on Planets Everywhere

A recent study says that habitable zone planets are downright common. This isn’t the first time claims like this have been made.

The thing I find most interesting about this study is the way that they did it. Most previous analyses of the number of planets did it by working out how many planets a survey was missing.

For instance, the Kepler mission looked at one patch of sky (105 square degrees, when the sky is more like 42,000 square degrees) just off of the plane of the Galaxy where the stars are, and could only measure stars brighter than a certain amount. So, it only saw a small fraction of the stars in the Galaxy. And then, the method Kepler used – planetary transits – is highly ineffective at finding planets: the star system has to be almost perfectly aligned (by chance) along the line of sight to have a chance of its planets transiting. Then you estimate how many objects were missed, and the numbers come out to be a staggeringly huge number of planets. Assuming there’s no hidden Galactic predisposition for planetary systems to be oriented exactly along the line of sight, or something.

This survey did something different. They used variations on the Titus-Bode law to determine the existence of planets.

The Titus-Bode law (because it’s calculated from observations but doesn’t propose a “why”, it’s a law) was for our Solar System, and noted a geometric relationship between the orbital distances of the planets. The formula was this: D = (P+4)/10, where P was one of a sequence 0,3,6,12,24,48,96…

Put in P=1 and you get the distance between the first planet and the Sun: 0+4 = 4, 4/10 = 0.4, which is roughly the distance from the Sun to Mercury. (0.38 AU)

P=2: 3+4 = 7, 7/10 = 0.7, Venus is 0.72 AU from the Sun.

P=3 gives 1.0 (the Earth), P=4 gives 1.6 (Mars is 1.52), P=5 gives 2.8, P=6 gives 5.2 (Jupiter). On the strength of this law, it was assumed that there must be a fifth planet at 2.8 AU, and that led directly to the discovery of the asteroid belt. But, it was decided that asteroids weren’t planets, so Jupiter is still the fifth planet. The Titus-Bode law also messes up on Neptune, which is 30 AU from the Sun, rather than 38.8.

The law fell into some kind of disrepute by the time I was taught about it in college, because it was seem as an amusing relic of a bygone age with no physical meaning behind it. But now it seems to be coming back. Newtonian mechanics does lead to the concept of resonances, which explain the orbital periods of Pluto (it orbits twice every time Neptune orbits three times) and Io, Europa, and Ganymede, with orbital periods on a 1:2:4 ratio. There’s been a suspicion for some time that the same kinds of ratios are being seen in extrasolar planetary systems: The Gliese 876 star system’s planets c, b, and e* are also in a 1:2:4 orbital period relationship**.

The people who did this study found that 124 of the 151 multi-planet systems (with 3 planets or more) might be following a Titus-Bode’s Law relationship, and based on that they predicted locations of other planets. What they came up with suggests that most of these systems have Bode-friendly orbit locations within their habitable zones.

Of course, this relies on Bode’s Law being correct, and Bode’s Law being correctly determined for a Solar System based on information about as few as three planets. There’s no guarantee that there IS anything there. But if Bode’s Law really does predict something related to orbital stability, maybe there are planets there. Or at least asteroid belts.

*Planets are named in order of discovery, not in order of distance from the star. It can be a headache.
**Fun question: They’re all Jupiter-sized objects or bigger, but if they’re locked in mutual orbital resonance with each other, do they qualify as planets under the gravitational dominance clause of the IAU definition of a planet?

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