Asimov’s Kalgash: a planet in permanent daytime (for real this time!)

This post is the sequel to Real-Life Sci-Fi Worlds 11: Kalgash, a planet in permanent daytime (from Asimov’s Nightfall).  Beware: the later parts feature rings of stars orbiting black holes (with some planets too)…


Nightfall. The classic Asimov story (and later, book) set on Kalgash, a planet that experiences permanent daytime except for once every 2049 years.

In a previous post I set up the Kalgash 6-star system according to the book:

kalgash.001

Unfortunately, the system falls flat.  The planet is not in permanent daytime.  Its longest stretch of permanent daytime is only 2 months (not 2049 years!).

Sorry, Asimov, your system doesn’t work.  But don’t worry, you are still one of my heroes! And I’m here for you. I’m going to fix the Kalgash system to make Nightfall work.

In this post I will build several different functional Kalgash systems in which the planet really is in permanent daytime.  In my opinion, the last couple systems are the coolest ones I’ve ever engineered

The original Kalgash system had 6 stars. That makes keeping its planet in permanent daylight seem like a complicated problem. But it’s really not.

Take any old planet orbiting any old star.  At any given time, half of the planet is lit up by the star.  A single star has already done half our job! Even more than half, since we’ll take advantage of the fact that on Earth, twilight keeps the sky bright until the Sun is about 15 degrees below the horizon. That gives us 10 hours of darkness per night (assuming the planet spins in 24 hours like Earth).

kalgash.009.jpg

All we need is to illuminate the half of the planet that’s pointed away from the central star. This is tricky, because at face value it would take a ring of stars to do this (more on that later — wink, wink).

We can create permanent daylight with just two more stars.  Put those stars on opposite sides of the sky, say off in the distance at 3 and 9 o’clock in the image. Then the side of our planet pointed away from the central star is always lit up.  Boom!

For this to achieve our purpose we need the right stars on the right orbits. We need stars that are bright enough to light up a planet (say, to make the surface at least 1% as bright as high noon). And they need to remain on opposite sides of the sky.

But stars can’t stand still (kind of like dogs or my kids).  Gravity is always sucking them in (kind of like the Sarlacc pit, but, actually, forget that, it’s completely different). To make our star system stable the stars need to orbit around each other.  Luckily we know how to do that (see previous posts here and here).

To maintain their opposite-side-of-the-sky configuration we want our stars to orbit as slowly as possible. This means that their orbits must be as wide as possible. Star systems are organized in a hierarchical way, with orbital sizes that follow a 1, 10, 100 pattern (rather than 1, 2, 3).

Let’s go from the outside-in.  In the past I’ve explained how the Galaxy disrupts very distant orbits. The widest plausible orbit is generally about 1,000 Astronomical Units (or AU; 1 AU is the Earth-Sun distance) but I’m feeling generous today so let’s make it 3,000.  That will be the size of the largest orbit in our first Kalgash system.  The next-closest one will be ten times smaller, 300 AU.

We need to choose stars that will appear bright enough in Kalgash’s sky.  The star on the 300 AU orbit must be at least 900 times more luminous than the Sun to appear at least 1% as bright as the Sun. The star on the 3000 AU orbit must be at least 90,000 times more luminous than the Sun.

There aren’t a lot of stars luminous enough to fit the bill.  Let’s go with a red giant like Aldebaran for the inner star and a blue supergiant like Rigel for the outer one.  Here is what our Kalgash 3-star system looks like:

kalgash.010.jpg

Of course, the stars move along their orbits so they aren’t always on opposite sides of the sky.  The time it takes for their configuration to change is mainly determined by the faster orbit of the closer-in star (which is why I stretched their orbits out a little farther than in the past). The red giant at 300 AU is little more massive than the Sun and takes a bit longer than 3000 years to complete an orbit.  Meanwhile, the blue supergiant is more than twenty times the Sun’s mass and takes more than 30,000 years.  (The image is centered on the central star — in reality all the stars are orbiting each other, or more precisely, their common centers of mass).

