A New “Mathematical” Definition Proposed for What Constitutes a Planet

In the current (heated) debate of what constitutes a planet, it seems everyone can agree at least one thing: The current definition put forth by the International Astronomical Union is actually quite vague and it really only applies to our own Solar System. So while the definition is unclear at best in our own neighborhood, it also doesn’t provide a framework for classifying the thousands of exo-worlds that are being discovered on almost a weekly basis.

Since math has been dubbed “the language of the Universe” it seems rather fitting and logical to use arithmetic to help in framing a better definition for planethood.

This week, UCLA professor Jean-Luc Margot has proposed a simple mathematical test that can be used to separate planets from other bodies like dwarf planets and minor planets. He says his new system is easy.

“One should not need a teleportation device to decide whether a newly discovered object is a planet,” Margot said.

The new approach would use estimates of the star’s mass and the planet’s mass and orbital period. Since the IAU’s definition is based primarily on the ability of a planet to “clear its orbit,” (whether it can accumulate or dominate small bodies in its orbital neighborhood), Margot’s test narrows this down to a specific timeframe of determining whether a body can clear a specific region around its orbit.

“A simple metric can be used to determine whether a planet or exoplanet can clear its orbital zone during a characteristic time scale, such as the lifetime of the host star on the main sequence,” Margot writes in his paper. “This criterion requires only estimates of star mass, planet mass, and orbital period, making it possible to immediately classify 99% of all known exoplanets.”

Under these criteria, all 8 planets and all classifiable exoplanets would be classified as planets. It also keeps the distinction between planets and dwarf planets. Some have pointed out that Margot’s criteria would make our Moon a planet. But, as Margot told Universe Today, that’s not necessarily so. “It really depends on how the IAU decides to define satellites and if or how they decide to define double planets,” he said.

Margot says his definition would be useful in generalizing and simplifying the definition of a planet, and that the information for applying this for exoplanets is easily obtained with Earth- or space-based telescopes.

“The disparity between planets and non-planets is striking,” Margot said. “The sharp distinction suggests that there is a fundamental difference in how these bodies formed, and the mere act of classifying them reveals something profound about nature.”

Margot also found that bodies that can clear their orbits — and therefore qualify as planets — are typically spherical.

“Because a quantitative orbit-clearing criterion can be applied to all planets and exoplanets,” Margot writes, “it is possible to extend the 2006 IAU planet definition to stars other than the Sun and to remove any possible ambiguity about what it means to clear an orbital zone.”

Margot presented his proposal at the annual meeting of the AAS’s Division for Planetary Sciences. It is not known whether the new approach will be considered by the IAU.

Further reading: Margot’s paper, UCLA press release

35 Replies to “A New “Mathematical” Definition Proposed for What Constitutes a Planet”

  1. This formula is not useful because it still relies on orbit clearing as the primary factor in determining whether an object should be classed as a planet. Requiring orbit clearing for planethood puts primacy on an object’s location rather than on its intrinsic properties. If Earth were in Pluto’s orbit, it would not clear that orbit either. This means the definition could result in the absurdity of the same object being classed as a planet in one location and as not a planet in another location.

    It makes no sense to artificially enforce a distinction between planets and dwarf planets. Dwarf planets are simply a subclass of planets, as are terrestrials and jovians. Dwarf planets have the same complex processes, geology, layering, and weather as their larger counterparts. Any definition that ignores their intrinsic properties and classifies these objects solely by their location is flawed.

    There aren’t eight planets in our solar system. According to the far superior geophysical planet definition, according to which a planet is any non-self-luminous spheroidal body orbiting a star, free floating in space, or orbiting another planet, our solar system has 14 planets and counting. The key to the geophysical planet definition is that an object has to be large enough and massive enough for its gravity to squeeze it into a round or nearly round shape. If it meets this criterion, it is a planet. Classifying a world as geologically active as Pluto as a non-planet makes no scientific sense.

    1. The previous poster obviously has no clue. Figure 1 in Margot’s paper shows that Earth would easily clear its orbit if it were in Pluto’s orbit.

      1. UTreader, I would not say “no clue,” just bad math/graph-reading skills and a (perhaps overly) passionate approach to her side of the argument. As it happens, the principle she outlines intuitively is MY primary argument against the IAU’s 3rd criterion — simply put, the farther an object orbits from its host star, the bigger it must be to be a planet — which I now lay out from the paper:

        Fig. 2 shows that according to this new formula Mercury is nearly as good at clearing its orbital area as Neptune is at clearing its own. This makes little intuitive sense, for as Table 1 shows, Neptune weighs in at 17.15 Earth masses, while Mercury only weighs in at 0.055 Earth masses, a difference of 3 orders of magnitude. (Mercury is only ONE order larger than Pluto, by comparison.) The only way this can be true is if orbital volume — and thus orbital distance — is also a primary determining factor, not just the mass of the body in question.

