- #1

- 5

- 1

I know all the pieces are stable as we have real life examples, but put together I don't know what would happen. Over all, they would be in a 8:4:3:2 orbital resonance.

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- Thread starter dragonfiremalus
- Start date

- #1

- 5

- 1

I know all the pieces are stable as we have real life examples, but put together I don't know what would happen. Over all, they would be in a 8:4:3:2 orbital resonance.

- #2

- 27

- 0

with Galilean moons it is easy, they can be written symmetrically 1:2:4 (

But taking your case with 8:4:3:2 as

if we convert it to

1: 2: 8/3: 4

And since I just wanted to ask the same question but using the

1:2:3:4

clearly this two are different ratios, although they both have representation that satisfies the 3:4 and 2:3 rules at one of the options.

which is the correct way? It is not 100% clear.

sorry if I hijacked your question, and you actually sorted this out already, please share your view.

Regards,

Qshadow.

- #3

- 5

- 1

- #4

tony873004

Science Advisor

Gold Member

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Here's a sim of this scenario. All planets are 1 Earth mass in circular orbits except #3. It has an ecc of 0.2 and a mass of 0.5 Earth masses. They orbit a sun-mass star with periods of: 10 days, 20 days, 80/3 days, and 40 days. From closest to farthest, each planet begins 60 degrees ahead of the previous one.

The bottom image shows a rotating frame holding the 4th planet stationary. It seems to be stable at least initially. See what happens if you let it run deep into the future.

- #5

- 5

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But your simulation started with that triangle tilted, like so:

But as I watched the simulation, I noticed that the orbit of the third planet changed, and the "triangle" traced by the third planet rotated until it was exactly where I wanted it to start:

Then began oscillating back and forth around that point. So that shows me that for this simulation at least, that orbit would seem to be very stable. After a thousand orbits or so, the orbits look exactly the same and this is the path the third planet has traced out with respect to the fourth. To me, this suggests pretty good orbital stability.

- #6

- 27

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Thanks for clarification.I have done a bit of research on the subject and by far the most common way I have seen to write orbital resonance is theratio of number of orbitscompleted in the same time interval.

And after seeing that nice simulation i wonder if we can generalize this law further, e.g. probably it work for orbit ratios that are powers of two:

32:16:8:4:2:1

But what about packing as much satellites as possible using the rule that we saw now, eg:

32:24:16:12:8:6:4:3:2

so each number between the powers of two is the sum of powers of two at (n-1) + (n-2)

would it be stable as well?

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