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Disclaimer: I know that the term ‘double binary’ isn’t real (yet).

Hypothetically, there is two pairs of binary systems with the center of gravity for the individual binaries are orbiting in a binary pair. Could this semi-chaotic orbit have planets that aren’t ripped apart by gravity?

Edit: all stars are G-type stars like our sun and the planets are orbiting at 10-20Au from the central center of gravity

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    $\begingroup$ Are you looking at a star system with two pairs of stars? That's a normal and non-controversial configuration for stars as long as the distance between the pairs is large enough - see for instance the six-member Castor system. $\endgroup$
    – Cadence
    Sep 6, 2022 at 18:09
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    $\begingroup$ It's complicated. I remember that some sort of back of the envelope calculations exist for the zones of stability. The distance between the stars or binary pairs and their masses are the key factors. You should expect stable zones around each star, each pair and each pair of pairs and so on. $\endgroup$ Sep 6, 2022 at 18:19
  • $\begingroup$ @Blue Skin and Glowing Red Eyes You really should look at my answer, even though you have already accepted a diferent answr. I think you will find it quite informative. $\endgroup$ Sep 8, 2022 at 20:18

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Even though there is an accepted answer, I guess I will answer anyway.

A "double binary" would be a form of star system with 4 stars. An astronomical term for a 4 star system is a quartenary system.

Some quartenary systems have two binary stars. Examples include:

Capella, a pair of giant stars orbited by a pair of red dwarfs, around 42 light years away from the Solar System. It has an apparent magnitude of around 0.08, making Capella one of the brightest stars in the night sky.

Mizar is often said to have been the first binary star discovered when it was observed in 1650 by Giovanni Battista Riccioli[44], p. 1[45] but it was probably observed earlier, by Benedetto Castelli and Galileo.[citation needed] Later, spectroscopy of its components Mizar A and B revealed that they are both binary stars themselves.[46]

https://en.wikipedia.org/wiki/Star_system#Quaternary

Other quartenary systems might include a binary and two single stars orbiting at various distances, like Xi Tauri.

It is posible for planets to form and have stable orbits in quadruple star systems.

The Kepler-64 system has the planet PH1 (discovered in 2012 by the Planet Hunters group, a part of the Zooniverse) orbiting two of the four stars, making it the first known planet to be in a quadruple star system.[47]

KOI-2626 is the first quadruple star system with an Earth-sized planet.[48]

https://en.wikipedia.org/wiki/Star_system#Quaternary

The quesiton includes:

Edit: all stars are G-type stars like our sun and the planets are orbiting at 10-20Au from the central center of gravity.

And that is a bit of a problem if you want one or more of the planets to be habitable for human beings or similar lifeforms.

As far as I know there are not yet any examples of any planet orbiting around more than two stars, even if there are other stars in that star system. So I can't say that there is proof by an example that a planet could have a stable orbit around four stars in a quadruple or quartenary system.

Suppose that the stars in each binary are separated by 0.01 to 1 AU. In that case the pairs of binaries should be separated by at least about 5 times that distance, or 0.05 to 5 AU. Planets in P type orbits around both stars in a binary need to orbit at several times the seprartion of the two pairs of stars. I expect the minimum ratio should be the same whether a planet orbits two single stars or two pairs of stars.

For a circumbinary planet, orbital stability is guaranteed only if the planet's distance from the stars is significantly greater than star-to-star distance.

The minimum stable star-to-circumbinary-planet separation is about 2–4 times the binary star separation, or orbital period about 3–8 times the binary period. The innermost planets in all the Kepler circumbinary systems have been found orbiting close to this radius. The planets have semi-major axes that lie between 1.09 and 1.46 times this critical radius. The reason could be that migration might become inefficient near the critical radius, leaving planets just outside this radius.[9]

So if the separation between the binary stars is about 0.05 to 5 AU, the minimum stable orbital distance around all four stars should be about 0.10 to 20 AU. Thus it would be possible for planets to have stable orbits around all four stars in a quartenary system at distances of 10 to 20 AU from the center of mass.

Of course it is also possible for all of the stars to be separated by much more than 10 to 20 AU in a quartenary star system.

Now asume that you want at least one of the planets to orbit at a distance where it will receive exactly the same amount of radiation from the four stars combined as Earth receives from the Sun. I call that distance the Earth Equivalent Distance, or EED.

If the system has four stars and each star has exactly the same luminosity as the Sun, the guarentary system will have exactly 4 times the luminosity of the Sun. According to the square root law, the EED of the quartenary star will be the square root of 4, or 2, AU from the center of mass of the quartenary star. And that is not consistent with the planets orbiting at about 10 to 20 AU. Not if you wabt any of those planets to have Earth like temperatures and be habitable.

