What astronomical considerations are necessary for the planet in this model to possibly be Earth-like?

I've been designing a world and wanted to base it on a rather interesting cosmology proposed by the ancient Greek philosopher Philolaus. He was a very early opponent of geocentrism, believing that both the Earth and the Sun orbited around a third body he called the Central Fire. He claimed that the Sun's orbit around the Fire took a year and the Earth's took a day, and that the day/night cycle took place because the Earth was tidally locked to the Fire and we all lived on the other side. For a visual description, take a look at this.

The other body you see there is Counter-Earth (or Antichthon in Greek), but that can just be ignored for now and I'll ask about its revelance in another question if I want to include it. It should also be assumed that the "Central Fire" is in fact just another sun, though I'm interested in replacing it with a black hole which I'll ask about in a seperate question.

So anyway, as my physics and astronomical knowledge is rather intermittent (and completely devoid of anything mathematical), this seems like an important place to start with questions. I want to make the "Earth" of this system have living conditions as Earth-like as possible (at least in the view of the Sun-side inhabitants). The most obvious concerns are:

1. Given that the orbiting sun would need to appear as Earth's, with presumably the same mass and at such a distance that it appears to be the same size, what does this mean for the central sun? More specifically, is there any possible configuration of mass or distance that allows it to hold the orbit of the other sun without making it impossible for the planet to be Earth-like (though obviously the face directed to the central sun will be scorched from 24 hour exposure). It's rather important for the model that one sun orbit the other, rather than them orbiting eachother, but I don't even know if this is actually even possible.
2. What would the result of the above look like to an observer on the planet, both on the side facing the orbital sun and on that facing the central sun? Are there any important planet-based observations arising from the model, or more specifically the way it arranges the orbits of the planet and the outer sun.

In terms of how much I understand, I'm pretty competent with elementary ideas (I recently found out that all lightlike paths beyond a black hole's event horizon warp towards the singularity such that moving towards it is inevitable, and I know enough about relativity for this to make sense to me), but I'm not really capable of determining how they all interact together. Thanks in advance to anyone who can shed some light on this for me, it would be greatly appreciated (and hopefully interesting for you to consider).

posted over 8 years ago

Kanderas‭

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