Or rather, you said that an orbit just inside a 2:1 Kirkwood resonance could be useful.) Useful in what way? Is it useful because the Galilean moons stay in their orbits thanks to their Kirkwood resonances? Or is it useful because Europa is subjected to the kind of tidal forces that might cause it to have an underground ocean?
My own hypothesis is that just as moon induced Earth tides have caused the Moon to "social distance" from Earth over time

Galilean moon induced Jupiter tides have caused the Galilean moons to "social distance" from Jupiter over time
  • ...starting with the closest Galilean moons.
Ergo:
  • 1) Io moved out until it started to approach the dreaded Europa 2:1 resonant "Kirkwood Gap" and
    1) Europa moved out until it started to approach the dreaded Ganymede 2:1 resonant "Kirkwood Gap"
    And Ganymede is currently in the process of moving out until
    it starts to approach the dreaded Callisto 2:1 resonant "Kirkwood Gap."
Anyway, that's my take on it.

Code: Select all

                      The Galilean moon system
...............................................................................              
Orbital radius (Gm)      Orbital period (days) 	 Mass (10 Yg)
...............................................................................
                       3:1  1.184 day Europa resonant "Kirkwood Gap"
...............................................................................
Io 	        0.4218      1.769 day 	 89.3
...............................................................................
                       2:1  1.776 day Europa resonant "Kirkwood Gap"
                       3:1  2.385 day Ganymede resonant "Kirkwood Gap"
...............................................................................
Europa  	0.6711 	    3.551 day 	 48.0
...............................................................................
                       2:1  3.577 day Ganymede resonant "Kirkwood Gap"
                       3:1  5.563 day Callisto resonant "Kirkwood Gap"
...............................................................................
Ganymede 	1.070 	    7.155 day 	 148. 
...............................................................................
                       2:1  8.345 day Callisto resonant "Kirkwood Gap"
...............................................................................
Callisto 	1.883 	    16.69 day 	 108. 
Art Neuendorffer

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Re: APOD: The Kepler-90 Planetary System (2020 Apr 28)

Post by Ann » Thu Apr 30, 2020 5:43 pm

neufer wrote:
Thu Apr 30, 2020 3:01 pm
Ann wrote:
Thu Apr 30, 2020 5:36 am

You said that a 2:1 Kirkwood resonance could be useful. (Or rather, you said that an orbit just inside a 2:1 Kirkwood resonance could be useful.) Useful in what way? Is it useful because the Galilean moons stay in their orbits thanks to their Kirkwood resonances? Or is it useful because Europa is subjected to the kind of tidal forces that might cause it to have an underground ocean?
My own hypothesis is that just as moon induced Earth tides have caused the Moon to "social distance" from Earth over time

Galilean moon induced Jupiter tides have caused the Galilean moons to "social distance" from Jupiter over time
  • ...starting with the closest Galilean moons.
Ergo:
  • 1) Io moved out until it started to approach the dreaded Europa 2:1 resonant "Kirkwood Gap" and
    1) Europa moved out until it started to approach the dreaded Ganymede 2:1 resonant "Kirkwood Gap"
    And Ganymede is currently in the process of moving out until
    it starts to approach the dreaded Callisto 2:1 resonant "Kirkwood Gap."
Anyway, that's my take on it.

Code: Select all

                      The Galilean moon system
...............................................................................              
Orbital radius (Gm)      Orbital period (days) 	 Mass (10 Yg)
...............................................................................
                       3:1  1.184 day Europa resonant "Kirkwood Gap"
...............................................................................
Io 	        0.4218      1.769 day 	 89.3
...............................................................................
                       2:1  1.776 day Europa resonant "Kirkwood Gap"
                       3:1  2.385 day Ganymede resonant "Kirkwood Gap"
...............................................................................
Europa  	0.6711 	    3.551 day 	 48.0
...............................................................................
                       2:1  3.577 day Ganymede resonant "Kirkwood Gap"
                       3:1  5.563 day Callisto resonant "Kirkwood Gap"
...............................................................................
Ganymede 	1.070 	    7.155 day 	 148. 
...............................................................................
                       2:1  8.345 day Callisto resonant "Kirkwood Gap"
...............................................................................
Callisto 	1.883 	    16.69 day 	 108. 
Thanks for your thoughts on this, Art. Interesting.

