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For a certain reason, I needed two habitable similar earth-like planets very close to each other. After various information gathering, I gave up on double planet and gas giant moons, because tidal forces would be too high. Eventually, one solution offered itself - planets around each of two binary sun-like stars.

Now, I have two similar planets orbiting two similar stars in binary star system, both around 1 AU from their own star. Now in this post, it has been answered that with stars orbiting at ~ 100 AU, everything seems fine. But my goal is to put the two stars closer, as close as possible without causing too much mess, ideally 25-30 AU range, but would like to know if even less is possible. My main concern are tidal forces, but there might be other factors I am not taking into account.

So, how close can we put two sun-like stars together for my planets to remain Earth-like?

Yes, I am aware that at those distances, second sun would be a very bright, so bright that it would be possible to see during the day, (as for example, at 25 AU, you'd get 500~600(24x24) times less intense light from second star than from the star you orbit, which is still 800 more than Earth gets from the moon). That is one exception to Earth-like standard I'm willing to concede.

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  • $\begingroup$ A very good question. I don't think that there is a definitive answer, the closer they get the less stable the system is. But I will give it some thought, it should be possible to come up with some sort of approximate answer... $\endgroup$ – Slarty Dec 10 '19 at 8:56
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    $\begingroup$ A non-circumbinary orbit may become unstable if the planet's orbital distance around its primary exceeds 1/5 the closest approach to the other star. This was based on the article below. Though not specified, my assumption is the result relies on roughly equally massive stars. en.m.wikipedia.org/wiki/Habitability_of_binary_star_systems $\endgroup$ – Christmas Snow Dec 10 '19 at 9:11
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    $\begingroup$ Take a look there: dsf.unica.it/~fiore/binaryth.pdf $\endgroup$ – Stefano Balzarotti Dec 10 '19 at 9:12
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I don't know why Fabius Maximus thinks that tidal forces would be too strong in a double planet or a a habitable moon of a gas giant planet.

Part One of two: Two habitable planets orbiting the same star.

But If Fabius Maximus thinks that is the case, the next logical step would be to have two habitable planets orbiting the same star in different orbits, close enough together to both be in the habitable zone of their star and have similar climates.

In old fashioned science fiction stories from the first part of the 20th century, it was quite common to depict Venus, Earth, and Mars as all being habitable planets within the Sun's habitable zone.

Modern astronomers still tend to believe that it is possible for more than one planet to orbit in the habitable zone of a star and thus have temperatures suitable for life.

Of course, from time to time a different team of scientists will team up to calculate the inner edge, or the other edge, or both, of the Sun's habitable zone. Thus there are several different estimates of the size of the Sun's habitable zone.

In this list here:

https://en.wikipedia.org/wiki/Circumstellar_habitable_zone#Solar_System_estimates1

There are some widely varying calculations about the size of the Sun's habitable zone.

Hart et al in 1979 made the narrowest estimate of the Sun's habitable zone, between 0.95 AU and 1.01 AU. That estimate would make it very improbable that any star could have two planets in its habitable zone.

Kasting et al in 1993 made the most commonly used estimate of the Sun's habitable zone, with a conservative zone between 0.95 and 1.37 AU, and an optimistic zone between between 0.84 and 1.67 AU. It would be much more probable to have two planets orbiting in Kasting's conservative zone than in Hart's, and more probable still for Kasting's optimistic habitable zone.

Other estimates put the inner edge of the habitable zone as far in as 0.38 AU (Zsom et al, 2013) and the outer edge as far out as 10 AU (Pierrehumbert and Gaidos, 2011).

Astronomers have discovered hundreds of systems with more than one planet, and those systems vary widely in their orbital and other characteristics.

The orbits of Kepler-70b & c are separated by only about 0.0016 AU or 240,000 kilometers, and it is possible that there could be a third planet orbiting between them.

