Is my map of prevailing winds on a binary planet realistic?

Question

My binary planet consists of a Venus sized earth-like planet, tidally locked to a mars sized “super mercury”, with their centers separated by about 7 Venus radii. I know the coriolis effect would behave very differently here, so I decided to figure it out for myself, but I want to know if it is plausible, because it is certainly interesting.

The coriolis effect, as far as I know, arises from the equator moving faster than the poles because it is a larger distance traveling over the same time. A good analogy would be a record on a player. As air moves from the poles south, it approaches land moving faster than it, and appears to fall behind. Air moving north approaches slower moving land, and appears to slip ahead. But In my case, my planet is like a circle sticker stuck on the record, the near side of the planet hardly moving at all, and the far side buzzing around as the planets orbit one another.

As you can see, the further you get from the barycenter the faster the planet is moving, which forms a series of concentric circles from the sublunar point to the sublunar antipode. Air on the near side would appear to flow similar to on earth, moving closer to the sublunar point, toward the barycenter axis, toward slower moving land, therefore being deflected in the prograde direction. But once you reach the meridian “equator”, you find traveling north and south does not change how fast that part of the planet is moving. Here, the wind would not be deflected anywhere, but move north or south. Beyond this meridian, on the far side, moving toward the equator brings you to faster moving land, and the wind reverses direction. Considering the near side far side line as the “prime meridians” you would find in a single convection cell, the wind blows away from one point on this circle, and towards it on the opposite side of the planet. Even more interestingly, the next convection cell would blow in the opposite direction, away from this point, and converging back where you started

In conclusion, I feel this would make for a very interesting world with civilizations having to navigate by these strange winds, sometimes with the guide, of the other planet, and sometimes alone without it. Is there anything I’m missing? And to whoever edits this for formatting feel free to rewrite some stuff cause my syntax is terrible when I dump information.

Answer 1

Background

So, they key consideration here is force diagrams in each reference frame. The major considerations are:

• Gravity of planet you are on
• Gravity of neighbouring planet (tidal forces)
• Accelerating reference frame (ultimately the coriolis force derives from getting nearer or further from the axis of rotation)
• pressure gradients

Ultimately I'd think about solving a static solution (where does the atmosphere generally end up -- for the Earth you get a convenient even-ish shell) and then consider what happens to a parcel of air moving within this background distribution (for Earth, Coriolis leads to Hadley cells & trade winds)

Answer

In this specific question I think OP has sketched out the static solution without considering tidal forces (but they align with the Barycentric rotation so don't super change the solution). Assuming Barycentric rotation dominates gravity, the dominant wind current would be as sketched, leading air to build up on the far side of the planet until pressure gradients matched the rotational force (if tidal force dominates, you get more air on the near side).

To estimate the wind pattern, when I consider the forces on a moving element of air, I believe you end up with something akin to the classic Earth hadley cells, but rotated 90deg so the "north pole" points at the Barycentre.

Unknowns:

• it is possible that the daily cycle of solar heating adds complexities to this that I can't fully map in my head.
• Tidal forces are actually very complicated (see: Earth's tides) at there might be standing waves in the atmosphere due to this. Add topography to the planet and Rossby waves derived from that would become an important part of the overall atmospheric dynamics

PS. I am only considering atmospheres here. For full hard sci-fi you may need to think about the stresses in the solid bodies of the planets in this setup, and whether the orbits are stable

Answer 2

I suspect the 2 planets as described would not have stabilised their orbits in the fashion you present.

What you are describing is effectively the Earth and the Moon - with their habitable atmospheres but the moon being insanely close to the Earth. I don't know the right way to calculate those orbital mechanics, but it feels intuitively wrong to have the smaller planet orbiting the larger at a distance of seven radii

It is most likely going to need to be at a similar distance of the Moon from Earth - Or even further...

The key point here, is that based on Orbital mechanics, I think your 2 atmospheres will not be able to interact at all