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A real issue I see with this world is that three stars isn't enough to banish night perpetually...these stars must orbit each other.

So the planet orbits one star, the sunlike star. The other two need to be far enough away to avoid perturbing the orbit of the planet. If they are close to the sunlike star, they will not light up the night sky, so that's out. So instead they will have to be distant. In this case the dim star, if far out past Pluto will likely be 'just another star' and not light up the night. The Red Giant, even if it does light up the night when the planet is between the sun and the giant, will not do so a half year later when the planet is on the other side of the orbit. Any odd configuration you set up will change as the suns orbit each other, with some period of hundreds to thousands of years or less.

When Asimov wrote Nightfall, he had considerably more suns in his sky. Six or Eight, and probably even this many could not be put in a configuration that would banish night forever. Even in the story all but one star was clustered in one part of the sky, and then another planet eclipsed it.

EDIT:

An interesting thought is for the red sun and the yellow sun to be in orbits like the Sun and Jupiter and then have a dwarf star in the L4 and L5 points of that system. Then these 4 suns would be orbitally locked with respect to each other, 60 degrees before and behind the yellow sun in its orbit. I'm not sure this would totally banish night for good even so, but the suns would be in fixed relation as long as the orbits held.

A real issue I see with this world is that three stars isn't enough to banish night perpetually...these stars must orbit each other.

So the planet orbits one star, the sunlike star. The other two need to be far enough away to avoid perturbing the orbit of the planet. If they are close to the sunlike star, they will not light up the night sky, so that's out. So instead they will have to be distant. In this case the dim star, if far out past Pluto will likely be 'just another star' and not light up the night. The Red Giant, even if it does light up the night when the planet is between the sun and the giant, will not do so a half year later when the planet is on the other side of the orbit. Any odd configuration you set up will change as the suns orbit each other, with some period of hundreds to thousands of years or less.

When Asimov wrote Nightfall, he had considerably more suns in his sky. Six or Eight, and probably even this many could not be put in a configuration that would banish night forever. Even in the story all but one star was clustered in one part of the sky, and then another planet eclipsed it.

A real issue I see with this world is that three stars isn't enough to banish night perpetually...these stars must orbit each other.

So the planet orbits one star, the sunlike star. The other two need to be far enough away to avoid perturbing the orbit of the planet. If they are close to the sunlike star, they will not light up the night sky, so that's out. So instead they will have to be distant. In this case the dim star, if far out past Pluto will likely be 'just another star' and not light up the night. The Red Giant, even if it does light up the night when the planet is between the sun and the giant, will not do so a half year later when the planet is on the other side of the orbit. Any odd configuration you set up will change as the suns orbit each other, with some period of hundreds to thousands of years or less.

When Asimov wrote Nightfall, he had considerably more suns in his sky. Six or Eight, and probably even this many could not be put in a configuration that would banish night forever. Even in the story all but one star was clustered in one part of the sky, and then another planet eclipsed it.

EDIT:

An interesting thought is for the red sun and the yellow sun to be in orbits like the Sun and Jupiter and then have a dwarf star in the L4 and L5 points of that system. Then these 4 suns would be orbitally locked with respect to each other, 60 degrees before and behind the yellow sun in its orbit. I'm not sure this would totally banish night for good even so, but the suns would be in fixed relation as long as the orbits held.

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A real issue I see with this world is that three stars isn't enough to banish night perpetually...these stars must orbit each other.

So the planet orbits one star, the sunlike star. The other two need to be far enough away to avoid perturbing the orbit of the planet. If they are close to the sunlike star, they will not light up the night sky, so that's out. So instead they will have to be distant. In this case the dim star, if far out past Pluto will likely be 'just another star' and not light up the night. The Red Giant, even if it does light up the night when the planet is between the sun and the giant, will not do so a half year later when the planet is on the other side of the orbit. Any odd configuration you set up will change as the suns orbit each other, with some period of hundreds to thousands of years or less.

When Asimov wrote Nightfall, he had considerably more suns in his sky. Six or Eight, and probably even this many could not be put in a configuration that would banish night forever. Even in the story all but one star was clustered in one part of the sky, and then another planet eclipsed it.