How Can Planetary Movements Affect Time and Illumination on an Inhabited Planet?

[delie]

Hey,I was wondering if anyone could point me to some reliable and vulgarized sources about complex planetary movements?

For instance, let's imagine an inhabited earth-like planet having four moons of various sizes and two suns. How can I reastically establish the "time decorum" on the planet? Would it be day all the time? Would the inhabitants of this planet go through eclipses like we go through political and ecological crises, as of late?
What material could help me solve these questions?

As an FYI, I can be considered as a total noob when it comes to space. But i make up for it with discipline!Cheers,
D.

 

[PeroK]

Hey,I was wondering if anyone could point me to some reliable and vulgarized sources about complex planetary movements?

For instance, let's imagine an inhabited earth-like planet having four moons of various sizes and two suns. How can I reastically establish the "time decorum" on the planet? Would it be day all the time? Would the inhabitants of this planet go through eclipses like we go through political and ecological crises, as of late?
What material could help me solve these questions?

As an FYI, I can be considered as a total noob when it comes to space. But i make up for it with discipline!Cheers,
D.

If a solar system has two stars of commensurate mass, then planetary orbits would in general be chaotic.

You could search for "three body problem". For example:

https://en.m.wikipedia.org/wiki/Three-body_problem

 

[delie]

If a solar system has two stars of commensurate mass, then planetary orbits would in general be chaotic.

You could search for "three body problem". For example:

https://en.m.wikipedia.org/wiki/Three-body_problem

Alright, this looks like a promising start. So based on your source, what I'm looking for specifically is called "classic mechanics", gotcha!

Moreover, if one sun is bigger than the other, then it would make the orbiting more "predictable"?

 

[PeroK]

Alright, this looks like a promising start. So based on your source, what I'm looking for specifically is called "classic mechanics", gotcha!

Moreover, if one sun is bigger than the other, then it would make the orbiting more "predictable"?

As long as one mass dominates, yes.

 

[anorlunda]

For the social aspects, consider the Isaac Asimov SF story, Nightfall.

 

[Borek]

These things are relatively easy to simulate, this is high school physics (classical mechanics plus gravitation) and programming (perhaps with some borrowing from undergraduate courses, but things like Runge-Kutta methods are not difficult to use). Could be there are some ready programs that do just that. Even if not it is a common exercise to do.

Not that it will answer all your questions, for example length of the day is a bit different problem. It depends on initial rotation speed of the planet, but also changes with the system age (in the end you can have a planet that has a day-half and a night-half, once it gets tidally locked).

 

[DaveC426913]

Note that there is more than one type of binary planetary system. For example:

- a planet might have a wide orbit about the barycentre of a tight binary
- a planet might orbit only star A while star B is a distant companion

 

[Astronuc]

I would expect the Alpha star to be the larger (and closer to the center of mass (COM)) or brighter of two stars in a binary system.

Hubble Space Telescope photo of Gliese 623 shows two stars separated by 2 AU.
https://sites.uAlberta.ca/~pogosyan/teaching/ASTRO_122/lect13/lecture13.html

https://www.atnf.csiro.au/outreach/education/senior/astrophysics/binary_intro.html

https://arstechnica.com/science/2012/01/tatooine-like-planets-may-be-common/

Exoplanets—planets in star systems other than our own—have been found in orbit around single stars, with a lone exception: Kepler-16b is circumbinary, having two host stars in close orbit. Now, researchers working with data from the Kepler space-based observatory have identified two more promising exoplanet candidates orbiting binary stars, known as Kepler-34b and Kepler-35b. While the planets most likely are gas giants, the host stars in Kepler-34b are more Sun-like than the Kepler-16 system. These observations indicate that giant exoplanets orbiting two stars may be fairly common, occurring in perhaps one percent of close binaries.

There are also binary systems of large stars
https://en.wikipedia.org/wiki/HD_38282

 

[Orodruin]

As stated, there are many many possibilities. The ones mentioned in #7 are just two of the more obvious examples that would tend to be relatively stable. Another interesting one would be a tidally locked planet in a stable Lagrange point of the double star system. Such a planet would have a large part of its surface lit by at least one star and the two stars would be essentially fixed in the sky.

