Can such planet orbit 61 Cygni A within a habitable zone?

Question

I have developed a fictional planet I described here in Worldbuilding Stackexchange: https://worldbuilding.stackexchange.com/questions/231162/length-of-seasons-on-a-planet-with-eliptical-orbit.

Since then, I have refined its parameters:

• its mass is 0,9 Earth;
• its day is 20 hours;
• it has 25.7 degrees axial tilt (it's for defining its climate);
• it orbits its host star in 1020 local days;
• Semi-major axis is 1.7561 AU;
• distance to the host star at the perihelion is 0.9278 AU;
• distance to the host star at aphelion is 2.5844 AU.

My question is: can such a planet orbit 61 Cygni A within its habitable zone?

Answer 1

There are two issues here: is the orbit stable in the A-B binary system, and is the planet within the life zone.

The 61 Cygni A-B orbit has a mean separation of 84 AU with a periapsis of 44 AU. That makes the fictional planet's orbit plausibly stable. A loose rule of thumb is that you can have stable orbits within 1/3 of the the periapsis distance (for more careful calculations, consider Hill spheres etc.)

The life zone where water is liquid is roughly between $0.7\sqrt{L/L_\odot}$ to $1.4\sqrt{L/L_\odot}$ AU; again one can try to refine this by considering temperatures, atmospheric effects etc. but for this kind of purpose we mostly care about the rough size of the region and the scaling. 61 Cygni A has $L=0.15L_\odot$. So the life zone will be about 0.27 to 0.54 AU from the star. That is bad news for habitability of this fictional planet: it is outside the zone at all times, likely frozen over.