Astronomy Without A Telescope – Plausibility Check

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So we all know this story. Uncle Owen has just emotionally blackmailed you into putting off your application to the academy for another year – and even after you just got those two new droids, darn it. So you stare mournfully at the setting binary suns and…

Hang on, they look a lot like G type stars – and if so, their roughly 0.5 degree angular diameters in the sky suggest they are both only around 1 astronomical unit away. I mean OK, you could plausibly have a close red dwarf and a distant blue giant having identical apparent diameters, but surely they would look substantially different, both in color and brightness.

So if those two suns are about the same size and at about the same distance away, then you must be standing on a circumbinary planet that encompasses both stars in one orbit.

To allow a stable circumbinary orbit – either a planet has to be very distant from the binary stars – so that they essentially act as a single center of mass – or the two stars have to be really close together – so that they essentially act as a single center of mass. It’s unlikely a planet could maintain a stable orbit around a binary system where it is exposed to pulses of gravitational force, as first one star passes close by, then the other passes close by.

Anyhow, if you can stand on a planet and watch a binary sunset – and you are a water-solvent based life form – then your planet is within the star system’s habitable zone where H₂O can exist in a fluid state. Given this – and their apparent size and proximity to each other, it’s most likely that you orbit two stars that are really close together.

But, taking this further – if we accept that there are two G type stars in the sky, then it’s unlikely that your planet is exactly one astronomical unit from them – since the presence of two equivalent stars in the sky should roughly double the stellar flux you would get from one. And it’s not a simple matter of doubling the distance to halve the stellar flux. Doubling the distance will halve the apparent diameters of the stars in the sky, but an inverse square relation applies to their brightness and their solar flux, so at double the distance you would only get a quarter of their stellar flux. So, something like the square root of two, that is about 1.4 astronomical units away from the stars, might be about right.

However, this means the stars now need a larger than solar diameter to create the same apparent size that they have in the sky – which means they must have more mass – which will put them into a more intense spectral class. For example, Sirius A has 1.7 times the diameter of the Sun, roughly twice its mass – and consequently about 25 times its absolute luminosity. So even at 2 astronomical units distance, Sirius A would be nearly five times as bright and deliver five times as much stellar flux as the Sun does to Earth (or ten times if there are two such stars in the sky).

So, to sum up…

It’s a struggle to come up with a scenario where you could have two stars in the sky, with the same apparent diameter, color and brightness – unless you are in a circumbinary orbit around two equivalent stars. There’s no reason to doubt that a planet could maintain a stable circumbinary orbit around two equivalent stars, that might be G type Sun analogues or whatever. However, it’s a struggle to come up with a plausible scenario where those stars could have the angular diameter in the sky that they appear to have, while still having your planet in the system’s habitable zone.

I mean OK you’re on a desert world, but two stars of a more intense spectral class than G would probably blow away the atmosphere – and even two G type stars would give you a Venus scenario (which receives roughly double the solar flux that Earth does, being 28% closer to the Sun). They could be smaller K or M class stars, but then they should be redder than they appear to be – and your planet would need to be closer in, towards that range where it’s unlikely your planet could retain a stable orbit.

So, at this point you should call shenanigans.

Further reading: Planets Thrive Around Stellar Twins (includes a permitted screen shot from a certain movie).