WBH Mean Temperature Luminosity

[Dodo98]

@Geir Hey Geir, I've got another question. In the section dealing with the calculation of mean temperature using a formula, it is not entirely clear to me which stars count as “inner” stars, i.e., those whose luminosity must be added together, and which count as “external” stars, i.e., those that are initially ignored. The rule text says that if a world orbits multiple stars, these “inner” stars are added together. If I now have a 3-star system with Primary, Primary Companion, and Near Star, and a world orbits the Near Star in a direct orbit, then theoretically it would also orbit the Primary and Primary Companion, wouldn't it?

Instinctively, I would have said that you add up the luminosity of all three stars. Since you also add up all the masses of the stars located closer than the star that is directly orbited when determining the orbital period, I am relatively confident in my assumption. But I wanted to be on the safe side, since none of the examples in the book deal with this specific case.

 

[Geir]

@Geir Hey Geir, I've got another question. In the section dealing with the calculation of mean temperature using a formula, it is not entirely clear to me which stars count as “inner” stars, i.e., those whose luminosity must be added together, and which count as “external” stars, i.e., those that are initially ignored. The rule text says that if a world orbits multiple stars, these “inner” stars are added together. If I now have a 3-star system with Primary, Primary Companion, and Near Star, and a world orbits the Near Star in a direct orbit, then theoretically it would also orbit the Primary and Primary Companion, wouldn't it?

Instinctively, I would have said that you add up the luminosity of all three stars. Since you also add up all the masses of the stars located closer than the star that is directly orbited when determining the orbital period, I am relatively confident in my assumption. But I wanted to be on the safe side, since none of the examples in the book deal with this specific case.

You should add them al together, though it will often not add much to the planet's variation in temperature. For a planet that orbits all the stars, then it is required, but even then it's simplified.

To do it right, you should figure out which geometry causes a maximum increase and which causes the least increase. That can get tricky, especially if you add in eccentric orbits. And since other factors such as orbital inclination, location and time of periapsis are not normally included (see page 28), then well, it depends on how important you think the detail is (the whole MOARN thing).

 

[rinku]

Keep in mind the inverse square effect. Any star that's close will be dominant over any star that's further away, unless the further away star is ESPECIALLY luminous; as an example, if a world is orbiting a star with one Solar luminosity at 1AU, a companion star of the same luminosity at 2AU from the planet is only providing 1/4 of the light. More likely setups would have the companion at much further distances - at 8AU it's only providing 1/64th of the light the main star is, or 1.5%. Enough to affect local weather a little and give brighter nights when it's in opposition, but can mostly be ignored.

If the star that was 8AU away was 64 times the luminosity of the one the planet was orbiting, they'd have the same effect, and you absolutely would need to work it out.

Edit:
Further thought - as a general rule of thumb, a habitable world has to be in a stable orbit. Two sizable stars means either it's orbiting both far away enough that they can be treated as one light source, or one of them is far away enough that it's just a thing in the sky. Potentially you might have a world located at a lagrange point for a binary pair, but those aren't as stable as most people assume, and that's probably only going to work if one of the stars is small (and so just becomes a local quirk. The big star will be providing the bulk of the light, with the small one giving an extended dawn or twilight at one end of the day, assuming the world is rotating more or less on the ecliptic)