Let’s take a look at the illumination on Kalgash. As we’ve done in the 5-Sun Earth series, it’s helpful to put Kalgash’s orbit on a clock face.  The blue supergiant is way off to the left (in the direction of 9 o’clock) and the red giant is off at 3 o’clock.

kalgash.011.jpg

When the two stars are diametrically opposed there is no darkness on our planet.  But the stars are moving: it takes the red giant about 275 years to pass between numbers on the clock face, and it takes the blue supergiant about ten times longer.

Our no-darkness-on-Kalgash setup only lasts as long as the red giant is between 2 and 4 o’clock.  It takes the red giant 550 years to move that far.  In that time the blue supergiant has shifted a little, so the two-stars-on-opposite-sides-of-the-sky configuration ends up lasting for about 600 years.

That is our first Kalgash system. And it works pretty well: 600 years without darkness is not too shabby!  But we’re not quite there.  We haven’t reached the 2000+ years of daylight like in the book.  And, even worse, this system has 600 years of constant daylight but that configuration only happens every few thousand years (a little less than once every red giant orbit).  Finally, when darkness falls in this system it would be very slow.  Much slower than a sunset on Earth or an eclipse (which is what happens in Nightfall).

Let’s build a better Kalgash system.

Let’s borrow a trick from the Ultimate Engineered Solar System.  In that system I showed that a ring of 42 Earths orbiting the Sun is perfectly stable for billions of years.  It’s weird but true!

Let’s take that idea a step farther. Could a ring of Suns be stable? Yes, as long as a few conditions are met:

  • There must be at least seven Suns in the ring.
  • They must all have the same mass and be evenly spaced along the same orbit.
  • They must orbit something a lot more massive.  After a little math it turns out that for a minimal ring of seven Suns, the central body must be at least about 1000 times more massive than the Sun.

No stars exist today that are 1000 times more massive than the Sun.  What this means is that the central body must be … drum roll, please … a black hole!  (Pretty much the coolest objects in the Universe!)

Let’s build a ring of stars around a black hole! We’ll use a black hole a few thousand times more massive than the Sun. Then we’ll make a ring of 8 Suns evenly spaced along their orbit. Here it is:

kalgash.012.jpg

The image of the central black hole is Gargantua from the movie Interstellar (Paramount/Universal)

We will use this ring of stars to provide the external illumination for our Kalgash 2 system. That means we need the planet (and its own central star) to be interior to the ring of Suns.

 

It is simpler if we make the planet’s central star a red dwarf star. Red dwarfs are fainter than the Sun. Let’s choose a half-Solar-mass star (just like for the original Ultimate Solar System). The planet orbits in the star’s habitable zone at about 0.2 AU. The star’s orbit around the black hole must be relatively wide to make sure that the planet’s orbit is stable. Let’s put it at 10 AU. The ring of stars is a bit farther out. It’s perfectly stable if we make the ring 20 AU-wide.

Here is what we’ve got:

kalgash.013.jpg

Again, the central black hole is an image of Gargantua from Interstellar (Paramount/Universal).

The Kalgash 2 system works!  As the planet orbits the star, the red dwarf-facing side is always lit up.  And its backside is never more than about 10 AU from another Sun-like star, which would provide 1% of the Sun’s brightness.  Boom!  Permanent daylight!  (Disclaimer: there are some times when the distance would be slightly above 10 AU but this is easily fixed by putting slightly more massive, brighter stars in the outer ring).

Is it possible to make the Kalgash system with a single ring of stars?  Just barely if we squeeze things. For stars orbiting a black hole there is a region around a star in which the star’s gravity is stronger than the black hole’s.  That is called the Hill radius (it’s also called the Roche lobe in some contexts). For a planet to orbit a star that orbits the black hole, the planet’s orbit around the star must be smaller than the Hill radius (smaller than half the Hill radius for a prograde orbit, smaller than the full Hill radius for retrograde).  To guarantee stability within the ring of stars, each star must be separated from its neighbors by at least 12 Hill radii.  Of course, the planet orbits within its star’s habitable zone, receiving about the same amount of energy from its star as the Earth does from the Sun. Other stars are fainter by the square of the relative separation.  So for the widest-possible prograde orbit at half the Hill radius, the closest stars are 24^2 = 576 times fainter than the main star. That is 5 times fainter than our 1%-as-bright-as-the-Sun cutoff.  For the widest-possible retrograde planet orbit, neighboring stars are 12^2 = 144 times fainter, just below our 1% cutoff.  Let’s be generous and make this thing happen.

