An Earth with five Suns in the sky

We Earthlings have just one Sun.  Tatooine has two.  Wouldn’t it be even cooler with three Suns in the sky?  Or four or five or twenty?

Several extra-solar planets have been found in triple- and even quadruple-star systems (for example, GJ 667C and PH1b).  But none of these planets has more than two Suns because some of the stars are so distant they would only appear as bright stars in the sky, not Suns.

Here we will ask the question: how many Suns could a planet have in its sky?  Is the number limited?  And if so, at how many?

Before we get into details, what does it mean to have a Sun in the sky?  Every star in the sky is a Sun (except for the planets and the Moon, of course!).  For this experiment let’s say that a “Sun” must clearly be a circle in the sky, not a dot.  For scale, our Sun is about half a degree across.  Let’s shoot for Suns being about the same size.

Let’s cook up a planetary system!  Our most important ingredients are stars.  This image shows the kinds of stars we can choose from. Stars span a monstrous range in size and luminosity (how much total light they give off).

The diagonal line from the bottom right to the top left is called the main sequence.  This is where “normal” stars sit, happily burning hydrogen in their cores.  Moving down to the right along the main sequence, stars become redder, smaller, fainter, and longer-lived.  Super-bright blue stars (top left) only live a few to 100 million years whereas faint red stars (bottom right) basically shine forever. The Sun is in the middle, among the yellow stars on the main sequence.

Above the main sequence are different types of giant and supergiant stars, which are larger and brighter than their main sequence counterparts. Giant stars represent a phase of evolution during which different elements are being used for fuel.  When massive stars completely run out of fuel, they explode as supernovae and toss their atmospheres into the Galaxy.  What is left behind is either a black hole or a neutron star.  Those are so faint that they don’t even show up on this plot.  Most stars end up as puny, faint white dwarfs (below the main sequence).  White dwarfs live forever and simply cool off slowly. (See here for an interesting story about white dwarfs and planetary debris).

Let’s get started putting our planetary system together.  We will only put one planet in the system to go with as many Suns as possible.

If we put a star in our system, it needs to be in the right place.  If Earth was 10 times closer to the Sun, the Sun would appear 10 times larger in the sky (and we would be fried).  But if Earth were ten times closer to a star that was ten times smaller than the Sun, then the star would be the same size in the sky as the Sun is now.  If Earth was 10 times farther from the Sun, the Sun would be 10 times smaller in the sky (and we would freeze).  But if Earth were ten times farther from a star that was ten times larger than the Sun, then the star would be the same size in the sky as the Sun.  See how it works?

There is also the constraint that we want our Earth to have the right temperature to be habitable.  We’ll come back to that at the end. (It won’t change much).

To kick things off, let’s Tatooine it up.  Earth’s orbit would be perfectly stable if instead of having one Sun at the center it had two Suns on a close orbit.  We have discovered a bunch of exoplanets that orbit two close stars.

To go father we need to worry about keeping Earth’s orbit stable.  We can’t just put another Sun on Mars’ orbit.  Systems with lots of stars in them are stable if they are in hierarchical configurations.  What that means is that each set of orbits is on a different size scale.  The sizes of stars’ orbits does not go 1-2-3, it goes 1-10-100.  So, a star can be only be really close to one other star.  After that, other stars must be really far away.

Here is a cartoon hierarchical 4-star system.

The system in this picture could easily contain two more stars.  Star c could be orbited by another star on a very close orbit, and so could star d.  The configuration of that system would still be hierarchical.  Plus, the system could contain even more stars on much more distant orbits.

So we need our system to be in a hierarchical setup.  We’ve already got a Tatooine binary with two stars on a very close orbit and our Earth on a more distant orbit.  In the image above, we’ve got stars a and b with Earth on an orbit like star c.

Next, we can add a star on an orbit like star d in the image.  For scale, we’re assuming that stars a and b’s mutual orbit is about one tenth the size of Earth’s orbit around the Sun; that is, 0.1 Astronomical Units.  Our planet’s orbit is the same size as Earth’s.  The next star will have an orbit about 10 times larger.  To look like the Sun in the sky, the star must therefore be about 10 times larger than our Sun.