 

[Devin-M]

The closest star to the Sun, Proxima Centauri has a roughly Earth sized planet within its habitable zone, and Proxima Centauri is part of a triple star system. The other 2 stars in the system are called Alpha Centauri A & Alpha Centauri B.

The star Proxima Centauri is a small red dwarf and the planet Proxima Centauri b orbits that star at about 0.05 AU (20x closer than the Sun-Earth distance), which is still considered “habitable” or able to have liquid water since Proxima Centauri is so small and dim (not even visible to the naked eye on Earth despite being the closest star besides the sun). The Proxima Centauri star orbits the other 2 stars at a distance of about 12950 AU from the center, completing one orbit of the other 2 stars every 550,000 years. The other pair of stars orbit each other once every roughly 79 years at a distance that varies between roughly 11 AU (Sun-Saturn distance) and 35 AU (Sun-Pluto distance)

 

[snorkack]

Hey,I was wondering if anyone could point me to some reliable and vulgarized sources about complex planetary movements?

For instance, let's imagine an inhabited earth-like planet having four moons of various sizes and two suns. How can I reastically establish the "time decorum" on the planet? Would it be day all the time?

Two possibilities for that, one likely, the other can be ruled out with simple reasoning.
The likely reason for "day all time" is tidal locking to star. In which case the near side has day all time.

Now, the ruled out case would be two stars opposite in the sky. It can be ruled out because there is no arrangement for three bodies in a line to be in a stable equilibrium. L1, L2 and L3 are all unstable. A planet can travel through opposition, but that will not be all time.

And then you have the question of defining "day". How many lx do you call "day"?

Would the inhabitants of this planet go through eclipses like we go through political and ecological crises, as of late?
What material could help me solve these questions?

 

[delie]

These things are relatively easy to simulate, this is high school physics (classical mechanics plus gravitation) and programming (perhaps with some borrowing from undergraduate courses, but things like Runge-Kutta methods are not difficult to use). Could be there are some ready programs that do just that. Even if not it is a common exercise to do.

Not that it will answer all your questions, for example length of the day is a bit different problem. It depends on initial rotation speed of the planet, but also changes with the system age (in the end you can have a planet that has a day-half and a night-half, once it gets tidally locked).

And these half-day/night cycles would happen, even with several suns within the vicinity?

I have already seen a simulation of the helical model. In my - uneducated - mind, it was possible for the earthlike planet to be stuck between the two suns within that rotation, making a perpetual day cycle.

In any case, those are some interesting leads you shared with me, thanks!

 

[Orodruin]

I have already seen a simulation of the helical model. In my - uneducated - mind, it was possible for the earthlike planet to be stuck between the two suns within that rotation, making a perpetual day cycle.

What you describe as a planet stuck between two Suns corresponds to putting it in the Lagrange point L1 of the double Sun system. As discussed in post 11, that Lagrange point is unstable and would be like trying to balance a knife on its edge.

 

[snorkack]

One source that looks reliable:
https://stjarnhimlen.se/comp/radfaq.html#10
Note that it is illumination of horizontal surface, not a surface facing sunlight. And Sun is visible when about -0,8 degrees from horizon: 35 minutes refraction plus 15 minutes radius.
Example of applying this for calculation:
Suppose that there were an earth-like planet in habitable zone of Alpha Centauri B.
Since Alpha Centauri B´s bolometric luminosity is 0,5 times Sun, it would be 0,71 AU from Alpha Centauri B. Giving a year of about 0,63 Earth years - about 230 days.
At periapse, Alpha Centauri B is 11,2 AU from A - so at opposition 10,5 AU from the planet.
Alpha Centauri A is about 1,5 times the brightness of Sun - in visible light.
It follows that A is about 70 times dimmer than Sun (10,5²/1,5)
Which means that A at zenith would give 129000/70=1800 lx light. Less than Sun 2 degrees above horizon.
That is day. But it will not be day all time, because as the planet rotates, A will get low on horizon.
When A is 6 degrees above horizon, A will be providing 5620/70=80 lux, and B being at opposition will be 6 degrees under, so 3,4 lux. When A is 4 degrees above horizon, it will be 3550/70=50 lux from A and 30 lux from B - total about 80 lux still.
75...80 lux total when A is low on horizon and B near below is not day (it is 405 lux when Sun is fully under horizon).

