I’d like to know if this is plausible: A habitable planet that’s always day. It kinda works like this: The planet orbits its largest sun, which is also orbited by three smaller suns that share the same orbit with each other. The smaller suns are further out than the planet, so that no matter where you are on the globe, the sun(s) are always shining. The planet’s temperature needs to be between 253 and 393 K, and humans can go on its surface without protective gear. Of course, a planet like that would be a boon for solar power, but what orbital radii and solar masses would allow for this to be a realistic scenario?
It won't form naturally, and plants will hate it.
So a Sun-Planet-Sun system can form by capturing a rogue star, however you're not going to get 3 smaller suns captured precisely in sync. Any slight perturbation and the planet or a sun will be slingshotted out of the solar system.
If a mega-advanced alien races sets it up - yeah it could last a few million years, especially if they drop by to repair the orbits every now and then.
However it will be a desert planet. Nothing we plant will grow under those conditions. Why? Plants do stuff at night - they respire (breath). In a recent answer I went over what plants will grow at what day lengths. The longest I found was 38 hours of constant light followed by 10 hours of darkness. Marijuana growers may use a 32-hour day with seedlings (24 light, 8 dark).
Any outdoor farms on your planet would need a roof in order to shield the crops from the sun for a few hours. Solar power would be nice - that could easily run an indoor hydroponic setup, or the louvers over the outdoor farm.
(After thinking about it for a bit - If your planet has high mountains at high latitudes in the shadows of those mountains you may be able to get a 6-8 hour light/dark cycle, that can grow some short-day plants - I'd look at strawberries and cauliflower.)
The exact radii of the planets and suns I can't give you an exact answer for - actual temperature depends on things like what kind of sun, how much fuel is left, the CO2 levels and planetary albedo. (But rule of thumb: If you double the distance you quarter the solar heat arriving, so if your stars are sol-like just put them about 2AU away from the planet and the radiated heat from all 4 suns should be about ballpark). If it's too hot remove some CO2 from your atmosphere or add some more white clouds, if it's too cold, add some CO2 or darken your clouds.
However that's only going to work if the planet->sun distances remain constant. They wont: Something to be concerned about with this setup that I don't think you've considered is the seasons as the planet gets closer to and further away from one of the outer stars. Earth->Jupiter distance varies from 588 million KM to 968 million KM away - that's an impressive variation in heat as the influence of that star will vary by a factor of 4. (For reference the Earth->sun distance varies by about 4 million KM over a year.) This would probably result in ~20 year cycles of half ice age, half intense heat.
To avoid the cyclic ice age problem, I'd suggest look at having a few really reflective moons instead - that way the distance between the planet and the heat sources isn't varying so wildly.
Why ? Ok so what you want is in a sense a Minimum of two Stars that are in a Binary Orbit. Which is not unlikly. But then you want that the Stars are so far apart that the Habital Zone fits into the Orbit of one Star while at the same time both being bright enough to make it day all the time.
The Problem here is Mass. IF the Planet has to Orbit one star, the other one has to be very far away. So far that it would be very dim. But, here me out, there is a way around that.
The Geocentric Model
Right after all these years, this Model actually has some use.
First lets get the Basics. Any two or 5690 for that Matter Orbiting Bodys have what is called a Barycenter. Thats the point where all the Forces of Gravity are zero. For example, the Barycenter of 2 Bodys with Equal mass is exactly in the Middle of Both.
Here is the idea, lets say we have two sun sized Stars in a big Binary Orbit. They too would have a Barycenter which would be more or less in the Center. If a Planet wopuld be there, it wouldnt move relative to the two Stars. The Stars would pretty much Orbit around it. Thus the Geocentric model.
Now you might say, wouldnt the Planet have to be exactly on the Center ? No ! The Planet too can ORbit the Center. So there is a bit of wiggle room but not much.
All of this is to say, something like this could form. Again its very unlikly but it can happen. If a single more or less evenly Gas Cloude collapses into 3 Bodys all the same distance apart you basically already have what you want. Other Planets could form too but then it gets messy with Gravity
So i am 100% sure this could form Natrually with a single Planet at the Center. Other Planets around one of the Star or around both can also form but nothing should be to close to the Center planet
So yes, this could form but not in the way you described.
Actually you could use more than 3 smaller stars in the shared outer orbit.
If you go to the PlanetPlanet blog, section on designing the Ultimate Solar System (one with the most habitable planets) and find the post the Ultimate Engineered Solar System.
It cites a paper claiming that seven to forty two equally spaced planets can share the same orbit around a star.
And in another post it is proposed that a ring of stars could orbit a more massive central object in a solar system.
However, even the dimmest of red dwarf stars would have to have about 75 to 80 times the mass of Jupiter, which is 1/1048 the mass of the Sun. So 7 to 42 stars each with the mass of of 75/1048 to 80/1048 the mass of the Sun, would total 0.5009 to 3.2061 times the mass of the Sun.
Could the habitable planet and the outer ring of stars have stable orbits around a star that massed between about 0.33 and 2.0 times their total mass, or would the system be unstable over long astronomical time?
You could just make the inner star more massive to increase its mass relative to the outer ring of smaller stars. But you can't go on increasing the mass of the central star too much. The more massive a star is, the faster it "burns" its fuel and the quicker it leaves the main sequence. It has been calculated that a spectral class F2V would be the most massive star that could possibly stay on the main squence long enough for any of its planets to become habitable.
But even the most mass type F stars, type F0, have a mass only 1.4 that of the Sun. If the inner star is a binary F2 it will have less than 2.8 times the mass of the Sun, if the inner star is a quadruple F2 it will have less than 5.6 times the mass of the Sun.
And that is a lot less than the ratio of central mass to orbiting mass in a normal star ystem.
But the next post in The Ultimate Solar System, The Black Hole Ultimate Solar system, it is proposed that a supermassive black Hole, a million times as massive as the Sun, could be at the center of that fictional solar system. That would make the central body thousands of times as massive as a ring of seven to forty two stars, even if the stars in the ring are a little more massive than the Sun. That mass difference should be enough for the orbits to be stable.
The habitable planet would be illuminated only by the outer ring of stars. But the light would come from every direction, since some of the stars in the outer ring would be on the other side of the black hole.
Or maybe there could be two rings of shining stars in the solar system orbiting the black hole, and the habitable planet in your story (along with many co-orbital habitable planets, since you wouldn't want to waste that set up on just one habitable planet) could orbit between the inner and outer rings of stars, if that is necesary for constant enough illumination and temperature.
Of course it would be extremely improbable for such a system to form naturally and it would proabably have been constructed by some super advanced civilization.
But I hope this suggestion helps you design your star system.
I went to the serach funtin at the top of the worldbuilding page and searched for "planet with eternal day" and found 44 results, some of which may be relevant to your question.