The biggest (and hottest) main sequence stars — called O stars — are about 10 times larger than the Sun.  But they are blue and way more than 100 times brighter.  If we put an OB star on a 10 AU orbit in our system the planet would get fried!   We could always put a slightly wimpier star there, an A star like Vega.  An A star would not be too bright, as they are typically only 10-100 times more luminous than the Sun.  But A stars are a bit small, only a couple times larger than the Sun.  So, an extra A star at 10 AU would look a lot smaller than the Sun in the sky.

A better choice would be a giant star, say a red giant.  Wimpier red giants are about 10 times as big as the Sun. So, if we put a giant out on a 10-ish AU orbit it would appear as big as the Sun in the sky. And why not put two of them on a relatively close orbit?  That way we get two more Suns!  Of course, the mutual orbit of the two red giants cannot be too small; the stars are huge and we don’t want them spilling onto each other too easily.  Let’s have the red giants orbit each other 2 AU apart and we’ll put them 20 AU away from the Sun.  We’ll choose red giants that are 20 times larger than the Sun, meaning that their radii are about 0.1 AU, the size of the entire orbit of the close (Tatooine) pair of binary stars.

There is still plenty space to put more stars farther out in our system.  At first glance it would seem like there is a lot of space, since stars can have orbits as wide as 10,000 AU and Oort cloud comets orbit the Sun out to 100,000 AU.  But there are no stars big enough to still look like Suns from that far away!

Still, let’s put one more star much farther out.  We’ll make it a big-ass star, say a hypergiant or a supergiant. These stars are huge: they are 30 to 1000 times the Sun’s.  They are also ridiculously bright: 10,000 to 1 million times brighter than the Sun.  This means that, to avoid frying our Earth, we need to keep any hyper- or supergiant stars far away, no closer than 100 AU from our planet.  We could choose a red supergiant like Betelgeuse, which is about 1000 times larger than the Sun and 10,000 times brighter.  So, if we put Betelgeuse 500 AU away it would appear twice as big as the Sun in the sky but only 4% as bright.  [Note that we’ll only include one supergiant, not a binary, because this type of star is extremely rare.]

If we put the pieces together, we can get a system with five Suns in the sky.  Here is what it would look like (not to scale):

To maintain the right conditions for life  we need to add an additional constraint: the total energy received by our planet must be the same as Earth’s is today (or fall within a reasonable range).  If our Tatooine binary is made up of two Sun-like stars then our Earth will receive its current energy budget from each and will be fried.  So, either the stars must be half as bright as the Sun or our Earth’s orbit must be widened.  The same goes for the other stars.  This is where it helps that our extra stars are red and not blue.  Red stars are much cooler so they can appear large in the sky without being as bright.  (Let me illustrate why this is important.  Take two stars with the same size.  One is blue and one is red.  The blue star is twice the temperature of the red star. The two stars would be the same size in our planet’s sky but the blue one would shine 16 times more brightly. )

It’s not too hard to keep our Earth habitable.  Here is one way to do it.  Let’s make the Tatooine binary out of K stars that are 20% as bright as the Sun.  Let’s choose pretty wimpy red giants that are only 100 times as bright as the Sun.  Orbiting at 20 times the Earth-Sun distance (20 AU), each red giant is one quarter as bright as the Sun. That leaves the red supergiant which, as we saw, only delivers about 4% of the Sun’s brightness at its distance of 500 AU.  If we add all of those up, it puts our total energy budget at 94% of the energy Earth receives from the Sun, comfortably within the habitable zone.

So there you have it: an Earth with 5 Suns in the sky!  Boom!

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Our story is not over yet.  In tomorrow’s post we will explore what it would be like to live on this planet, what the motions of the heavens would look like.  It turns out that insomnia would be a big problem for the inhabitants because night time is hard to come by….

And in Thursday’s post we will burst the bubble on this planetary system.  We will explore how a planetary system like this could be created and whether it really makes sense from an astronomical point of view.

Stay tuned!