Where Are the To-Scale Diagrams of Alpha Centauri's Orbits?

[snorkack]

Compare Moon.
Moon is strongly perturbed by Sun. For Sun is close to Moon, with only 13 months in a year.
The result is that the dragon moves rapidly - the eclipses do not only happen in two fixed seasons. And the apsides of the Moon move even more rapidly. Also the nominal eccentricity of the Moon changes rapidly.
And yet all these perturbations are periodic and stable. In a long term, the perturbations by Sun change neither the length of month, eccentricity of moon nor inclination of moon outside the range of their periodic variability.
A habitable zone planet of either α Centauri component, if on a low inclination orbit, would be similarly stable with purely periodic perturbations.

 

[Devin-M]

Strangely, one thing I was not able to successfully simulate was Proxima Centauri in a stable orbit around Alpha Centauri A & B...

First I set Alpha Centauri B to have an orbit around Alpha Centauri A with a Pericenter distance of 11.2 AU and an Apocenter distance of 35.6...

Next I set Proxima Centauri with a Pericenter distance of 4300 AU and an Apocenter distance of 13000 AU... I note the orbital speed near Apogee is on the order of the speed of an airplane... about 733 kilometers per hour.

The orbit immediately becomes unstable:



Even after I cheat by re-circularizing the orbit it still immediately becomes unstable.

 

[Vanadium 50]

Why do you think Proxima's orbit is stable? It probably isn't.

The period must be close to a million years. That's comparable to the motion of the "external" stars - for example, Gliese 710 will become the closest star to the sun in about a million years. The present orbit has almost certainly been perturbed by other stars, and it will continue to be perturbed in the future.

 

[Vanadium 50]

see whether the presence of Alpha Centauri B

I think your stability problem is with gas giants farther away - B perturbs the gas giant and the gas giant perturbs the terrestrials. If Jupiter's orbit where chaotic, well, there goes the neighborhood.

 

[snorkack]

I think your stability problem is with gas giants farther away - B perturbs the gas giant and the gas giant perturbs the terrestrials. If Jupiter's orbit where chaotic, well, there goes the neighborhood.

If gas giants are farther away.
If the gas giant is in the habitable zone, B perturbs or does not perturb it just as much as it perturbs a terrestrial planet or an asteroid.
What precisely is Pandora´s orbital period around Polyphemus?

 

[Ibix]

The orbit immediately becomes unstable:

Rounding error? To what precision are distances, velocities and accelerations stored? What's the time step and how is the integration performed?

 

[Devin-M]

There weren't any planets in the system, just 3 stars - Alpha Centauri A, Alpha Centauri B and Proxima Centauri, all with the appropriate masses.

This page describes the N-Body integrator: https://universesandbox.fandom.com/wiki/N-Body_Simulation

I did 2 more tests to try to make the system more stable, one of which was successful.

In the first (successful) test, Alpha Centauri A & B were simplified into a single star with their combined mass of 2 solar masses and 0 momentum. Then I placed Proxima Centauri in orbit with an apogee of 13000AU and a perigee of 4300 AU. This test remained completely stable and completed multiple orbits:



The next test, both Alpha Centauri A & B were used with the appropriate masses, but their orbits were simplified to have 0 eccentricity and 0 net momentum with a separation distance of 35.6 AU. Next Proxima Centauri was added with the appropriate mass, and placed in an orbit with an apogee of 13000AU and a perigee of 4300 AU. This test resulted in Proxima Centauri being flung from the system before completing a single full orbit:

 

[Devin-M]

I was able to get Proxima Centauri to complete multiple orbits at close to 400 AU from the barycenter... I also think I identified the problem with getting a semi-stable orbit solution. When you have 2 bodies you can just type in the orbital parameters and the resulting orbit comes out correctly, but when you have 3 bodies, typing in the desired orbital parameters doesn't give the correct results, probably because it can't compute the future time steps in advance. But by starting with an approximate orbit, then continually modifying the parameters I was able to bring the orbit into a state of metastability (skip to 8:00).

 

[Devin-M]

In this one by continually adjusting the paramaters in the beginning, I was able to get the orbit somewhat stable, somewhat close to the actual orbital parameters (but not exact - skip to 16:25 for final orbit)...

 

[Vanadium 50]

The issue of inner planet stability is separate from the issue of Proxima's stability.

Gas giants make inner planet stability more complicated. I would not be surprised if there are no terrestrial planets orbiting A if there are (maybe even were) any gas giants in the system.

Proxima's orbital stability is highly questionable. It's barely bound, and in its history lots of stars are likely to have made close approaches. I would not be in the least surprised if throughout its history it has been both bound and unbound. The age of Proxima is usually given assuming co-evolution with A and B, but there is not a lot of observational evidence there: models range between 4 and 7 Gy or so. If I had to bet, I'd bet that it co-formed rather than captured, but I don't think it's 100% settled.

 

[Devin-M]

You could have a gas giant in the habitable zone with an exomoon.

 

[snorkack]

You could have a gas giant in the habitable zone with an exomoon.

Just why I inquired about the orbital period of Pandora around Polyphemus.

 

[Devin-M]

There’s an unconfirmed observation of a potential Neptune sized gas giant in the habitable zone about 1.1 AU from Alpha Centauri A discovered in Feb 2021 but it has yet to be fully confirmed:

https://en.m.wikipedia.org/wiki/Candidate_1

The discovery image of Candidate 1, taken by the NEAR instrument at ESO's Very Large Telescope in 2021.

https://www.universetoday.com/150088/possible-super-earth-in-the-habitable-zone-at-alpha-centauri/