PLANETPLANET

Isaac Asimov‘s sci-fi stories are one reason I wanted to become an astronomer (I talked about this in a recent interview). So I’m a little sad to shoot down a classic….

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Nightfall is a classic Asimov story (and later, novel). The residents of a planet called Kalgash live in system of six stars that leaves the planet in permanent daytime or at least twilight.  The rest of the Universe is invisible because it is never dark enough for the stars to come out, except for once every 2049 years when darkness falls (and everyone goes nuts!).

Let’s build Kalgash’s planetary/star system and see how it compares to the one proposed by Asimov.  In this post I’ll take the setup in Nightfall at face value and see whether it makes sense (spoiler: not so much).  In my next post I’ll create a couple of reasonable alternative systems that could indeed work.  Be prepared: Kalgash System 3 will be amazing (and reminiscent of the Ultimate Engineered Solar System).

Here is what we know from Nightfall (the book). On Kalgash it never gets dark.  There is always at least one “Sun” in the sky, although the brightness is not constant.  For our purposes, let’s assume that at all times there is a star that’s at least, say, 1% of the Sun’s brightness.  That is bright enough to drown out the stars (constellation-type stars, that is).

The Kalgash system contains six stars. The central star (called Onos) is similar to the Sun, and Kalgash’s orbit is similar to Earth’s.  There is a binary pair of bluish stars (Trey and Patru) about 10 times farther away.  There is another binary pair of whitish stars (Tano and Sitha) that is just 10% farther away than the bluish pair.  Finally, there is a red dwarf star called Dovim whose exact position is not clear.  However, Dovim plays a key role: it is the one star in the sky when Kalgash’s distant moon (called Kalgash 2) eclipses it once every 2049 years, sending the planet into chaos. None of the stars orbits is wider than about 15 Astronomical Units (AU; the Earth-Sun distance).

A quick recap of our potential ingredients in building a multiple-star system (the stars, that is):

To be stable, star systems must be organized in a hierarchical setup. This means that the spacing of orbits follow a 1, 10, 100 pattern rather than 1, 2, 3.

Kalgash’s central star is just like the Sun. The binary pair at 10 Astronomical Units must be close to as luminous as the Sun, since its apparent brightness drops by a factor of 100 (since they are 10 times farther from the planet), and we need each star to be at least ~1% as bright as the Sun.

The second binary pair of stars orbiting just past the first is a no-go; it would render the system unstable.  The only solution is for the two pairs of binary stars to actually orbit each other.  So each binary pair must orbit close to each other (say at a separation of 0.1 AU), then the two pairs would orbit each other at a wider separation, say of 1 AU.  That would be stable but it would also mean that, viewed from Kalgash, all four stars must be relatively close in the sky at a given time.  To drown out the darkness, each star should be as bright as — or brighter than — the Sun.  The simplest solution would just be to use four Sun-like stars, although they are supposed to be white/blue in color rather than yellowish.  There is a trade-off: we could widen the four stars’ orbit around the planet and increase the brightness (and bluish-ness) of the stars. For now, let’s just keep it simple and make them all Sun-like, and forget about their colors.

The sixth star Dovim is tricky. As a red dwarf it is significantly fainter than the Sun (see the diagram above). But to play its role in the story Dovim must be bright enough in the sky to drown out the (distant) stars.  This means that Dovim must orbit significantly closer than the main, Sun-like star.  For stability purposes let’s put Kalgash on a 0.1 AU-wide orbit around Dovim. But this is not meant to be the main star in the story, so Dovim should be significantly fainter than the Sun-like star.  Let’s assume Dovim is a very faint red star like Proxima Centauri, barely massive enough to undergo fusion in its core.  That makes Dovim about 1000 times less luminous than the Sun.  On an orbit ten times closer than the Sun-like star, Dovim is still ten times fainter than Onos.