 

[delie]

What you describe as a planet stuck between two Suns corresponds to putting it in the Lagrange point L1 of the double Sun system. As discussed in post 11, that Lagrange point is unstable and would be like trying to balance a knife on its edge.

Indeed! I realized that after I responded to the post above. With all the material that has been shared with me here, my downtime is booked for the next few weeks =))

 

[snorkack]

As long as one mass dominates, yes.

And "dominating" does not need to mean that one mass is bigger than the others. It just means that the gravity of one mass must be bigger than the others due to mass and distance.
Examples:
Earth and Venus are similar in mass and distance. Yet both are stable because Sun is much more massive than either.
Triple stars are abundant in sky. And stable. And commonly comparable in mass (they are all stars). But they are stable because they are usually hierarchical multiples - some pairs are much closer to each other than to the rest of stars. Like Castor - a sextuple star. Consists of a pair of stairs and a third which is much further than the two... except that each of the three is itself a pair much closer than the distance to any others. Non-hierarchical multiples, like Orion Trapezium, are unstable and rare.
A wide orbit around barycentre of a tight binary basically means that there is a star which is always near Sun, orbiting it like Mercury or closer.
An orbit around one star while the other star is a distant companion means the other star is slow moving in sky, like Saturn, while the nearby star circles the whole sky.

 

[Devin-M]

This probably is irrelevant but a major plot point of the fictional Star Trek: Picard TV series S01E08 was an “Octanary” star system supposedly that had been assembled by an ancient alien race…

https://www.womenatwarp.com/picard-recap-broken-pieces-season-1-episode-8/

“On a planet at the center of an eight-star system, the woman we know as Commodore Oh (Tamlyn Tomita) leads a group of women – including Narissa and Ramdha (Rebecca Wisocky) – in an initials ritual. There is a “storehouse of preserved memories” on the planet, that warns of the danger of synthetic life.”

 

[delie]

And "dominating" does not need to mean that one mass is bigger than the others. It just means that the gravity of one mass must be bigger than the others due to mass and distance.
Examples:
Earth and Venus are similar in mass and distance. Yet both are stable because Sun is much more massive than either.
Triple stars are abundant in sky. And stable. And commonly comparable in mass (they are all stars). But they are stable because they are usually hierarchical multiples - some pairs are much closer to each other than to the rest of stars. Like Castor - a sextuple star. Consists of a pair of stairs and a third which is much further than the two... except that each of the three is itself a pair much closer than the distance to any others. Non-hierarchical multiples, like Orion Trapezium, are unstable and rare.
A wide orbit around barycentre of a tight binary basically means that there is a star which is always near Sun, orbiting it like Mercury or closer.
An orbit around one star while the other star is a distant companion means the other star is slow moving in sky, like Saturn, while the nearby star circles the whole sky.

I know this expression has been used to oblivion, but... this is mindblowing! I won't be following up with a question, as I need to first go through the above material to interlock all these new concepts in my mind.

 

[delie]

This probably is irrelevant but a major plot point of the fictional Star Trek: Picard TV series S01E08 was an “Octanary” star system supposedly that had been assembled by an ancient alien race…

https://www.womenatwarp.com/picard-recap-broken-pieces-season-1-episode-8/

“On a planet at the center of an eight-star system, the woman we know as Commodore Oh (Tamlyn Tomita) leads a group of women – including Narissa and Ramdha (Rebecca Wisocky) – in an initials ritual. There is a “storehouse of preserved memories” on the planet, that warns of the danger of synthetic life.”

