Does (Brown and Batygin’s) Planet 9 (or Planet X) Exist?

What exactly is the evidence that there may be a “Super-Earth” lurking in the outer reaches of the Solar System?  Accounts differ, so I’ll review what I’ve read (ignoring the mainstream media storm around 20th January!), to try to minimise confusion.

New Scientist

If you read your New Scientist a couple of weeks ago, you’ll probably have seen the cover-story feature article Last Great Mysteries of the Solar System, one of which was Is There a Planet X? [paywall for full article – if, that is, unlike me, you can even get your subscription number to give you access].  The article discussed the dwarf planets Sedna and 2012VP113.  The orbits of these planetoids – and another 10 or so not quite so distant bodies – according to New Scientist and the leaders of the teams that discovered Sedna and 2012VP113, Mike Brown and Scott Sheppard, respectively, could indicate “there is something else out there”.

Apparently, says NS:

“[the orbits of Sedna and 2012VP113] can’t be explained by our current understanding of the solar system…  Elliptical orbits happen when one celestial object is pushed around by the gravity of another.  But both Sedna and 2012VP113 are too away from the solar system’s giants – Jupiter, Saturn, Uranus and Neptune – to be influenced.”  Something else must be stirring the pot.”

“Elliptical orbits happen when one celestial object is pushed around by the gravity of another.”  This is nonsense.  Elliptical orbits are quite usual, beyond the 8 planets (i.e. for “trans-Neptunian objects”) which is where we’re talking about.  The fact that the orbits of Sedna and 2012VP113 are elliptical is not why there may be another decent-sized planet way out beyond Uranus (and little Pluto).

I see that the online version of New Scientist’s article Is There a Planet X? has a strap-line:

“Wobbles in the orbit of two distant dwarf planets are reviving the idea of a planet hidden in our outer solar system.”

Guess what?  The supposed evidence for Planet X is nothing to do with “wobbles” either.

The New Scientist article was one of several near-simultaneous publications and in fact the online version was updated, the same day, 20th January, with a note:

Update, 20 January: Mike Brown and Konstantin Batygin say that they have found evidence of “Planet Nine” from its effect on other bodies orbiting far from the sun.

Exciting.  Or it would have been, had I not been reading the print version.  The link is to another New Scientist article: Hints that ‘Planet Nine’ may exist on edge of our solar system [no paywall]. “Planet Nine”?  It was “Planet X” a minute ago.

Referencing the latest paper on the subject, by Brown and Batygin, this new online NS article notes that:

“Brown and others have continued to explore the Kuiper belt and have discovered many small bodies. One called 2012 VP113, which was discovered in 2014, raised the possibility of a large, distant planet, after astronomers realised its orbit was strangely aligned with a group of other objects. Now Brown and Batygin have studied these orbits in detail and found that six follow elliptical orbits that point in the same direction and are similarly tilted away from the plane of the solar system.

‘It’s almost like having six hands on a clock all moving at different rates, and when you happen to look up, they’re all in exactly the same place,’ said Brown in a press release announcing the discovery. The odds of it happening randomly are just 0.007 per cent. ‘So we thought something else must be shaping these orbits.’

According to the pair’s simulations, that something is a planet that orbits on the opposite side of the sun to the six smaller bodies. Gravitational resonance between this Planet Nine and the rest keep everything in order. The planet’s high, elongated orbit keeps it at least 200 times further away from the sun than Earth, and it would take between 10,000 and 20,000 Earth years just to complete a single orbit.”

Brown and Batygin claim various similarities in the orbits of the trans-Neptunian objects.  But they don’t stress what initially sparked the idea that “Planet Nine” might be influencing them.

Scientific American and The Argument of Perihelion
Luckily, by the time I saw the 23rd January New Scientist, I’d already read The Search for Planet X [paywall again, sorry] cover story in the February 2016 (who says time travel is impossible?) issue of Scientific American, so I knew that – at least prior to the Brown and Batygin paper – what was considered most significant about the trans-Neptunian objects was that they all had similar arguments of perihelion (AOPs), specifically around 0˚.  That is, they cross the plane of the planets roughly at the same time as they are closest to the Sun (perihelion).  The 8 (sorry, Pluto) planets orbit roughly in a similar plane; these more distant objects are somewhat more inclined to that plane.

