Would the following hypothetical planets in the 61 Cygni binary star system have stable orbits?

Question

To clarify, I realised that I kind of ran into a problem trying to check the orbital stability of two fictional planets in orbit around the real life 61 Cygni binary star star system.

To explain: 61 Cygni A and B are a pair of K-class stars located at a distance of 11.41 light years from Earth, in the direction of the Cygnus constellation. The two stars orbit at a semi-major axis of 84 AU, have a periapsis of 44 AU and apoapsis of 124 AU. 61 Cygni A is a BY Draconis variable star and 61 Cygni B is a flare star, which is suspected of having a circumstellar disk as of 2018 (confirmed in 2024, with both 61 Cygni Ab and 61 Cygni Ac being confirmed in 2071 in-setting).

Regarding both planets, 61 Cygni Ab is a distance of 0.34 AU away from the star, well within its habitable zone of 0.26 AU - 0.58 AU, compared to 61 Cygni B's 0.24 AU - 0.50 AU habitable zone. It is home to complex life, the ruins of an technological civilisation, whose survivors have struggled to recover by the time humans colonise the planet, and has at least a relatively large moon. 61 Cygni Ac is a mini-Neptune located at a distance of 1.2 AU from 61 Cygni A (not sure where the frost lines of the two stars are located), which has at least 19 moons, 5 of them being ice moons, which are also colonised by humans in the setting.

61 Cygni Ab happens to have a mass of 1.2 Earth masses and has a radius of 1.1 Earth radii, which gives me a density of 4,954 kg/m^3, whereas 61 Cygni Ac has a mass of 16 Earth masses, and 3.1 Earth radii, which gives it a density of 2,951 kg/m^3. As for both worlds' gravities, they are 9.72 m/s^2 and 16.31 m/s^2 respectively.

Here is the link to the Wikipedia article for more information.

I would also like to ask about the habitability potential of BY Draconis variable stars as well, but that is either on another SE or, for our purposes, a separate question.

With that out of the way, are both planets stable in terms of their orbits for 61 Cygni Ab to develop complex life in the first place? Or would they both be flung out into space before 61 Cygni Ab has the chance to do so?

Answer 1

I don't know if I've messed up the maths, but Cygni A has an estimated mass of 1,4E30 kg while Cygni B is 1,25E30 kg. With Cygni B being 44 AU away in the periapsis, the gravity atraction between Cygni Ab and Cygni A is nearly 20,000 times greater than that between Cygni Ab and Cygni B, so I don't see why the planet's orbit wouldn't be stable.

You haven't said anything about the mass of your mini-Neptune, but I bet his gravitational pull is way bigger than that of Cygni B, being just below 1 AU away, so your main threat to orbit stability probably comes from that angle.