On the contrary! This type of "assemblage" never crossed my mind. Also, I never had the opportunity to check out Star Trek (discouraged by the re-booted movies and swayed by the reviews of the Picard series).

Are you aware of more works describing these types of - I'm not even sure we can call it that - "synthetic manipulation of stars"?

 

[DaveC426913]

Are you aware of more works describing these types of - I'm not even sure we can call it that - "synthetic manipulation of stars"?

Klemperer Rosette

Larry Niven's Puppeteers organized their home system into a five planet Klemperer Rosette.

 

[Devin-M]

I numerically simulated an 8 star system today... It was stable for a while but it eventually turned chaotic... It was wide binary consisting of 2 Betelgeuse sized stars (11 Solar masses each) separated by about 1000AU, and each was closely orbited at 1AU by a Proxima Centauri sized star, then a Sun sized star at 50AU and finally a second sun sized star at 100AU. Video below...

 

[Borek]

I numerically simulated an 8 star system today...

What program is it?

 

[snorkack]

A probably septuple star system which is a naked eye, "northern" sky star with a Greek letter... but not α
ν Scorpii. Declination -19°27´. Magnitude rarely quoted but brighter than +4.
Telescope will resolve it into 4 components, designated with Latin majuscles: A, B, C or D
A is +4,38... total, you´ll see!
AB separation is lately 1,3´´.
B is +5,4.
AB-CD separation is 41´´, so not separated by eye.
CD are separated by about 2,4´´. C is +6,3, D is +7,4, also total.
Now two of the 4 visible components are themselves known multiples. And the invisible components are designated by Latin minuscles, following the visible component majuscle when applicable, as is the case in ν Scorpii ABCD.
ν Scorpi A is a known triple. Aab-Ac separation is about 63 m´´ (period 5,7 years), and Ac magnitude estimated at +6,6. Aa-Ab separation is about 1 m´´ (period 5,5 d), and Ab magnitude about +6,9.
ν Scorpi D is a suspect double... but its orbit and magnitudes do not seem to be known.
The very uncertainty about D calls the whole multiplicity of ν Scorpi into question. You have 3 more assumed single components at safe distance from others - Ac, B and C. Resolve any of them, and you have your octonary star.
Oh and remember: Latin minuscles designate any invisible components, whether stars or planets. You could easily have both in the same system. Does the lettering then take account of which are stars, which planets?

 

[Devin-M]

What program is it?

This page describes the N-Body integrator: https://universesandbox.fandom.com/wiki/N-Body_Simulation

 

[Borek]

Hardly helpful

Apparently everyone writing the documentation and using the program assumes everyone knows it, so there is no need to explain it is a physics based commercial space simulator, called Universe Sandbox, available from several sources (Steam included).

 

[Devin-M]

I was able to numerically simulate an Earth sized planet that was temporarily stable in a habitable zone in a octonary system. The Earth sized planet was orbited by a moon, & the moon was orbited by a 4km diameter asteroid 33434 Scottmanley ( https://ssd.jpl.nasa.gov/tools/sbdb_lookup.html#/?sstr=33434 ), and asteroid Scottmanley was in turn orbited by the great pyramid. The Earth sized planet orbited a Sun sized star, outside the habitable zone of the Sun sized star, but the Sun sized star orbited within the habitable zone of 21 solar mass star Rigel, and Rigel was a distant binary of another Rigel. Each of the Rigels were orbited closely by a 1/10th solar mass Proxima Centauri & 2 Suns, for a total of 8 stars, an earth sized planet, a moon of the planet, an asteroid orbiting the moon, and the great pyramid orbiting the asteroid.

The system remained stable enough for liquid water to remain on the Earth sized planet for quite some time, roughly 10k Earth years. Unfortunately, after that period of relative tranquility an orbital perturbation made the planet's parent star drift too close to the overall barycenter of the entire system, which further perturbed & degraded the Sun's orbit around its Rigel sized parent star. First the planet froze with an average surface temp of -5F close to the overall system barycenter, then the Sun & its planet took a death plunge directly towards the very close vicinity of the Rigel sized star where the surface of the planet exceeded 1600 degrees Fahrenheit, & next the planet was stripped of the sun it was orbiting by a close pass with another star and then the planet was thrown clear of the entire system through a gravitational slingshot effect, though it retained its moon. Together the planet & its moon froze as they drifted away into the emptiness of space.

