Graduate How is the Trappist 1 system stable?

[Sherwood Botsford]

The N body problem has no closed solution, and in many cases closely spaced bodies around a major body kick members out. In our solar system we have Titus Bode relationships that space orbiting bodies out in a geometric series.

Various resonances are common.

In Trapp1st 1, the planets are
.011
.015
.021
.028
.037
.045
.06

AU, but most of them have Earth like masses.

With the difference between a and b being .004 AU, compared to the .3 AU difference for Earth/Venus, the interplanetary forces will be (.3/.004)^2 = 5700 times as great.

I wasted an afternoon one day playing with an orbital simulator trying to find out if all those sci-fi novels with multiple moons showing disks were possible. I was unable to find any.

Anyone on this list have access to the equivalent of the Digital Orrery who can plug in the numbers for Trappist -1 and see if it's stable?

Secondly: Any generalization about under what conditions large moons of a planet are stable in numbers larger than 1?

 

[jonesdave]

According to Wikipedia:

"The orbits of planets b-g are nearly in resonance, having relative periods of approximately 24/24, 24/15, 24/9, 24/6, 24/4 and 24/3, respectively, or nearest-neighbor period ratios (proceeding outward) of about 8/5, 5/3, 3/2, 3/2 and 4/3 (1.603, 1.672, 1.506, 1.509 and 1.342). This represents the longest known chain of near-resonant exoplanets, and is thought to have resulted from interactions between the planets as they migrated inward within the residual protoplanetary disk after forming at greater initial distances.[22]"

[22] refers to the paper just published, which you can find here:
http://www.eso.org/public/archives/releases/sciencepapers/eso1706/eso1706a.pdf

 

[tony873004]

Anyone on this list have access to the equivalent of the Digital Orrery who can plug in the numbers for Trappist -1 and see if it's stable

Here's a simulation you can run in your browser of this system.
http://orbitsimulator.com/gravitySimulatorCloud/simulations/1487806670373_trappist1.html

You can also analytically calculate how far interior and exterior to each planet that space is unstable for other objects using the interior reach and exterior reach calculators on this page:
http://orbitsimulator.com/formulas/

 

[mfb]

You can also analytically calculate how far interior and exterior to each planet that space is unstable for other objects using the interior reach and exterior reach calculators on this page:
http://orbitsimulator.com/formulas/

Even with the maximal eccentricity, I don't see collisions. If the orbits are very circular, which is the most plausible case, the orbits are well separated and stable.

 

[Jenab2]

Most likely, a lot of material was ejected by the Trappist-1 system. Everything that couldn't find its way to a stable orbital niche in time got the gravitational boot. What was left were the winners that we've detected. Natural selection brings out working dynamic systems that would be difficult for even the best minds to design.

 

[Sherwood Botsford]

Even with the maximal eccentricity, I don't see collisions. If the orbits are very circular, which is the most plausible case, the orbits are well separated and stable.

I haven't figure out what the conditions for stability are for a multi body system. Circular orbits and no collisions aren't sufficient. Several others have mentioned the near resonances as being why it's stable. But in our solar system Saturn's rings have gaps that correspond to resonances. My initial expectation is that a resonance would increase the eccentricity of the orbits until they collided, or until it detuned the resonance.

 

[mfb]

See the formulas linked in post 3. Circular orbits and no collisions are not sufficient, but if you consider the masses and the distances between the orbits the system is stable, independent of resonances.