Check the stability of this planet's orbit for me please

[Junghalli]

Binary star system:
1.5 solar mass primary star
.6 solar mass companion
8.9 AU perigee, 21 AU apogee
Planet orbits primary star at 2.7 AU (near-circular orbit)

If the planet is unstable in a prograde orbit, what about a retrograde orbit?

This is supposed to be an Earthlike planet in the Procyon system for my hard SF uni. And yes, I'm well aware of all the reasons Procyon is a terrible candidate for an Earthlike planet - the planet was originally moved into its present orbit and terraformed by an alien race sometime in the last hundreds or tens of millions of years (sometime after Procyon B became a white dwarf) and since abandoned. I'm really mostly just concerned about whether the orbit is stable. A Hill sphere calculator and some figures I found on the net tell me it should be but I don't trust my own near non-existant expertise in this.

Thanks for your help.

[Ariphaos]

If I recall correctly, to have a long-term stable orbit in a binary system you want the orbit to be less than one-fifth of the point of closest approach.

[Junghalli]

If I recall correctly, to have a long-term stable orbit in a binary system you want the orbit to be less than one-fifth of the point of closest approach.

That's a rule of thumb for if the stars are basically the same mass though, IIRC. It would logically vary depending on the mass of the stars in question; in this case the primary star is not quite a good 3X the mass of the secondary, so its zone of stability should extend further, while that of the companion is less.

Hill sphere calculator gives a Hill sphere of 4 AU for the companion and 8 AU for the bigger star (stability region should be about half the Hill sphere radius IIRC - .47 for a prograde orbit and .67 for retrograde). Doing the same with Alpha Centauri seems to overestimate the stability region vs the figures given by Solstation by a factor of about 1 AU, but that should still leave room for at least a stable retrograde orbit.

[Bottlestein]

^ Out to 10^15 periods - it is stable (retrograde): at least according to my friend's Hill Sphere calculator

I don't know which algorithm is better though - my friend's program only has a 2nd order Runge Kutta scheme for the integration.