        This is borne out by Fig.1: if Mercury (or even Mars!) orbited at the distance of Eris, voila: “planet” Mercury is dead; long live “dwarf planet” Mercury. And while it is true that Earth would still be a planet at Plutonian distance, NONE of the “Inner Planets” would make it were they orbiting, exempli gratia, at Sedna’s distance (semi-major axis of ~524.4AU); even Uranus & Neptune would only just pass muster in a similar orbit. Also from Fig. 1, and perhaps even more damning, both Pluto and Eris would have to be considered full-grown planets, if only they traveled in Mercury’s orbit.

        I do accept to some degree the author’s logic that “Some scientists dislike the concept of a planet definition that depends on
        context and would prefer to focus on intrinsic properties.
        However, there are instances in which context justifiably
        prevails in the classification (e.g., asteroid vs. meteorite,
        magma vs. lava, cloud vs. fog), and there is no reason
        to dispense with a useful distinction in the taxonomy of
        planets.” In my opinion, this is justification enough to call Luna a satellite of Earth’s, and Charon a co-orbiting body of Pluto’s (we can argue “double planet” some other time). However, that which may be defined as a planet orbiting at 0.3 AU ought to remain a planet at 300AU and beyond, provided all other things remain equal.

        This new formula, while useful in precisely defining the IAU criterion, and perhaps also as a tool for preliminary classification of exoplanets (dwarf or otherwise), is thus still nothing more than a glorified planetary BMI scale which relates (planetary) body mass to orbital diameter. Like laurele, I prefer a system which uses hydrostatic equilibrium as the determinant of “planet/not planet,” with further classification dependent upon composition, mass, size, temperature, etc.

      2. UTreader – Margot’s paper includes something that the I.A.U.’s definition does not, a (completely arbitrary and – I would argue – faulty) measurement of what constitutes “clearing its neighborhood”. In spite of “Figure 1”, Laurele is correct – relatively tiny Earth would not “clear” Neptune from “its neighborhood” if placed where Pluto is (of course, the whole idea that Neptune – which never gets closer than 18 A.U.’s to Pluto, is somehow in “its neighborhood” is , like the I.A.U.’s definition of “planet” itself, preposterous).

        More importantly, as I said above, the point is moot. “Clearing it’s neighborhood” should have nothing to do with whether an object is considered a planet or not – because it is not relevant.

        The 2006 I.A.U. decision had nothing to do with the science, and everything to do with politics – science driven by politics is bad science. The reality is that there is no real science “problem” to solve, because the “solution” is as simple as it is obvious:

        Is it round? Yes.
        Does it directly orbit a star or stars? Yes.

        Then it’s a planet.

    2. Of course a definition based on intrinsic properties would be better. The IAU’s definition is ridiculous!

      The problem is, any definition based on intrinsic properties runs the risk of generating an incorrect value of N (where N=number of planets in our solar system). N must not exceed 10 because school children only have 10 fingers.

      The IAU learned its lesson when it failed to address the definition of “moon” in time. The number of moons got totally out of hand… just look at what happened with the Jupiter system! Good luck devising a mnemonic for that!

      But the IAU could have done better. I propose a new, simpler definition which any school child (or IAU member) can remember easily:

      Planet (noun)
      1. any one of the 10 heaviest objects, excluding stars, in a primary orbit about a star.

      1. It’s a shame the IAU had yet to be founded when Amalthea was discovered in 1892. I think a reasonable upper limit on ‘number of moons per planet’ would be four. If someone with a bit of foresight had nipped the problem in the bud we wouldn’t have the mess we’ve got now.

  2. What struck me in this article and the original Fraser linked on Twitter was this sentence:
    “The sharp distinction suggests that there is a fundamental difference in how these bodies formed, and the mere act of classifying them reveals something profound about nature.”

    People speaking for the IAU have always said that they had to distinguish between planets and non-planets because otherwise we’d potentially have dozens or hundreds of planets. So it’s clear to me that classifying them says something about the nature of human learning, not something profound about the cosmos. They just wanted a quantity of planets that could be easily memorised by children and could be illustrated neatly and completely in a small graphic. Either that, or they weren’t honest in their justification.

  3. A dangerously simple idea. I like the concept that a body has to clear its orbit to be considered a planet versus a dwarf planet. The relationship between Neptune and TNOs very nicely illustrates this. Just using mass and shape isn’t enough. Indeed the moon would be big enough to call a planet if it wasn’t orbiting the earth.

