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Distance from the sun for tidally locked world
I am creating a terra-type planet which is tidally locked and characterised by three differing types of environments. A hot to scorched solar pole marked by unstable weather, a very broad terminator with warm to cool temperatures, and a night-side characterised by being covered by ice.

The planet is located in a twin sun system with a yellow Sol-like star (A) and a red dwarf (B). The planet orbits (A). How long from (A) must it be to not become "too" scorched?

Here is a rudimentary map. Interpret it yourself. ^^
Do you have luminosity values for both stars? That would really help.

Assuming its a sol like star(G2V) the hab zone would exists between 0.8-2.0 au... However where it lies in the zone is dependent on a variety of factors such as it's size, atm pressure, water%, star age, etc...
Planetology is not my strong suit, but a bit of quick googling turned up some descriptions of what might happen to the Earth if it became tidally locked to the sun:

Based on these, it might be good for the planet to be farther from the star than Earth, although there are probably limits to how far you can put it. You might also make the star somewhat cooler than Sol. The biosphere might also influence the climate and local conditions to some degree, allowing it to either be closer to or farther from the star that might otherwise seem apparent at first blush.

Another factor here would be just how exotic the biosphere might be. OA has naturally evolved biospheres on planets that are totally uninhabitable by our current standards. So, depending on how much you want it to be 'terra like' there might be some flexibility there as well.

Hopefully, one of our planetary folks can weigh in on this, but my WAG on distance would be no closer than Earth's current distance (unless the star is significantly cooler), and probably not as far out as Mars.

My 2c worth,

Greetings. I haven't decided on any luminosity values or star size, but the star is cooler than the sun, and also probably a little bit smaller. The complicating factor is (B), but (B) is still quite important for the novel/novellas in question.

The planet in question have two dominant species. A mammalian species that has developed several bronze age civilizations in the temperated zones, characterised by maritime trade and religious stringency, and a wasp-like species living in the wastes of (A) ("the solar pole"). Due to the proximity of (B), civilization is regularly destroyed by cataclysms during the warmest period, when (B) is the closest in proximity. Firstly, the sea levels rise during those periods, covering a large part of the islands and the lowlands, secondly it messes with the mating habits and courting behaviour of the males of the civilization, and thirdly it leads to an explosion of the wasp-like creatures living around the solar pole, who extend the area on which they breed and hunt for food.
If the system is stable, the red dwarf B must either be in a P-type orbit, where the planet orbits both stars (which are very close together) or an S-type orbit, (where the planet orbits one star, and the other is at least three times as far away). If you are describing an S-type system, the red dwarf will be at least 3 times as far away from the planet as the primary, so it will have only a minimal effect on the planet's weather (although it could make the nights appreciably warmer and brighter on occasion).
The biomes are largely "Terran". Carbon-based life-forms. Plants that live on photosynthesis, water and nutrients, animals living on plants and other animals. The atmosphere is slightly denser and richer, and also marked by turbulence centered on the solar pole. There are plant and animal life in the atmosphere, and gravity is slightly lower than on Earth due to a slightly lower mass.

Steve: It is a S-type system, where the planet in question orbits (A).

The main sapient species are basically humanoid, but have lagomorph-like lower bodies and amphibian-like skin. They are mostly relying on sight and on hearing, and began as a hunter-gathering species living near the dim rim of the ice sheets (look at the map). They have two sexes, male and female, and were originally colony-dwelling (much like rabbits), with matriarchal overtones.

During the summer period, when (B) is on the side of (A) in regards to the planet in question, this stimulates the hormones, causing increased sexual behaviour, which in most cultures have resulted in a solution whereas males are living outside the main settlements, "in the wilderness", and mating is surrounded by courtship rituals, as well as ritual combat between males. The reason for the periodic expulsion of the male population during the summer is to prevent the breakdown of social order.

Most religions (which belong to a common mythos reminiscent of henotheistic-polytheistic mythologies on Earth) basically portrays (A) as a feminine goddess of life, warmth and fertility, and (B) as Her husband "the hunter", who during the winter is wandering the Nightlands, bringing prey to His spouse. The cosmology is built on the idea that the world is flat and surrounded by eternal sheets of ice.
One interesting possibility is for the Earth-type planet to be orbiting the red dwarf and tidally locked to it, with the red dwarf providing most of the heat - with the red dwarf in turn being in orbit around the G-type star somewhat outside the Goldilocks zone of the G-type; maybe a distance corresponding to the middle of Sol's asteroid belt.

The orbit of the planet would be stable because to get any decent amount of heat out of the red dwarf, the orbit has to be close; WAG would be 2 million km.

It's also worth noting that photosynthesis would probably rely heavily on the G-type sunlight; deep red and infrared light aren't all that good at breaking chemical bonds.
Some points to consider:

1) At a given distance, a more massive planet is going to become tidally locked with respect to its star sooner than a less massive world.
2) If the planet has an indigenous biosphere, it might be helpful for the captured rotation to precede or coincide with (more or less) the emergence of life, so that evolution has only one rotation period to contend with.
3) An issue with habitable tidally-locked planets is that at least 100 millibars (CO2 equivalent) of "greenhouse" gases are required to prevent the day-side atmosphere from condensing out on the night-side.
4) The sub-stellar "hot spot" on the surface directly beneath the primary star's zenith will be substantially warmer than the surrounding terrain; the "hot spot" is not a fixed point, as the planet is (slowly) rotating beneath the zenith. The path described around the globe is determined by the world's orbital inclination and axial tilt.
5) The atmosphere will circulate more or less radially from high above the "hot spot" to the "cold pole" on the opposite side of the planet, where it will begin its return journey in the form of surface winds blowing back towards the "hot spot." Clouds will stream away from a clear region above the "hot spot" and condense soon after crossing the terminator.

Putting these together with the basic plan you described, the most straightforward solution is to place the planet in a low-eccentricity orbit just beyond the primary star's liquid water zone; to preclude the mass of the planet from growing far past your stated preferences, an orbit around the red dwarf star might be preferable.

"I'd much rather see you on my side, than scattered into... atoms." Ming the Merciless, Ruler of the Universe
As well as thicker atmosphere, I understand increasing the orportinal amount of methane has more of a warming effect, than CO2. Perhaps life had this effect,there are methane producing micro-organsims,maybe there are a few more of them there.
How would weather patterns be affected by the solar pole region of this world?

The solar pole is within the red circle. One question is the habitability of the region around it.

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