Orbital resonance in binary star systems

[Sanduleak]

An interesting example here: small planet Occam is making an orbit around its parent star Razor. Razor is part of a binary star system, the second star in the system is called Paradigm.

Every 43 years, Occam makes a dangerous approach near Paradigm, and gets even closer to it than to its  parent star. Although Razor is much bigger than Paradigm, the later causes 25% wobbling in Occam's orbital period. Still, the system is stable. How is it possible?

1) Occam motion is retrograde. If it was moving the other way around, the small planet would be quickly ejected from the system.
2) Occam is in a safe 2:1 orbital resonance with Paradigm.
3) Orbits have small eccentricities.

See attachment if you want to experiment.

Chris

 

[Sanduleak]

3 pictures attached:

1) Occam's minimum orbital period 38.7 years just before encounter with Paradigm. See that Occam's motion is retrograde
2) Occam's maximum orbital period 50.9 years just after encounter, it is 14.2 AU from parent Razor
3) Same spot showing that Paradigm is 24.6 AU from Razor. Here Occam is about 10.5 AU from Paradigm, that's closer than Razor, and that's even just within Paradigm's Hill sphere!