The orbits of Kepler-36b & c are separated by a larger absolute distance but a smaller relative distance, with the orbit of Kepler-36c only 11 percent wider than Kepler-36b.

https://en.wikipedia.org/wiki/List_of_exoplanet_extremes2

The star TRAPPIST-1 has four potentially habitable planets in its habitable zone, and they orbit very close to each other.

The orbits of the TRAPPIST-1 planetary system are very flat and compact. All seven of TRAPPIST-1's planets orbit much closer than Mercury orbits the Sun. Except for b, they orbit farther than the Galilean satellites do around Jupiter,[41] but closer than most of the other moons of Jupiter. The distance between the orbits of b and c is only 1.6 times the distance between the Earth and the Moon. The planets should appear prominently in each other's skies, in some cases appearing several times larger than the Moon appears from Earth.[40] A year on the closest planet passes in only 1.5 Earth days, while the seventh planet's year passes in only 18.8 days.[38][35]

The orbit of TRAPPIST-1e is only 1,050,000 kilometers wider than the orbit of TRAPPIST-1d.

The orbit of TRAPPIST-1f is only 1,380,000 kilometers wider than the orbit of TRAPPIST-1e.

The orbit of TRAPPIST-1g is only 1,250,000 kilometers wider than the orbit of TRAPPIST-1f.

https://en.wikipedia.org/wiki/TRAPPIST-1#Planetary_system3

The average distance of Earth from the Sun is defined as 1 Astronomical Unit, or AU.

If you make the star in your solar system exactly as luminous as the Sun, you could put one of your habitable planets at a distance of 0.96 AU and the other one at a distance of 1.0656 or 1.070 AU. The inner planet would receive slightly more heat from its star, and the other planet would receive slightly less heat from its star, than Earth gets from the Sun. The orbits of the two planets would be separated by about 16,170,000 kilometers.

Part Two of Two: Two habitable planets orbiting two different stars in the system.

In a binary or double star system, there are two possible types of orbits for planets. One is a circumbinary or P-type orbit, where a planet orbits around both of the stars. The other is an S-type orbit where a planet orbits around one of the two stars.

Since the luminosities, masses, and orbits of the two stars in a binary can vary widely, there are many binary systems where a planet could not have a stable orbit in the habitable zone of either star or around both of them. But there are many other binary systems where planets can have stable orbits, either P-type or S-type, in a habitable zone.

The OP asked for a binary system with two habitable planets in S-type orbits, one around each star. That is certainly possible. It has been calculated, for example, that planets could have stable orbits in S-type orbits with the habitable zones around both Alpha Centauri A and Alpha Centauri B.

According to one list, the closest known distance between stars with a planet orbiting one of those stars is about 12 to 17 AU, with a planet orbiting about 0.7 AU.

https://en.wikipedia.org/wiki/List_of_exoplanet_extremes2

http://www.openexoplanetcatalogue.com/planet/OGLE-2013-BLG-0341L%20B%20b/4

http://ogle.astrouw.edu.pl/cont/4_main/epl/ogle_0341/ms.pdf5

In my opinion, it would probably be safe to have the two stars in the system have a nearest approach of about 10 to 20 AU, and each have a habitable planet orbiting it at about 1 AU, as well as other planets in S-type orbits around either star, and possibly other, not habitable, planets in P-type orbits at great distances from the two stars.

And of course there are various scientific discussions about which separation of stars is best for long term stable planetary orbits.

https://arstechnica.com/science/2013/01/binary-star-systems-make-for-unstable-planets/6

https://www.aanda.org/articles/aa/pdf/2005/16/aa0238-04.pdf6

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I don't think tidal forces would be much of a problem. Our sun is responsible for roughly a third of the tidal forces felt on Earth, and if the other star is 25 AU away, the nearer planet would receive 1/625 the tidal forces from that. It will also receive 1/625 the heat and light from the farther sun than from the nearer; not enough to significantly change climate.