If you don't desire any of those planets to be habitable for liquid water using life, there is no problem putting them at distances between 10 to 20 AU, or even at 100 to 200 AU, or 1,000 to 2,000 AU.

If you desire that any of the planets orbiting at 10 to 20AU behabitable for humans or for other liquid water using lifeforms, there is some hope.

A planet can be habitable for oxygen breathing humans in particular or liquid water using lifeforms in general if it orbits its star closer or father than the exact EED and gets more or less radiation than Earth gets from the Sun. There is a range of distances from the star where a planet would be in the Goldilocks zone or circumstellar habitable zone.

So how much closer to or farther from the star (or stars in this case) than the EED does the habitable zone extend? Nobody knows for certain.

You could simply multiply or divide the luminosity of the star relative to the Sun to fiind the inner and outer edgesof the cricumstallar habitable zone. But there is considerable disagreement about the inner and outer edges of the Sun's circumstellar habitable zone.

This lists includes about a dozen different estimations or calculations.

https://en.wikipedia.org/wiki/Circumstellar_habitable_zone#Solar_System_estimates

One of the most widely used, that by Hart et al, 1979 is very narrow, from 0.958 to 1.004 AU. In your system, the Hart habitable zone would extend from 1.916 to 2.008 AU.

Another one very widely used, that by Kasting et al, 1993, is much wider, with a conservative zone from 0.95 to 1.37 AU and an optimistic zone 0.84 from to 1.67 AU. So in your system the Kasting conservative zone would go from 1.9 to 2.74 AU, and the Kasting optimistic zone from 1.68 to 3.34 AU.

Pierrehumbert and Gaidos, 2011, calculated that the outer limit of the habitable zone could extendout to 10 AU.

https://www.semanticscholar.org/paper/HYDROGEN-GREENHOUSE-PLANETS-BEYOND-THE-HABITABLE-Pierrehumbert-Gaidos/8e28074aa2e2fd9f4fe3b7f758e37039d2b6b530

Thus in your system there could habitable planets 10 to 20 AU from the center of mass of he 4 stars.

However, they mean habitable for liquid water using lifeforms in general and not for oxygenusing lifeforms in particular. The planetary atmospheres necessary to have liquid water temperatures that far out would include a lot of hydrogen. Hydrogen combines with oxygen to form water. So large amounts of hydregen and oxygen in the same atmosphere are not very probable. Furthermore their calculations use very dense atmospheres, atmosphere so dense that they kill beings with the same requimements as humans, no matter what gases they wre composed of.

So having planets 10 to 20AU from the center of mass of the 2 stars is fine if you don't want any life on those planets.

It is fine if you want lifeforms with an hypothetical alien biochemestry who can live at very clold temperatures.

It is even fine if you liquid water using lifeforms, if the planets are kept warm enough for liquid water by dense and hydrogen rich atmospheres and none of those lifeforms breathe oxygen.

But it is not fine if you want thoes planets to be inhabited by lquid water using and oxygen breathing lifeforms like humans or with similar requirements. Because an atmosphere breathable for oxygen breathers is inconsistent with liquid water tempertures at distances of 10 to20 AU from a set of 4 stars each with the luminosity of the Sun.

Of course if there is a planet with a hydrogen rich atmosphere warm enough for liquid surface water, and if that planet does have lifeforms, humans could visiting that planet and wlak the surface wearing breathing gear. Of course hydrogen has very tiny parrticles which easily infiltrate most gas proff barriers, so they would likely have higher and higher concentrations of hydrogen mixed in the with oxygen they breathed over time. Thus there should be a strict time limit to how long it would be safe to spend outdoors even with bottled oxygen and breathing masks.

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Planets may not survive in a double binary system

As told here

There is a star system 146 light years from Earth that is quite strange. At its centre is a set of binary stars, and around that loops another binary pair. In between is a ring of dust and gas that’s set at a very odd angle.

The dust and gas of this system, which is called HD 98800, are part of a disc that may be forming planets in a kind of cosmic nursery. Instead of lying on the same plane as the central stars, this disc’s orbit is perpendicular to that.

Grant Kennedy at the University of Warwick in the UK, who used the Atacama Large Millimeter Array telescope to image the system, says,

Any planets that form here might not survive this bizarre setup. The inner stars orbit one another every year, and a planet in the disc would orbit them every 3 years. On a tilted planet, seasons would be affected by both of these movements. If you were on such a planet, you’d have two shadows some of the time, and one or two stars over the horizon at times. There would be some degree of chaos.

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