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I would like to know how close two planetary systems could be without having an adverse effect on each other. My goal is to drastically improve the chances of having habitable planets near enough that humans having the technology of today could realistically send manned spacecraft to other planetary systems and even have useful communication and trade.

I'm thinking specifically about our own solar system, and to reduce the guessing, let's assume the other system is identical to ours: same sun, same planets. Their "Earth" could be lifeless, I don't think it affects anything.

More difficult to define is what it means to "adversely affect" our own system. I have a few ideas, but these are not 100% set in stone:

• The other sun should not be brighter in our sky than Venus at its brightest.


• It should not be possible to detect any gravitational effects on our outer planets due to the presence of the other system using the best instruments to date.¹ - No stealing of planets.


• There should be no weird electromagnetic effects like auroras from the other sun other than the visible light and whatever else is expected from observing another star.


• I do not care about the Oort cloud, simply because I hope that the distance will be less than 1 ly.


• I also don't care about any effect on human mythology. Early astronomers would likely find that this star is special and much brighter than the others, which is fine.

A bonus question: Would it change if we imagine a number of these systems packed in a sphere-packing formation? If I understand correctly, it would amount to 12 neighbors equidistant from the Sun.

^{1. I admit having no clue how much we can detect, so this is one requirement that may have to go.}

The other sun should not be brighter in our sky than Venus at its brightest.

This is your tightest constraint. Astronomers are even now doing searches for Planet X and even for brown dwarfs out in the Oort cloud, and have not yet concluded that nothing is there. This shows that current technology can't with certainty even detect the gravitational effects of a Sun-like star at lightyear distances. There are certainly not large gravitation effects (other than the discounted Oort cloud disruptions) from a sun-like start 1 light year away.

OTOH, Venus peaks out at -4.9 magnitudes while Alpha Centauri i at -0.3. So Alpha could get 4.6 magnitudes brighter before it was brighter than Venus. 5 magnitudes is a factor of 100 (a difference of one magnitude is a change in brightness of the fifth root of 100), so if Alpha got about 73 times brighter it would be as bright a Venus. 73 times brighter is 8.5 (the square root of 73) times closer, which is about a half a light-year distant instead of its current 4.3 ly.

So a half light year is probably the limiting distance for a Sun-like star appearing no brighter than Venus. Dimmer stars (which are still capable of having life-bearing planets) could get closer and still not be brighter than Venus.

I very much doubt that having twelve of them would be significantly different than having one -- though the sky would be pretty spectacular!

I Agree with Mark Olson that having the nearest star appear no brighter than Venus in the sky is the main factor setting a minimum distance for the neighboring stars. And I think that half a light year away is not a very great distance improvement. That would allow the nearest star with the same absolute magnitude as the Sun to be 8.6 times as close as Alpha Centauri, or 11.62 percent as far as Alpha Centauri, which is very helpful, but still heart breakingly far for current space travel technology. It would be a much better improvement to make the nearest star one percent as far as Alpha Centauri, or 0.1 percent as far as Alpha Centauri, or 0.01 percent as far as Alpha Centauri.

If all the neighboring stars are very dim red dwarfs, or if it is permissible for them to look many times as bright as Alpha Centauri, they could be much closer than 11.62 percent as far as Alpha Centauri, and it would be much easier to reach them.

Note that the planets in our solar system have stable orbits despite being 4.37 light years or 1.339 parsecs, from the nearest star system, Alpha Centauri. So it is obvious that 4.37 light years or 1.339 parsecs is larger than the minimum separation between stars necessary for planets orbiting those stars to have stable orbits.

There are many double and multiple star systems in which two or more stars orbit each other. And if two stars in a binary system are far enough apart they can both have planets orbiting in stable orbits around them.

For example, Alpha Centauri C, or Proxima Centauri, is probably part of the same star system as Alpha Centauri A & B. The distance between Proxima and Alpha Centauri A & B is 12,947 plus or minus 260 Astronomical Units (AU), or 1.94 plus or minus 0.04 trillion kilometers. A planet was discovered orbiting Proxima Centauri in 2016. Planet Proxima Centauri b is estimated to have at least 1.3 times the mass of Earth and orbits at a distance of about 0.0485 AU with a period of 11.186 Earth days. Proxima Centauri b
orbits within the habitable zone of Proxima Centauri.

Since there are approximately 206,264.806 AU in a parsec, and Alpha Centauri is about 1.339 parsecs or 276,188.56 AU from the Sun, the distance from Proxima Centauri to Alpha Centauri A & B is about 0.0468773, or 4.68 percent, of the distance between Alpha Centauri and the Sun. And that distance is great enough for Proxima Centauri b to have a stable orbit around Proxima Centauri within the habitable zone of Proxima Centauri. (Proxima Centauri is a flare star so there is doubt whether Proxima Centauri b could be habitable)

Alpha Centauri A, or Rigil Kentaurus, and Alpha Centauri B, or Toliman, orbit each other at distances ranging from 11.2 AU (1.68 billion kilometers) to 35.6 AU (5.33 billion kilometers), or from about the distance of Saturn from the Sun to about the distance of Pluto from the Sun.