There is one more issue. Three stars in a ring do not form a line.  As viewed from the middle star, the two neighboring stars are 135 degrees apart in the sky.  This is 45 degrees  from a straight line (which would be 180 degrees in this way of measuring).  As twilight only works down to 15 degrees below the horizon, this means that there is a 15 degree-wide slice of the planet’s orbit around its star in which night can fall. For 1 month every year there would be 1 hour of darkness.  That’s no good!

We can fill this hole by using a 12-star ring.  That way neighbors are never more than 30 degrees apart on the sky.

Here is the Kalgash 3 system made with a single ring of stars:

kalgash.014.jpg

Central black hole is Gargantua from Interstellar (Paramount/Universal).

Here is another fun variation on the ring of stars theme. Let’s have the planet orbit the black hole in between two rings of stars.  The inner ring of stars is 1 AU from the black hole, the outer ring is at 5 AU and the planet is in between.  That gives us the Kalgash 4 system:

kalgash.015.jpg

Central black hole is Gargantua from Interstellar (Paramount/Universal).

There are a plethora of twists on this theme. Here are a few:

  • With a more massive black hole, more stars could fit on the same orbit.  At 1 AU you could end up with up to 104 stars per ring!  (Assuming the star can never be larger than its Hill radius)
  • Adjacent rings of stars could orbit in opposite directions (a la Ultimate Retrograde Solar System).
  • The planet could orbit a star in the middle ring of a multi-ring system.
  • You could fill a whole system with rings of stars like I did with planets in the Ultimate Engineered Solar System.
  • The planet could be in a Trojan configuration with its star in a system with inner and outer rings of stars.
  • The inner ring could be made of red/yellow stars and the outer ring of blue stars, to give a gradient in the sky color throughout the day. Since the blue stars are much brighter than the Sun (let’s take A stars that are ~10 times as luminous) the outer ring must be a little farther out, at ~20 AU. We’ll keep the inner ring at 1 AU and made of Sun-like stars.  Let’s call this one Kalgash 5:

kalgash.016.jpg

The list of variations goes on.  And all of those possible systems would be just awesome.

There is one last detail to think about.  What could make darkness fall on the planet in these systems? 

The simplest situation is the Kalgash 3 system with its single ring of stars.  If the planet had a large moon, it could occasionally eclipse a neighbor star and create darkness.  It’s questionable whether such a moon would be stable (because of tidally-driven orbital changes) but for now let’s go with it.  Even though these eclipses would create darkness it’s not clear why darkness would only fall very rarely. Instead, eclipses should be relatively frequent, even if the moon’s orbit is tilted with respect to the orbit of the ring.

The Kalgash 2 system, with an outer ring of stars, might provide a solution.  Imagine that the planet in this system has two large moons. Since the central star is not within the ring there is no issue of stability of the moons. Each moon occasionally eclipses one of the stars in the outer ring.  But only extremely rarely would there be simultaneous eclipses of the two closest outer stars, the only ones that could provide any significant illumination.  That could explain the very rare darkness.

For systems with many rings of stars it’s challenging to imagine how darkness could ever fall.

OK, that wraps us up.  You might say that I “engineered” four Kalgash systems for Dr Asimov, with a multitude of possible variations. Boom!

All the settings I found to work include a ring of stars.  I have not come up with a viable Kalgash solution that is not engineered in this way.

 

Questions, comments, words of wisdom?

 


Additional resources

 

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33 thoughts on “Asimov’s Kalgash: a planet in permanent daytime (for real this time!)

    • The black hole would distort the light from stars behind it — stars on the opposite side of the ring, that is. It could in some cases create extra images of those distant stars and make them brighter, providing an extra light source.

  1. I didn’t realize that a star could be as close as 10AU to a black hole, and not be sucked in. Ref: Kalgash 2, what would be the closest it or a moon could get to the black hole, assuming it’s the smallest known?