Ann
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Re: APOD: The Kepler-90 Planetary System (2020 Apr 28)

Post by neufer » Tue Jun 09, 2020 10:03 pm

neufer wrote:
Thu Apr 30, 2020 3:01 pm
Ann wrote:
Thu Apr 30, 2020 5:36 am

You said that a 2:1 Kirkwood resonance could be useful. (Or rather, you said that an orbit just inside a 2:1 Kirkwood resonance could be useful.) Useful in what way? Is it useful because the Galilean moons stay in their orbits thanks to their Kirkwood resonances? Or is it useful because Europa is subjected to the kind of tidal forces that might cause it to have an underground ocean?
My own hypothesis is that just as moon induced Earth tides have caused the Moon to "social distance" from Earth over time

Galilean moon induced Jupiter tides have caused the Galilean moons to "social distance" from Jupiter over time
  • ...starting with the closest Galilean moons.
Ergo:
  • 1) Io moved out until it started to approach the dreaded Europa 2:1 resonant "Kirkwood Gap" and
    1) Europa moved out until it started to approach the dreaded Ganymede 2:1 resonant "Kirkwood Gap"
    And Ganymede is currently in the process of moving out until
    it starts to approach the dreaded Callisto 2:1 resonant "Kirkwood Gap."
Anyway, that's my take on it.

Code: Select all

                      The Galilean moon system
...............................................................................              
Orbital radius (Gm)      Orbital period (days) 	 Mass (10 Yg)
...............................................................................
                       3:1  1.184 day Europa resonant "Kirkwood Gap"
...............................................................................
Io 	        0.4218      1.769 day 	 89.3
...............................................................................
                       2:1  1.776 day Europa resonant "Kirkwood Gap"
                       3:1  2.385 day Ganymede resonant "Kirkwood Gap"
...............................................................................
Europa  	0.6711 	    3.551 day 	 48.0
...............................................................................
                       2:1  3.577 day Ganymede resonant "Kirkwood Gap"
                       3:1  5.563 day Callisto resonant "Kirkwood Gap"
...............................................................................
Ganymede 	1.070 	    7.155 day 	 148. 
...............................................................................
                       2:1  8.345 day Callisto resonant "Kirkwood Gap"
...............................................................................
Callisto 	1.883 	    16.69 day 	 108. 
https://www.syfy.com/syfywire/titan-has-had-enough-of-saturn-leaving-the-planet-100x-faster-than-expected wrote:
Titan has had *enough* of Saturn, leaving the planet 100X faster than expected
Contributed by Phil Plait@BadAstronomer
SyfyWire, Jun 9, 2020

<<Personally, if I were orbiting Saturn, I'd want to stick around as long as possible. But Titan, however, is not me, and is hightailing it away from the planet — receding from Saturn 100 times faster than expected. Not that it's exactly zipping away; it's moving at 11 centimeters per year from Saturn.

The reason it's moving away at all is due to tides. Titan is a gigantic moon, the second largest in the solar system and almost as big as Mercury (if Saturn weren't there, we'd be tempted to call it a planet in its own right). It raises a pretty decent tidal bulge in Saturn… but in some cases this whole process depends very strongly on the distance of the moon and the planet (double the distance and things slow by a factor of nearly 50). At Titan's distance of 1.2 Gm, it was thought that it would barely recede at all, only 0.1 cm per year.

For Titan they used data from the Cassini mission, which orbited the ringed planet for 13 years and passed very close to Titan well over a hundred times. Using radio data from the spacecraft, they could measure its exact position to very high accuracy, and from that determine just where Titan was.

