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How would my planet develop an acceptable climate, without a sun ?
There is no (visible) sun, but the climate permits STP, and there are 1 or more luminous, rocky moons providing some light.
Perhaps the star exists, but is somehow not visible. Perhaps there is no star and the planet receives energy by other means. Perhaps the "moons" are artificial power-generation devices.
Anything goes!
Brown dwarf sun.
https://en.wikipedia.org/wiki/Brown_dwarf
Brown dwarf emissions are almost all infrared. They do not put out much visible light and what they do is red.
Here are compared the emission spectra from 2 different brown dwarfs with that of the sun. Brown dwarfs are from
https://www.eso.org/public/usa/images/eso9709b/?lang Sun is from wikipedia.
Note the brown dwarfs are in angstroms and the sun in nm. Divide angstroms by 10 to get nm.
Red light is 700 nm / 7000 A and almost all of the emission from the brown dwarfs are longer than that - invisible infrared.
Thus orbiting a brown dwarf you could get plenty of heat but very little light. This is your warm night world. The little bit of visible red light put out by the star makes the days red.
You could have a rogue planet moving inside a dense nebula, the ecosystem driven by the radioactivity of its nucleus. Or the "world" could be the liquid shell beneath the ice crust of said planet, the ecology driven by thermal springs on the bottom.
Or it could be a variation of Robert Forward's Dragon's Egg.
Let's make up a story (yours free of charge!)
How about, the planet itself, the size of Earth, was thrown from the orbit around its own sun by a rogue star traveling through it's solar system. But the technology on this planet was thousands of years ahead of our own.
Their technology was not enough to save their planet from being thrown from orbit, and not enough to steer the planet.
But it was enough to construct matter-to-energy devices that generate enough heat to keep the planet habitable. That is what those luminous moons actually are. They aren't natural. That luminosity is intentional, but more importantly, there is a strong infrared component that warms the atmosphere.
They are moons to distance themselves (and their radiation) from the surface, close up that infrared is intense. It needs to be spread out over thousands of miles and hundreds of miles of atmosphere.
Generations of the populace devoted their lives to this life-saving project, and succeeded. They genetically engineered plants to photosynthesize this light coming from the moons.
The system is entirely automated, run by very advanced AI, but the AI is not conscious in any sense, it is just a machine that keeps the planet warm and keeps the system and itself in good repair. It doesn't "care" about anything else, just this one singular task. It would do this task even if the planet was barren and devoid of life; this AI is just an emotionless machine.
On the planet itself, just like Earth, generations come and go. Species arise and go extinct. Societies crumble and new ones are born. Millions of years later, nobody on the planet knows why their planet is warm, or why they fly through interstellar space. They just do.
And it is always, always, twilight at best. But of course, they and their animals have evolved so the light that they have lets them see as well as we do on a bright day; with the large nocturnal eyes, with hypersensitive retina, we see in strictly nocturnal animals on Earth.
Some power-hungry Kardashev I or II civilization came and set up a Dyson sphere around the star. Unfortunately for anyone on the planet, the sphere is in a lower solar orbit than their own world, which means no light for them.
All the radiation the planet gets is now in the UV range due to technobabble that we don't understand. The moon is rich in stuff that shines under UV so that's how she glows.
It’s actually just a really small star, perhaps like EBLM J0555-57Ab or GRW +70 8247. You may need more than one of these to have day all the time, or you could just use some actual rocky moons. These other moons potentially look very similar to the star(s) which is why someone on that planet might not notice that there actually is a star. There could also be a large amount of dust occluding the stars and moons making it even more difficult to distinguish.
The planet is a super earth, also known as a massive rocky planet. Perhaps of similar size to TOI-849b, maybe larger somehow. This could add to the believability that the star is just a moon, due to the comparative sizes of the planet and the stars if the they are at the right distances.