During the time that the orbits had remained relatively stable, the Pyramid had 6 different orbital parents:

Pyramid -orbited-> Asteroid -orbited-> Moon -orbited-> Earth -orbited-> Sun (1 solar mass) -orbited-> Rigel (~21 solar mass) -orbited-> Barycenter (~46 solar mass total system)

 

[delie]

I was able to numerically simulate an Earth sized planet that was temporarily stable in a habitable zone in a octonary system. The Earth sized planet was orbited by a moon, & the moon was orbited by a 4km diameter asteroid 33434 Scottmanley ( https://ssd.jpl.nasa.gov/tools/sbdb_lookup.html#/?sstr=33434 ), and asteroid Scottmanley was in turn orbited by the great pyramid. The Earth sized planet orbited a Sun sized star, outside the habitable zone of the Sun sized star, but the Sun sized star orbited within the habitable zone of 21 solar mass star Rigel, and Rigel was a distant binary of another Rigel. Each of the Rigels were orbited closely by a 1/10th solar mass Proxima Centauri & 2 Suns, for a total of 8 stars, an earth sized planet, a moon of the planet, an asteroid orbiting the moon, and the great pyramid orbiting the asteroid.

The system remained stable enough for liquid water to remain on the Earth sized planet for quite some time, roughly 10k Earth years. Unfortunately, after that period of relative tranquility an orbital perturbation made the planet's parent star drift too close to the overall barycenter of the entire system, which further perturbed & degraded the Sun's orbit around its Rigel sized parent star. First the planet froze with an average surface temp of -5F close to the overall system barycenter, then the Sun & its planet took a death plunge directly towards the very close vicinity of the Rigel sized star where the surface of the planet exceeded 1600 degrees Fahrenheit, & next the planet was stripped of the sun it was orbiting by a close pass with another star and then the planet was thrown clear of the entire system through a gravitational slingshot effect, though it retained its moon. Together the planet & its moon froze as they drifted away into the emptiness of space.

During the time that the orbits had remained relatively stable, the Pyramid had 6 different orbital parents:

Pyramid -orbited-> Asteroid -orbited-> Moon -orbited-> Earth -orbited-> Sun (1 solar mass) -orbited-> Rigel (~21 solar mass) -orbited-> Barycenter (~46 solar mass total system)

Those are some nice representations, Devin!

So, if I'm interpreting the conclusions of your simulations correctly, not only it is important to conceptualize a stable orbit, but also account for an eventual natural "drift" within that orbit - relatively to the properties of the planets composing said system -, correct?

Assuming that we're referring to suns when we talk about "stars", this "chaotic drift" will always be correlated to the number of stars and their properties, within a system, yes? From what I've solely read on this forum page, a system with 2 stars having the same mass would be more chaotic compared to an octonary system with stars having significantly different masses and distances from one another. Am I on the money, or should I go back to class?

Enfin, given that our system only has one star, then these types of chaotic drifts couldn't occur unless some other natural causes happen?

 

[Orodruin]

Enfin, given that our system only has one star, then these types of chaotic drifts couldn't occur unless some other natural causes happen?

Well, the main perturber of this more stable setting within our solar system would be Jupiter. In fact, Jupiter probably played a significant role in the formation of the solar system itself.

 

[snorkack]

Well, the main perturber of this more stable setting within our solar system would be Jupiter. In fact, Jupiter probably played a significant role in the formation of the solar system itself.

That´s not obvious to me.
Jupiter is 318 times the mass of Eart, but stays 4 AU away with 12 year period.
Venus is 0,8 times the mass of Earth, but approaches to 0,3 AU with 0,6 year period.
Which of these does a better job staying a regular, periodic and limited perturbation?