They also used good old-fashioned astrometry; that is, Earth-based telescopic observations of the satellites (dating back to 1886!) as well as Cassini observations to measure their positions over time as well. Using these measurements for the moons, and combining the radio data for Titan, they were able to measure how strongly Saturn affects the moons through tides, and found that the distance is not nearly as strong a factor as thought in this case.

The very cool thing about this is that the two methods both independently agree with a hypothesis proposed in that earlier paper a few years ago. There, the scientists proposed that tidal forces from the moons act differently than thought for Saturn. In most cases, the tides create friction inside of a planet, which generates heat, and this gets dissipated throughout the planet, lessening the effect. But the new idea is that Titan creates a resonance inside Saturn, pumping energy into it more efficiently. In this case, the orbital motion of Titan synchs up with motions inside Saturn, increasing the efficiency of the tidal process.>>
Art Neuendorffer

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Re: APOD: The Kepler-90 Planetary System (2020 Apr 28)

Post by BDanielMayfield » Tue Jun 09, 2020 11:04 pm

isoparix wrote:
Tue Apr 28, 2020 9:46 am
I'm surprised you can pack eight large planets stably within an eath orbit. If eight is possible, what's the maximum?!!!
neufer wrote:
Wed Apr 29, 2020 4:17 pm
isoparix wrote:
Wed Apr 29, 2020 9:34 am

I still want to know how you pack eight Jupiters stably, in between Earth and Mercury....
First: there are only 2 Saturn/Jupiters (on the outside).

And it probably helps that none of the planets lies in the
dreaded 3:1 or 2:1 resonant "Kirkwood Gaps" of any other (larger) outer planet:

Code: Select all

                       The Kepler-90 planetary system
                       
         (AU) 	        Orbital period (days) 	  Radius
...............................................................................
b 	0.074 ± 0.016  	     7.008151 day 	 1.31 R⊕
...............................................................................
                       2:1   7.22 day i resonant "Kirkwood Gap"
...............................................................................
c 	0.089 ± 0.012 	     8.719375 day 	 1.18 R⊕
i 	0.107 ± 0.03 	    14.44912 day 	 1.32 R⊕
...............................................................................
                       3:1  19.91 day d resonant "Kirkwood Gap"
                       2:1  29.87 day d resonant "Kirkwood Gap"
                       3:1  30.65 day e resonant "Kirkwood Gap"
                       3:1  41.64 day f resonant "Kirkwood Gap"
                       2:1  45.57 day e resonant "Kirkwood Gap"
...............................................................................
d 	0.32 ± 0.05 	    59.73667 day 	 2.88 R⊕
...............................................................................
                       2:1  62.46 day f resonant "Kirkwood Gap"
                       3:1  70.20 day g resonant "Kirkwood Gap"
...............................................................................
e 	0.42 ± 0.06 	    91.93913 day 	 2.67 R⊕
...............................................................................
                       2:1 105.30 day g resonant "Kirkwood Gap"
                       3:1 110.53 day h resonant "Kirkwood Gap"
...............................................................................
f 	0.48 ± 0.09 	   <a href="tel:124.9144">124.9144</a> day	         2.89 R⊕
...............................................................................
                       2:1 165.80 day h resonant "Kirkwood Gap"
...............................................................................
g 	0.71 ± 0.08 	   <a href="tel:210.6070">210.6070</a> day 	 8.13 R⊕
h 	1.01 ± 0.11 	   <a href="tel:331.6006">331.6006</a> day 	11.32 R⊕ 
But primarily the relative stability of the system has been tested:
https://arxiv.org/abs/1310.5912 wrote:
A Hill stability test and an orbital integration of the system shows that the system is stable.
But regarding isoparix's original question, given that a 7 exoplanet system (TRAPPEST 1) has been found tightly orbiting inside what would fit inside Mercury's orbit, I'd guess that we'll find systems having 10 or probably even >10 planets inside 1 AU from their star. A speculative assumption, but with so many systems, I think it's a safe one.

Bruce
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