Lord Smurf asks

I can just about get my head around a planet orbiting two suns, but this: http://www.bbc.co.uk/news/science-environment-19950923 confuses me. I notice that it says two of the suns are ‘circling’ the planet, rather than ‘orbiting’. Is there a difference? I always think of suns as the giants of solar system so I don’t understand how they can orbit a planet, rather than the other way round. How does this system actually work because all the articles are telling me how amazing this is but none of them actually say how the damn thing works.

That news article is rather spectacularly contentless. Fortunately – and unsually for the BBC – they included a link to the paper in the article (do this more often, journalists) which does explain what is going on pretty well. It’s written in the usual scientific hieroglyphics, but then that’s what you have me around for, isn’t it?

The title of the paper is a big clue as to what is going on: it’s called “Planet Hunters: A Transiting Circumbinary Planet in a Quadruple Star System”. There’s two stars orbiting a common barycentre in a classic binary setup, and this is what the planet they’ve found is orbiting, as seen below:

What you’re looking at here are the various dips in the overall intensity of the light observed from this binary system as the objects within it pass in front of each other; when they do this they block some of the light from reaching the Earth just like an eclipse. The primary and secondary eclipses labelled on the graph are caused by each of the binary star pair eclipsing the other. I’m going to take a wild guess and say the primary is bigger than the secondary, which is why it blocks more light and results in a bigger dip in the light graph when it eclipses. However, there’s also a couple of tiny, tiny dips not associated with either member of the binary system, and this is caused by the planet they’ve found.

Planets orbiting binary systems aren’t hugely unusual, and they can orbit one or both stars in the binary without any apparent ill-effects. The surprising thing about this particular discovery is what happened when the astronomers zoomed out a little bit.

The second point of light in the bottom left hand corner – catchily termed the 0.7” contaminator – is a second binary star system orbiting the first at a distance of greater than 1000 AU, effectively making it a quadruple star system. This second pair of stars is rather small and dim in comparison to the first, orbiting at a distance of about 40 AU from each other, and since both of them are so far away there’s nothing that says a planet can’t exist perfectly happily in an orbit close in to the primary binary system (the paper mentions that something called “eccentricity pumping” happens in models where the second binary system is closer than that, which I imagine refers to repeated gravitational perturbations from the second binary gradually stretching out the orbit of a planet into an increasingly elliptical shape until it finally breaks free and is ejected from the star system entirely).

And that’s it, really. That BBC news article is awfully written and mixes up what is orbiting what, when it’s actually a fairly simple thing to understand: the primary binary system has most of the gravitational pull in this system and it’s this the planet orbits. The secondary binary is weakly bound to the primary in a circular orbit and is both smaller and much further away from the planet than the primary, which is what allows the planet to survive.

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Barycentre, barycentre. It’s the kind of word that sounds like it should be easy to pun, but really isn’t.

In preparation for the post on Lagrange points coming later on I should start by defining the concept of a gravitational barycentre (or centre of mass). For a single roughly-spherical object like a planet we can treat this as a single point mass located at the very centre of the sphere – that is, if we took the planet away and replaced it with a single infinitesimally small object with the same mass located at the planet’s centre of mass, this tiny object would (broadly) be gravitationally indistinguishable from the planet. If we add in another spherical object – say a moon – and attempt to calculate the centre of mass of the planet-moon system, things get a little trickier. The planet exerts a gravitational force on the moon and the moon exerts a gravitational force on the planet, meaning that the gravitational centre of mass of the combined system will be located somewhere in between.

This is actually kind of a bad picture for illustrating the concept because m₁ is the heavier mass, and yet it’s rendered as smaller than m₂. Never mind. Pretend m₁ is made of something really dense, like neutronium. The centre of mass of a two body system is defined by factoring each body’s mass by its distance from some arbitrary reference point – in this case x₁ and x₂ – and dividing by the system’s total mass. Since the reference point is entirely arbitrary we can cheat and say it’s located at the centre of mass of m₁; this means that x₁ is zero, x₂ is now the distance d between the two centres of mass and the equation reduces to

 In other words the centre of mass of the two body system is located a distance X_cm from the centre of mass of m₁along a line connecting the centres of mass of m₁ and m₂. This is the gravitational barycentre of the system, and it’s very important when considering orbital mechanics because in a two-body system like a moon and a planet, or a planet and the sun, both bodies will orbit the gravitational barycentre. If you have two masses of comparable size like a binary star system the barycentre will lie roughly in the middle of the two bodies, leading to very obvious mutual orbital behaviour like this:

(This is actually wikipedia’s example for Pluto + Charon, but I don’t like the one for the binary star system because it implies the stars have exactly the same mass, which would be unlikely.)

If one body is very much larger than the other, however, then X_cm will be smaller than the radius of the larger body, which is another way of saying that the gravitational barycentre will be located inside the larger mass. The existence of the barycentre is much less obvious in this case since the centre of mass of the combined system is so close to the centre of mass of one of the bodies. For example, in the case of the Earth-Sun system the barycentre is located

or about 450km away from the Sun’s centre of mass. Given that the Sun has a radius of 696,000km this does not produce much appreciable movement on the part of the Sun! I mention this so that the following gif doesn’t give you the wrong idea.

This is a very exaggerated portrayal of the sort of motion we’re talking about here; in actuality for most planets the motion on the part of the Sun will be tiny, and even a really big planet like Jupiter can only shift the barycentre of their mutual orbits to roughly the surface of the Sun, meaning that it’s less of a mutual orbit than it is a slight “wobble” on the part of the Sun. Nevertheless this motion can be detected, and as previously mentioned it’s one of the methods we use to detect exoplanets orbiting other stars. Hopefully by this point it should be obvious why we’ve mostly only found really big exoplanets, since they’re the ones which produce the biggest wobble in the motion of their parent star.

Now, remember, this applies for all two-body systems. The Earth and the Moon orbit a mutual gravitational barycentre. The Sun and Pluto orbit a mutual gravitational barycentre. Even tiny satellites like the Martian moons Phobos and Deimos will cause Mars to shift slightly in position, orbiting a mutual gravitational barycentre. This is an important factor to take into consideration when plotting celestial trajectories, and it also gives rise to some interesting side-effects which I’ll tackle on Thursday.

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