It is likely that both planets will be in orbital resonance with the orbits of the stars around each other, as such orbits have greater stability. Two sun-sized stars orbiting their common center of gravity in circular orbits at a distance of 25 AU will have an orbital period of ca. 32,250 days or ca. 88 years. Since your planets, in order to be Earth-like, must have orbits close to one year, there are many available resonances, including 1:88. Hence, I don't foresee any major problems with having the suns 25 AU apart.

You could probably have them even closer, say at 10 AU, or roughly twice the distance between the Sun and Jupiter. Tidal forces and solar infall from the more distant star will then be 1/100 that of the nearer star; still fairly negligible. The orbital period of the two stars will then be ca. 8,150 days or ca. 22 years, and you can have orbital resonance of e.g. 1:22.

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  • $\begingroup$ Tide falls with the cube of distance, not the square. $\endgroup$ – Anton Sherwood Dec 11 '19 at 1:54
  • $\begingroup$ @AntonSherwood. Ok, thanks! I just assumed that tide was proportional to gravitational pull. Which factor did I miss? $\endgroup$ – Klaus Æ. Mogensen Dec 12 '19 at 9:51
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    $\begingroup$ The tide exerted by A on B is the difference between A's gravity on the near side of B and that on the far side. This is proportional to the product of B's diameter and the derivative (that's calculus-talk for slope) of A's g-field with respect to distance. The first derivative of r^(-2) is -2r^(-3). $\endgroup$ – Anton Sherwood Dec 13 '19 at 3:54
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Well, if what you want is two Earth-like planets extremely close together, the best solution would be to just have them both orbit one parent star in orbits at different distances. If you look at this chart, Earth is actually on the near end of our sun's habitable zone (https://en.wikipedia.org/wiki/Circumstellar_habitable_zone#/media/File:Diagram_of_different_habitable_zone_regions_by_Chester_Harman.jpg)

It could be conceivable that two planets around a sun-like star could have orbits of 1 AU and 1.2 AU and both be very Earthlike, on stable orbits relative to each other, and quite close for much of their orbits. You may want to consider this straightforward if rather plain approach.

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  • $\begingroup$ My problem was I need almost same atmosphere, almost same air pressure, almost same climate. Hence why I didn't choose that option. $\endgroup$ – Failus Maximus Dec 10 '19 at 12:12
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    $\begingroup$ That is completely still possible! By changing around the masses and tilts, two planets could have the exact same climate even at different differences from the star. You could even change the densities to preserve the acceleration due to gravity on both. It would at the very least be a more likely scenario than two binary stars each with its own earth-like planet both on stable orbit. A stable orbit is incredibly difficult on any 3-body system where two of the bodies are of roughly equal mass. $\endgroup$ – Anthony Khodanian Dec 10 '19 at 13:04
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    $\begingroup$ I have just asked a question here: astronomy.stackexchange.com/questions/34271/… which I believe might help in resolving your question - watch this space $\endgroup$ – Slarty Dec 10 '19 at 17:08
  • $\begingroup$ As a side issue you might find this of interest worldbuilding.stackexchange.com/questions/163206/… the point being do you have two biogenesis events, one on each planet or just one spreading from one planet to the other? One might make the organisms on each world a little more compatible (based on the same core biochemistry perhaps and could be achieved by a cometary impact and material traveling between the planets). Two would likely mean the biochemistries are very alien and probably mutually toxic to each other. $\endgroup$ – Slarty Dec 11 '19 at 17:17
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I don’t think that it’s possible to give an exact answer to this question as there is no viable general solution to the 3 body problem. However in S type non-circumbinary planets (those that orbit a single star in a binary system rather than P type circumbinary which orbit both stars) it has been suggested that the orbit of the planet should be at least 5 times closer to one star than the other to be in a stable orbit.

I suggest making it 10 times closer to be on the safer side. So if the distance between star A and star B is 10 AU the distance between each planet and its parent star can be 1 AU. Probably best to ensure that both stars and planets have near circular orbits, any significant eccentricity would mean the stars need to be further apart.

Additional reference

With thanks to @userLTK for help from the Astronomy stack exchange

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