    • The black hole itself is tiny, only about the size of Earth. But even with a gigantic mass, a planet would need to pass very close to be torn apart, within a fraction of the Earth-sun distance (something like 5-10% of an AU by my simple calculation).

  2. Some other possibilities:

    You could get longer eclipses if the stars were white dwarfs orbited by giant planets.

    Binary planets could shade each other, and if the continents were only on inner sides sailors traveling to distant islands could miss Nightfall and return home to collapsed civilizations with no idea what happened.

    • These are awesome ideas, I love them! The binary planet one definitely seems worth digging deeper into… Especially in combination with unevenly-distributed continents! Good stuff!

      • I also thought about having the binary planet orbit a giant planet orbiting a star in the ring to get long eclipses but didn’t see how to avoid having it provide reflected light to prevent Nightfall.

  3. Are the rings of stars stable if they are in different planes? What if you put those in different planes at much greater distances, say 10 or 100 times farther out to replicate the Stars of Nightfall?

    • Let’s see — the rings need to stay coplanar to keep them closely packed (a la secular perturbation theory). But for 2 very distant rings I think it would be stable, although the stars/planets would be stretched into ellipses rather than circular rings, and they’d have to maintain careful spacing… So, I’m not 100% sure.

  4. What if the planet orbited a brown dwarf? What would its temperature need to be for the sky turn blood red, perhaps with more distant stars visible through it, when the bright stars were not visible?

    • Playing around with excel, calculating blackbody curves, then adding Rayleigh scattering, I believe a star with a temperature around 1500 K would have a deep red sky. But due to the opacity of various molecules cool stars are anything but blackbodies. Looking at some spectra I fthink a planet orbiting warmer star would have a red sky, perhaps something like Wolf 359. How a species that evolved under it would perceive it would depend on whether it was also lit by bluer stars. I expect a species that only had a relatively cool sun would perceive it as white or yellow the way we see our sun.

  5. Pingback: Real-life Sci-Fi world 11b: Kalgash, a planet in permanent daytime (from Asimov’s Nightfall) | PLANETPLANET

  6. These systems are awesome! Any habitability concerns being so close to a black hole? I guess if this was engineered then they would have cleaned things up…

  7. Interesting paper:

    Saturn’s formation and early evolution at the origin of Jupiter’s massive moons
    https://arxiv.org/abs/1804.02892

    Saturn scatters material as it grows some of which Jupiter captures to form its moons. Reminds me of your earlier post describing the population of the asteroid belt with water bearing asteroids.

  8. I was thinking about some possible options regarding this bit about Kalgash 3:

    “So for the widest-possible prograde orbit at half the Hill radius, the closest stars are 24^2 = 576 times fainter than the main star. That is 5 times fainter than our 1%-as-bright-as-the-Sun cutoff. For the widest-possible retrograde planet orbit, neighboring stars are 12^2 = 144 times fainter, just below our 1% cutoff.”

    Some things I came up with:

    Alternate similar mass dwarf stars and red giants in the rings with Kalgash orbiting one of the dwarf stars
    Kalgash orbits a close binary, two 0.5 solar mass stars have lower luminosity than one 1.0 solar mass star
    Alternate 2.0 solar mass stars with 1.0 solar mass (would this still be stable?)

    Letting my imagination go with the binary theme, a mix of different ratio close binaries in the star rings of Kalgash 5 could allow an interesting variety of nearby stars during the year and seasons on the planet.

    Some more exotic combinations could be thrown in, for example, ongoing mass transfer between stars in a binary or a white dwarf accreting matter from its companion.

    I wonder if the ring would be stable if a binary-binary pair was included.

    • Or tragically, one of the rings could contain a close binary neutron star that eventually spiraled together, merging and exploding, killing everyone.

  9. The simplest solution would be to have a small star orbiting a large one, and Kalgash at the L1 point of the system (analogous to the Soho satellite at the Earth-Sun L1 point). But I suppose that wouldn’t be stable for very long?

  10. Would this work?

    Kalgash orbits a large black hole, a smaller black hole is in a more distant orbit, three stars orbit the larger black hole in a 3:2 resonances with the smaller black hole (like the HIldas in resonance with Jupiter) with their closest approaches at 12, 4, and 8 o’clock.

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