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Habitable planets in binary star systems
There are two types of planetary orbits in binary star systems. The first type are “S-type” planets which have a planet only orbiting one star and the second being “P-type” planets which orbit around both binary stars. This theory is based on the assumption of similar-sized binary stars.

Observation on planet types
S-type planets will have a period when the entire planet is relative day, with the side facing towards the star it is orbiting being the brightest. There will also be night when the two binary stars eclipse each other relative to the planet. The side of the planet not facing the two star eclipse will be night. To avoid one side from burning up, the planet requires rotational velocity.

The orbital velocity of P-type planets has to be either substantially faster or slower relative to the orbital velocity of the star orbiting in the same direction relative to the planet as well as rotate in order to not burn one side up. An observer on this planet will observe the same thing as we do on Earth except they will witness two relative suns, one larger than the other, appearing to keep running into each other.

requirements for planets in their respective system types
To ensure the habitability of these planets, they will need to have basic necessities such as a moon, an at least 20% oxygen atmosphere and flora and fauna. But living around binary stars requires special conditions such as a core extremely hot and rich in iron and other magnetic materials to protect the planet against solar flares and coronal mass ejection of two stars.These planet’s oceans will have much strong tidal forces due to the presence of multiple stars.

For P-type planets, they will have to be located in the goldilocks zone of the two binary stars the size of our sun and have a high atmospheric water vapour concentration to provide more cloud cover as protection from the photon radiation of the binary stars but this makes the planet highly susceptible to industrial pollution due the ease of pollutants such as sulfur to dissolve in the wet atmosphere and become acid rain. Plants living in rainforests that are going extinct will find this place a safe haven although it will be much snowier around the poles.

For S-type planets, they will have to be located in a binary star system with two white dwarfs as white dwarfs do not radiate as much electromagnetic energy as other stars and have a goldilocks zone closer to the white dwarf that other stars while having the same mass as our sun to ensure that the planet is safe from being pulled by the other planet.

conclusion
With far-future technology such as wormhole construction and high-speed terraforming, life around binary stars is definitely possible.