A planet of Alpha Centarui B, Alpha Centauri Bc, was announced in 2013. If it is real it orbits at a distance of about 0.10 AU and a year about 12 Earth days long. It is closer to Alpha Centauri B than the habitable zone and probably has lakes of molten lava.

This indicates that two stars can get as close as 11.2 AU without disrupting the orbits of their closest planets, though obviously planets orbiting at the distance of Saturn or farther out would have their orbits disrupted.

It has been calculated that the habitable zone of Alpha Centauri A would be about 1.25 AU out and the habitable zone of Alpha Centauri B would be about 0.7 AU (100 million Kilometers) out. It has also be calculated that planets in those habitable zones would have stable orbits, though none have been discovered yet.

If two stars can get as close as 11.2 AU to 35.6 AU without disrupting the orbits of their inner planets, then two stars can get within 0.0000405 to 0.0001288, or 0.00405 percent to 0.01288 percent, of the separation between the Sun and Alpha Centauri without disrupting the orbits of their inner planets.

The Wikipedia article Habitability of Binary Star Systems says:

In non circumbinary planets, if a planet's distance to its primary exceeds about one fifth of the closest approach of the other star, orbital stability is not guaranteed.[5]

http://www.solstation.com/habitable.htm#sthash.UNS47OKi.dpbs1

This implies that if a planet's orbital distance is less than about one fifth of the closest approach of the other star, its orbital stability should be or might be guaranteed.

So if Earth was part of a binary star, and the nearest approach of the other star to the Sun was farther than about 5 AU, the orbit of the Earth would remain stable and almost unchanged.

However, these observations and calculations are for planets orbiting stars in binary systems where the two stars have elliptical orbits around their common center of gravity and thus travel at the correct orbital velocities.

Two stars separately orbiting the center of the galaxy that happen to pass close to each might have significantly greater relative velocities. And that might mean that they would have to pass at distances many times as great as 5 AU to avoid disrupting the orbits of planets in their habitable zones.

Anyway, such close passes would certainly disrupt the orbits of small bodies in the outer solar systems of the two stars which might result in multiple extinction events caused by asteroid and comet impacts on any habitable planets.

Not difficult at all.

Here is an artist's concept of what noon look on Pluto (about 30 AU away)

If you go out a few light weeks away (1 light week is ~ 1200 AU) you can easily have a Sun-like star appear as bright as Venus.

As gravitational effects go - the force of gravity is inverse of the square of the distance, so it's fades very quickly. Sun's gravitational pull at 1 AU (the average Sun-Earth distance) is tiny portion of Earth's gravity ( https://van.physics.illinois.edu/qa/listing.php?id=184 ) but obviously that's enough to keep Earth orbiting around it. Stealing of planets could still happen, but if it does, it will at galactic speed - over hundreds of millions of years. We'll still be able to detect it - we use the gravitational effects to detect exoplanets hundreds of light years away, but it won't have any practical effects on our planet.

This far out there won't be any auroras, the solar wind of the other sun will be way too dispersed for that and the solar wind of our Sun will keep it out of our solar system.

This all assumes that the neighboring star is similar to the Sun. However, the Sun is bigger than your average star, it's G2V star, so you can easily postulate that the other star is smaller, less luminous star.

So in short - a few light weeks will probably be enough to keep the visible effects to a minimum.

As for having a cluster of such solar systems close by - also not a problem. The Solar system is in a region of the Milky Way known as the Orion arm, which is not very dense - the solar systems are on average 3 - 4 light years away.
If we were in the galactic center, we would have a lot other solar systems that are a lot closer to us. If you want a bunch of neighbors that are close, just place the Solar system in a denser part of the galaxy.

https://en.wikipedia.org/wiki/Orion_Arm#/media/File:OrionSpur.png

It Depends.

Two stars may be gravitationally bound, or not.

If bound, they may remain a binary system for billions of years, and orbits of all planets and comets will get adjusted to having two heavy bodies in the system.

If not bound, the stars are going to pass away from each other in a few tens of thousand years. While passing, they will definitely disturb each other's Oort's clouds, sending number of comets into the inner systems. Possibly, planet's orbits will also be disturbed, and some asteroids will be set on collision course with inhabited planets - but this will likely take longer time (100,000s, maybe millions years) to play out, so doomsday will come long after stars had passed each other.

As far as the distance go, Sun-like star needs to be about 0.4 light years away to look as bright as Venus (calculator). For a smaller K-type star, distance can be shorter, like 0.2 light years. This is probably enough for the stars to be gravitationally bound, forming a stable binary system.