# How Big Can the Habitable Zone Be in a G-Type Binary System?

Here's the basic setup:

There is a binary solar system somewhere in an elliptical galaxy (said to be more suitable for habitability than spiral galaxies like our Milky Way.) The first star is a G-type main-sequence star, a yellow dwarf, a sun. The second star is another of the same type, orbiting the first star from a distance of 150 million miles.

With this information, measured either in miles or AUs, how far from the stars and how wide would the habitable zone be?

• I have revised and expanded my answer. Sep 23, 2020 at 2:41

The stars are too far apart at 150 million miles to have a single habitable zone around both of them. And probably way too close to have stable planetary orbits in their separate circumstellar habitable zones. The separation between the stars you have selected is probably close to the worst possible separation between two stars with about the same luminosity as the Sun.

You should look up Stephen H. Dole's Habitable Planets for Man (1964, 2007).

https://www.rand.org/content/dam/rand/pubs/commercial_books/2007/RAND_CB179-1.pdf[1]

If there are two stars orbiting close together, and they have almost identical luminosity, at a specific distance from the pair the intensity of radiation received from the two stars will be twice that received from only one of them.

Imagine that a planet orbited the Sun at a distance twice the distance of the Earth from the Sun. Because of the inverse square law, that planet would recieve only a quarter of the radiation from the Sun that the Earth gets. So if you doubled the sunlight emitted by putting two stars with the luminosity of the Sun in the position of the Sun, a planet orbiting the two stars at twice the distance of the Earth would receive only half the intensity of radiation which the Earth receives from one Sun.

For a planet orbiting two stars which are both equal in luminosity to the Sun to receive the same intensity of radiation as Earth receives from the Sun, that planet would have to orbit aroudn the two stars at a distance from the two stars which is the square root of two times the distance betweeen the Earth and the Sun. So that planet would orbit around the two stars at a distance of about 1.4142 times the distance between Earth and the Sun.

Similarly, the inner edge of the habitable zone around both of the stars of luminosity equal to the Sun's would be 1.4142 times the distance of the inner edge of the Sun's circumstellar habitable zone, and the outer edge of the habitable zone around both of the stars of luminosity equal to the Sun would be 1.4142 times the distance of the outer edge of the Sun's circumstellar habitable zone.

You should read my answer to the question

https://worldbuilding.stackexchange.com/questions/151028/what-is-the-theoretical-maximum-number-of-habitable-planets-in-one-solar-system/151066#151066[2]

In it, I also mention the simple rule that the way to find the inner and outer edges, and thus the total width, of a star's circumstellar habitable zone (or the cirmstellar habitable zone around two close stars) is to multiply the inner and outer edges (and thus the todal width) of the Sun's circumstellar habitable zone by the luminosity of that star (or stars) relative to the luminosityof the Sun.

So what is the size of the Sun's circumstellar habitable zone?

My answer points how that serveral scientists have estimated or calculated the inner or outer edges, or sometimes both, of the Sun's circumstellar habitable zone, and that their figures differ, sometimes by a little and sometimes by a lot.

The broadest possible range (combining different estimates) for the Sun's circumstellar habitable zone is about 481 times as wide, and about 1,436,139,559 kilometers wider, than the narrowest possible range (combining different estimates) for the Sun's circumstellar habitable zone.

If someone is writing a story where there is one planet with life in a fictional solar system, and they want to be absolutely certain the planet orbits at a distance from its star where life is possible, they should make the planet orbit at a distance equal to some distance within about 0.5 percent of the Earth's average distance from the sone, multiplied by the star's luminosity compared to the sun's luminosity.

If they make the planet orbit its star at an average distance somewhere between 0.995 and 1.005 times the distance of the Earth from the Sun, multiplied by the star's luminosity relative to the Sun, there should be very little probabilty that later scientific discoveries will prove that their planet is too close or too far from its star to have temperatures suitable for life.

But if a science fiction writer wants to have two or more planets orbiting within the circumstellar habitable zone of their star (or stars in a binary star system) they will have to decide which estimates for the inner and outer edges of the Sun's habitable zone seem most plausible to them, and then multiply those inner and outer edges by their star's luminosity relative to the Sun, to find the edges of their star's habitable zone. And then try to figure out if two or more planets can have orbits within that circumstellar habitable zone that will be stable for the billions of years that it may take for planets to become interesting for a science fiction story.

I should note that there are about a dozen estimates of the inner or outer edges, or both, of the Sun's circumstellar habitable zone, made since Dole's estimate in Habitable Planets for Man in 1964. Many of them use far more up to date scientific knowledge and more advanced computations than was available to Dole. Thus some of them may be far more accurate than Dole's estimate.

however, most estimates of the Sun's habitable zone are estimates of the habitable zone for carbon based lifeforms which use liquid water. As we all know, there are countless thousand of species of lifeforms on Earth which fourish in habitats which would be instantly fatal for humans and all lifeforms with similar environmental requirements to humans.

But the habitable planets desirable for science fiction writers are usually ones where large land dwelling multi celled animals which breath oxygen can live, and often planets where humans can survive and flourish. It is quite possible that the circumstellar habitable zone for humans and for lifeforms with similar requirements may be much narrower than the circumstellar habitable zones for water using lifeforms in general.

Thus it is possible that Dole's estimate of the Sun's circumstellar habitable zone might still be the best one for science fiction writers.

• "If you are interested in the size of the habitable zone areound two close stars in a binary system, I do discuss that." How close? Sep 22, 2020 at 22:54
• @JohnWDailey As pointed out in the answer linked to, one can simply multiply the inner and outer edges of the Sun's habitable zone by the luminosity of the other star (or two stars) to get the size of the habitable zone of that star or stars. Of course, as I discuss in that answer, the size of the Sun's habitable zone is highly uncertain. Sep 23, 2020 at 1:23