Our stable, Asimov-approved Kalgash system looks like this:

Now the big question: would Kalgash avoid seeing darkness in this system?  Does Nightfall’s setup hold up?

We can use the same approach as for an Earth with five Suns in the sky.  Let’s build the system one step at a time, from the inside out. First, let’s just take a look at Kalgash’s orbit around the red dwarf star Dovim. The star lights up the side of the planet facing it, but assuming Kalgash’s atmosphere is like Earth’s, the planet is in twilight about an hour before sunrise to an hour after sunset, making the typical length of a day about 10 hours.

Let’s visualize this using a clock face as a guide. Kepler’s third law tells us that Kalgash completes an orbit around Dovim about once a month (36.5 days to be precise).

Now let’s add in the main Sun-like star Onos.  The side of Kalgash facing Onos is illuminated, but what matters is the relative positions of the two stars.  When the planet is between the two stars, then the planet’s entire surface is lit up (one side by each star).  In practice it looks like this.

When the planet is between 2 and 4 on the clock face, the whole planet is illuminated and there is no night. However, when the planet is at the 9 on the clock face the two stars are in the same part of the sky, so darkness lasts a full 10 hours. In between, at the 6 and 12 on the clock, darkness lasts 4 hours.  Standing on the surface of the planet when it is at the 6 on the clock, Onos would rise, followed 6 hours later by Dovim. Then Onos would set, followed later by Dovim, and then 4 hours of darkness.

The pair of Dovim and Kalgash take one year to complete an orbit around Onos. But Kalgash orbits Dovim ten times per year.  So in the above image, Kalgash basically makes a complete loop in a month or so. That means that, including only Onos and Dovim, Kalgash is in darkness for only about 1/6th of each orbit around Dovim, or about 6 days.  We’re still a long ways off from the 2049 years in Nightfall.

Now let’s add in the four other stars (the double-binary).   It’s important to realize that even though there are four of them, they form a bound system to maintain stability.  This means that all four stars are confined to within about 5 degrees in the sky so we can think of them as a single distant source of illumination.

There are some configurations in which the quadruple star system banishes darkness from Kalgash:

When the quadruple stars are between 8 and 10 on the clock face, all sides of Kalgash are illuminated and there is no darkness.  How long does this represent? What matters is the relative alignment of Onos and the quadruple stars. Their relative alignment is determined by the shorter orbit relative to Kalgash, which is Onos’ 1-year orbit.  So the time it takes the quadruple stars to pass between 8 and 10 on the clock face is about 2 months.

The rest of Kalgash’s orbit around Onos some part of Kalgash is in darkness.  When the quadruple stars are aligned with Onos then the setup becomes the same as the previous one and Kalgash is completely illuminated for just 6 days out of each orbit around Dovim.  When the quadruple stars are a month past the no-dark zone and are located at the 7 on the clock face the system looks like this:

Another month later night time has lengthened further and the system looks like this:

The longest Kalgash can go without darkness is 2 months. Our Asimov-approved, stable Kalgash system is totally busted. 

Remember: in Nightfall Kalgash is perpetually illuminated at least to the level of twilight (to drown out the constellations). The only reason night falls at all is because of an eclipse by Kalgash’s large moon. I didn’t even get to the moon part because we couldn’t keep our planet lit up.

Sorry, Isaac Asimov. 😦

But don’t worry, you are still one of my heroes!  And guess what? I’m going to help fix Nightfall!  I have a few ways to build systems that are not too far from the specs in the book but that work.  Kalgash 2, 3, 4 and 5 really are in permanent daylight! I will build and vet those systems in an upcoming post.

Questions, comments, words of wisdom?

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Relevant resources:

• A semi-technical attempt to put the Kalgash system in context (download here).  This is nicely explained and laid out, although the system they created is not stable.
• Previous posts that build toward Kalgash: Earth with five Suns in the sky (parts one, two, and three), The Ultimate 16-star Solar System, and The Biggest Tragedy in the history of the Universe