 

[Vanadium 50]

but stays 4 AU away

Maybe today. https://en.wikipedia.org/wiki/Nice_model

 

[snorkack]

One thing that counts for both stability of system and basic lighting is orbital inclinations.
Note how everything that orbits in inner solar system does so close to ecliptic. With two significant exceptions.
One is inner satellites of Uranus and inner (i. e. all) satellites of Pluto, which orbit near primary equator instead. Note how they are very far from Sun, but fairly near their primary. And the other is long period comets.
In contrast, short period comets orbit near ecliptic even when, like Halley Comet, they do so in retrograde direction.
The reason is that large inclination orbits are perturbed far more strongly than low inclination ones.

 

[gmax137]

Are you aware of more works describing these types of - I'm not even sure we can call it that - "synthetic manipulation of stars"?

https://www.physicsforums.com/threads/best-sf-books-of-this-century.1012149/post-6644817

 

[snorkack]

A professional source, but classic and hopefully not too hard for the results:
https://articles.adsabs.harvard.edu//full/1916ApJ...43..103R/0000114.000.html
Includes phase curve of Moon to 150 degrees.
Note how powerful is the opposition surge of full Moon and how dramatically crescent Moon fades.
Moon 30 degrees from full shows 14/15 of the disc, yet only 1/2 of the light. At 150 degrees, the crescent is 1/15 the area of the disc, yet about 1/250 the brightness.
Jupiter does NOT fade that way. True, Earth comes closer to Jupiter at opposition - if Jupiter is 5 AU from Sun on average, then it is 4 AU at opposition and 6 AU at conjunction, making Jupiter 2,25 times dimmer.
But Jupiter at opposition is about 16 000 times dimmer than Moon. Which means that if Jupiter near conjunction fades to twice dimmer than at opposition, and Moon is 250 times dimmer as narrow crescent, ten Jupiter is still over 100 times dimmer than the crescent Moon.
Jupiter outshines all fixed stars, but does not illuminate night sky like Moon does.
Now note that for an observer on rotating Earth, Sun is above horizon half the time. So is Moon.
Moon is plainly visible in blue daytime sky. It stays in place when clouds drift by.
Over a month, the Moon varies to being visible no part of night (new Moon) through increasing part of evening (waxing crescent and gibbous), whole night (full Moon) to decreasing part of morning (waning moon). As the monthly average, one half of time at night is moonlight... on average, at least a small part of every night is moonlit (since moon is not exactly in conjunction) and at least a small part is not (moon is not exactly full - indeed, exact full moon is eclipsed). 3/4 of all time, Sun, Moon or both are above horizon and 1/4 time both are below.
Since Moon is dim to start with and fades when not full, a night lit by a narrow crescent moon is not very bright.

Now consider a planet of binary star. Like α Cen Ab.
At its periapse, B comes to 11,2 AU of A. Since Ab is in habitable zone, the A-Ab distance is about 1,2 AU.
Because of the stability requirement, we can find compelling reason why the A-Ab orbit should be at a low inclination to A-B orbit - like Moon is within 5 degrees of ecliptic, and Jupiter too.
Therefore, α centauri B must come to opposition and to conjunction with A for Ab regularly.
But unlike the case with Moon, and like the case with Jupiter, the period of oppositions and conjunctions of α centauri B must be close (not exactly equal) to α centauri A orbital period - the local year. (Which is close to 1,3 Earth years).

In case of moonlight, full Moon is around 1000 times brighter than combined light of stars. Full moon used to have drastic effects on activity of people. Social events set at full moon or maybe waxing gibbous moon (You can stay out late if when it the time to get home the night is moonlit rather than just starlight+airglow!). Street lighting not lit when moonlight made it superfluous. Lunacy.
Now consider α Cen Ab. At opposition B is at 11,2-1,2=10 AU. B is 2,2 times dimmer than Sun in visible light. So it is 220 times dimmer at the distance of Ab - but since full Moon is 400 000 times dimmer than Sun, it still makes 1800 times brighter than full Moon. Comparable to twilight with Sun around horizon...

