Stability of a binary/double planet system

[Somes J]

Hello. I have a question concerning the stability of a hypothetical binary planet system.

The hypothetical system is an Earthlike planet orbiting a relatively bright K class star at a distance of maybe .5-.7 AU. The planet is roughly Earth-sized and it has a very large moon, around 1/3 the mass of Earth (the idea here is that the moon would also be capable of supporting an Earthlike environment - basically this is the old Earthlike double planet concept). The moon would orbit the planet at a distance of around 40-50,000 km, with a period of around 30-35 hours, and both the planet and moon would be tidally locked to each other (like Pluto and Charon in our solar system). The planet's axis would be inclined at roughly 20-25 degrees (like Earth's) and the moon would orbit in the plane of the planet's equator. The planet would have no other natural satellites.

Now, the issue that's troubling me is tides. There would be huge tides (thousands of times ours), obviously, but since the planets are mutually tidelocked they'd be fixed so I imagine they'd only show up as a distortion in both worlds' overall shape, as generally unnoticed as the equatorial bulge on Earth. But there might also be variable tides, created by the eccentricity of the moon's orbit and any precession-type motions of the axis of the planet relative to the moon's orbital plane etc. Given how close together these worlds are even relatively small secondary variable tides could be catastrophic at the surface (oceans being raised many meters and penetrating deep inland etc.).

Say the moon starts out with a very very low eccentricity, like Neptune's moon Triton. Both planets may have been terraformed at some point in the deep geologic past, so maybe the aliens adjusted the orbit or something if that's necessary to justify it. But that was long, long ago, so my concern is would such an extremely circular orbit naturally stay extremely circular? From what I've heard strong tides tend to circularize orbits, and I've read that tidal dissipation scales by radius^6 whereas the strength of the tides only scales by radius^3, so based on that I'd think the near-perfectly circular orbit would be quite stable (the two worlds would gradually draw closer together as the solar tide took angular momentum out of the arrangement but it shouldn't become much more eccentric) but my knowledge of the relevant physics is extremely limited. I'm only an aspiring science fiction writer, not a professional astronomer.

Similarly I'd imagine that the huge tidal forces involved would keep the rotational axis of both the planet and the moon very close to 90 degrees to the plane of the moon's orbit, but again I lack the knowledge to be sure.

Would the inclined plane of the moon's orbit relative to the plane of the planet's orbit around the sun be a complication?

Basically I'm asking whether these worlds could realistically stay nice and Earthlike without artificial intervention or whether, once the terraformers were gone, we'd be back to looking at some sort of Io-like hellhole with massive ocean tides in a geologic instant. And if the latter, what could I do to make such an arrangement more plausibly stable?

Also, suppose we had a similar scenario but the moon was smaller, more like our moon or Mercury. Would that also be stable?

Sorry if this was a little long. Thanks, it'd be a huge help if I could get an answer.

[korjik]

If they are that close after tidelocking, then I would imagine that the orbits would have to be very circular. At that point the main problem would be the effect solar tides would have on the system. I think that with a small star the tides would be enough to destabilize the orbits pretty quick. Your terraformers would probably want to align the ecliptic and equators (give them a zero degree axial tilt). Otherwise, I think that the two planets would end up crashing together pretty quick.

[swampyankee]

Since the two bodies are tidally locked, the only tides would be due to their primary, and to various perturbations from circularity exist in their mutual orbits -- and there will be some, if only because of perturbations from other objects in the system. As for the stability, that's going to be dependent on the other bodies in the system, too, in a quite complex way.

[Somes J]

I think that with a small star the tides would be enough to destabilize the orbits pretty quick. Your terraformers would probably want to align the ecliptic and equators (give them a zero degree axial tilt). Otherwise, I think that the two planets would end up crashing together pretty quick.

Are you sure?

The sun's gravity at the moon is ~2.2X stronger than the Earth's gravity at the moon (simple calculation from masses of the two bodies and inverse square law). On the other hand for this planet the planet's gravity at the moon is 27X stronger than the sun's gravity at the moon. Compensating for the sun being .6 AU away and .9 solar masses I still get the planet's gravity being ~11X stronger than the sun's gravity at the moon. Even the moon's gravity at the planet is ~3.6X stronger than the sun's gravity at the planet.

This is comparable to but less extreme than the situation with the Martian moon Deimos, where I calculate Mars's gravity at Deimos is ~80X as strong as the sun's gravity at Deimos. Deimos has an eccentricity of .0002 and orbits within less than 1 degree of the Martian equator.

With tides the planet even more heavily dominates over the sun since tides scale by r^3. At .6 AU from a .9 solar mass star the solar tide would be around twice our lunar tide. But the permanent tide raised on the moon by the planet is more than 30,000X Earth's lunar tide.

I'm not saying you're wrong, if I actually knew what was plausible here I wouldn't be asking this question (plus I'm terrible at math so I may have messed up somewhere there). I'm just wondering how confident you feel in that assertion and what it's based on.