Scientific American reports the findings by two groups of researchers, citing a paper by each.  One is a letter to Nature, titled A Sedna-like body with a perihelion of 80 astronomical units, by Chadwick Trujillo and Scott Sheppard [serious paywall, sorry], which announced the discovery of 2012 VP113 and arguably started the whole Planet X/9/Nine furore.  They quote Sheppard: “Normally, you would expect the arguments of perihelion to have been randomized over the life of the solar system.”

To cut to the chase, I think that is a suspect assumption.  I think there may be reasons for AOPs of bodies in inclined orbits to tend towards 0˚, exactly as observed.

The Scientific Papers

The fact that the argument of perihelion is key to the “evidence” for Planet X is clear from the three peer-reviewed papers mentioned so far.

Trujillo and Sheppard [paywall, still] say that:

“By numerically simulating the known mass in the solar system on the inner Oort cloud objects, we confirmed that [they] should have random ω [i.e. AOP]… This suggests that a massive outer Solar System perturber may exist and [sic, meaning “which”, perhaps] restricts ω for the inner Oort cloud objects.”

The Abstract of the other paper referenced by Scientific American, Extreme trans-Neptunian objects and the Kozai mechanism: signalling the presence of the trans-Plutonian planets, by C and R de la Fuente Marcos, begins:

“The existence of an outer planet beyond Pluto has been a matter of debate for decades and the recent discovery of 2012 VP113 has just revived the interest for this controversial topic. This Sedna-like object has the most distant perihelion of any known minor planet and the value of its argument of perihelion is close to 0 degrees. This property appears to be shared by almost all known asteroids with semimajor axis greater than 150 au and perihelion greater than 30 au (the extreme trans-Neptunian objects or ETNOs), and this fact has been interpreted as evidence for the existence of a super-Earth at 250 au.”

And the recent paper by Konstantin Batygin and Michael E Brown, Evidence for a Distant Giant Planet in the Solar System, starts:

Recent analyses have shown that distant orbits within the scattered disk population of the Kuiper Belt exhibit an unexpected clustering in their respective arguments of perihelion. While several hypotheses have been put forward to explain this alignment, to date, a theoretical model that can successfully account for the observations remains elusive.

So, whilst Batygin and Brown claim other similarities in the orbits of the trans-Neptunian objects, the key peculiarity is the alignment of AOPs around 0˚.

Is There a Simpler Explanation for ~0˚ AOPs?

Let’s consider first why the planets orbit in approximately the same plane, and why the Galaxy is also fairly flat.  The key is the conservation of angular momentum.  The overall rotation within a system about its centre of gravity must be conserved.  Furthermore, this rotation must be in a single plane.  Any orbits above and below that plane will eventually cancel each other out, through collisions (as in Saturn’s rings) and/or gravitational interactions (as when an elliptical galaxy gradually becomes a spiral galaxy).  Here’s an entertaining explanation of what happens.

This process is still in progress for the trans-Neptunian objects, I suggest, since they are inclined by up to around 30˚ – Sedna’s inclination is 11.9˚ for example – which is much more than the planets, which are all inclined within a few degrees of the plane of the Solar System.  What’s happening is that the TNOs are all being pulled constantly towards the plane of the Solar System, as I’ve tried to show in this schematic:

Now, here comes the key point: because the mass of the Solar System is spread out, albeit only by a small amount, because there are planets and not just a Sun, the gravitational pull on each TNO is greater when it is nearer the Sun (closer to perihelion) than when it is further away. There’s more of a tendency for the TNO (or any eccentrically orbiting body) to gravitate towards the plane of the system when it’s nearer perihelion.

This is true, I believe, even after allowing for Kepler’s 2nd Law, i.e. that the TNO spends less time closer to the Sun.  Kepler’s 2nd Law suggests the time an orbiting body spends at a certain distance from the centre of gravity of the system is proportional to the square of that distance, which you’d think might cancel out the inverse square law of gravity.  But the mass of the Solar System is not all at the centre of gravity.  The nearest approach of Neptune to Sedna, for example, when the latter is at perihelion is around 46AU (astronomical units, the radius of Earth’s orbit) but about 476AU when Sedna is at aphelion.

The most stable orbit for a TNO is therefore when it crosses the plane of the Solar System at perihelion, that is, when its argument of perihelion (AOP) is 0˚.  Over many millions of years the AOPs of the orbits of Sedna and co. have therefore tended to approach 0˚.

I suggest it is not necessary to invoke a “Super-Earth” to explain the peculiarly aligned arguments of perihelion of the trans-Neptunian objects.