When B is near "full", then the whole night is going to be in "twilight" range of 50...500 lx. Which is not day - but neither is it "moonlit night", because that is in range of 0,25...0,05 lx.

 

[delie]

A professional source, but classic and hopefully not too hard for the results:
https://articles.adsabs.harvard.edu//full/1916ApJ...43..103R/0000114.000.html
Includes phase curve of Moon to 150 degrees.
Note how powerful is the opposition surge of full Moon and how dramatically crescent Moon fades.
Moon 30 degrees from full shows 14/15 of the disc, yet only 1/2 of the light. At 150 degrees, the crescent is 1/15 the area of the disc, yet about 1/250 the brightness.
Jupiter does NOT fade that way. True, Earth comes closer to Jupiter at opposition - if Jupiter is 5 AU from Sun on average, then it is 4 AU at opposition and 6 AU at conjunction, making Jupiter 2,25 times dimmer.
But Jupiter at opposition is about 16 000 times dimmer than Moon. Which means that if Jupiter near conjunction fades to twice dimmer than at opposition, and Moon is 250 times dimmer as narrow crescent, ten Jupiter is still over 100 times dimmer than the crescent Moon.
Jupiter outshines all fixed stars, but does not illuminate night sky like Moon does.
Now note that for an observer on rotating Earth, Sun is above horizon half the time. So is Moon.
Moon is plainly visible in blue daytime sky. It stays in place when clouds drift by.
Over a month, the Moon varies to being visible no part of night (new Moon) through increasing part of evening (waxing crescent and gibbous), whole night (full Moon) to decreasing part of morning (waning moon). As the monthly average, one half of time at night is moonlight... on average, at least a small part of every night is moonlit (since moon is not exactly in conjunction) and at least a small part is not (moon is not exactly full - indeed, exact full moon is eclipsed). 3/4 of all time, Sun, Moon or both are above horizon and 1/4 time both are below.
Since Moon is dim to start with and fades when not full, a night lit by a narrow crescent moon is not very bright.

Now consider a planet of binary star. Like α Cen Ab.
At its periapse, B comes to 11,2 AU of A. Since Ab is in habitable zone, the A-Ab distance is about 1,2 AU.
Because of the stability requirement, we can find compelling reason why the A-Ab orbit should be at a low inclination to A-B orbit - like Moon is within 5 degrees of ecliptic, and Jupiter too.
Therefore, α centauri B must come to opposition and to conjunction with A for Ab regularly.
But unlike the case with Moon, and like the case with Jupiter, the period of oppositions and conjunctions of α centauri B must be close (not exactly equal) to α centauri A orbital period - the local year. (Which is close to 1,3 Earth years).

In case of moonlight, full Moon is around 1000 times brighter than combined light of stars. Full moon used to have drastic effects on activity of people. Social events set at full moon or maybe waxing gibbous moon (You can stay out late if when it the time to get home the night is moonlit rather than just starlight+airglow!). Street lighting not lit when moonlight made it superfluous. Lunacy.
Now consider α Cen Ab. At opposition B is at 11,2-1,2=10 AU. B is 2,2 times dimmer than Sun in visible light. So it is 220 times dimmer at the distance of Ab - but since full Moon is 400 000 times dimmer than Sun, it still makes 1800 times brighter than full Moon. Comparable to twilight with Sun around horizon...

When B is near "full", then the whole night is going to be in "twilight" range of 50...500 lx. Which is not day - but neither is it "moonlit night", because that is in range of 0,25...0,05 lx.

You've beaten me to it! Once, I parsed the material above and resolved my celestial mechanics headache, I was planning to dive deeper into these celestial "colorimetrics". Your article will be most useful =)

 

[snorkack]

Note that α sun refers to constellation, not star system. 4 constellations out of 88 do not even contain α star (these are LMi, Nor, Pup and Vel). In around 30 of the rest, α is not the brightest (though usually one of the brightest). Also, note that in some constellations, Latin minuscles and majuscles are used, and Centaurus is one of them... α Cen, a Cen and A Cen are three completely different stars, and do not confuse A Cen with α Cen A either!