  4. Hi Greg. I don’t have a problem with the moon being big enough to call a planet in Margot’s model: after all, Jupiter’s moon Ganymede and Saturn’s moon Titan are both bigger than Mercury. Margot suggested that this aspect (binary planets v. satellites) could be settled separately by the IAU, since they haven’t defined them so far.

    However, your teaser about the relationship between Neptune and TNOs got me thinking. Pluto fails to meet IAU’s “planet” status because it hasn’t cleared its neighbourhood. But maybe you’re pointing out that Pluto may have cleared its neighbourhood but for Neptune’s influence, kicking stuff about in the Kuiper Belt. That has the ring of truth: the IAU definition suggests that would-be planets are the masters of their own destiny.

    But if we swapped the locations of Mercury and Pluto, would Mercury clear that particular neighbourhood or would Pluto then be a planet and Mercury not?

    More controversially, what if we swapped the locations of Earth and Pluto? Would Neptune prevent Earth from clearing out that neighbourhood, or (by IAU definition) would we be living on a dwarf planet if Earth had Neptune for a neighbour? UTReader says it would and Laurele thinks it wouldn’t… It’s an interesting thought.

  5. The problem is that the I.A.U. definition of planet is convoluted. “Clearing its neighborhood” has nothing to do with whether something is a planet.

  6. Leave the Moons alone. Regardless of size/mass, the designation “Moon” is clearly understood as an object orbiting a planet or dwarf planet. As such, at a minimum, any object orbiting another object (other than a star) ought not, without exception, be considered a planet. To do otherwise adds much more confusion to an already convoluted planetary designation process.

    1. But in some cases (all, if you want to be literal, but to lesser degrees) moons with a size to planet ratio large enough, the objects are orbiting each other, so that makes your black and white definition inaccurate. These things can be tricky in the details… 😉

      1. Pluto/Charon orbit around the same gravitational point. Hence, that would not fit my definition of one object orbiting another object. Curious if you are aware of any other planetary system with a similar orbiting dynamic as Pluto/Charon?

      2. Hey 2stepbay…. actually the very question you asked about Pluton/Charon orbiting around a barycentre external to them both was just the question I was wanting to ask you, when I read your earlier comment. This is the part that complicates the planet v. moon understanding, isn’t it: the absence of a binary planet v. satellite definition.

      3. If neither Pluto nor Charon are objects orbiting another object, and therefore neither are planets (which I think is what your definition is suggesting), what does that make them?

        I think that no matter what definitions we come up with for planets, moons or other objects, there will always be exceptions and edge cases throwing up problems, and there will never be a ‘right’ answer (not that we shouldn’t try to come up with classification systems – just that we should accept their limitations)

        In the case of moons, rings throw up a problem. A tiny rock in a ring of, say, Saturn, is an object orbiting a planet, but we don’t want to call that rock a moon. So now we have to add another qualifier, perhaps to do with size or clearing orbit, so that ring-rocks don’t get confused with moons. Then there are the “shepherd moons” – are they big enough to be true moons? Are they clearing their orbit? (hard to say since they clearly have a gravitational influence on the ring, but not the kind of influence that sweeps them up.) Or are they constituents of the ring, and if so, what can be said about them to distinguish them from the trillions of ring-rocks?

        It’s a real brainer.

        A lot of people like to claim they have the answer to object classification in space (and I do admit it is very interesting to read their ideas, since I find the topic fascinating), but I don’t think there is an ultimate answer in classification that the universe is waiting for us to discover, because the universe doesn’t come with any guarantee of such. Classification in biology and chemistry is similarly fraught with problems, despite initially seeming quite simple.

  7. We Humans create our own problems by over complicating everything common sense tells us what a Planet or a Moon is and if a Moon has a Moon is that not still a Moon? I would go as far as to say our own beloved Moon is a Planet because it is a Sphere orbiting another Sphere which in turn orbit our Sun, And yes Pluto and Charon do the same thing…

    1. So just to throw in one more over-complication, how about Haumea, which has three times the mass of Sedna and presumably would be roughly spherical if its incredibly fast spin hadn’t stretched like pizza dough? I’m not sure whether such a phenomenon could apply to a Mercury-plus sized planet, but should planet status be withheld by fiat, even if would-be planet comes an excuse note?

      1. Haumea is roughly halfway between Ceres & Pluto in mass, but I’m not sure from where you’re getting the number for Sedna; since it has no satellites, any number you find is likely to be a wild guess-timation based on its possible composition vs. its albedo/size.

        Regardless, all of the planets are thicker at their respective equators because of their spin, but Jupiter — the most massive — is the most noticeably un-round due to its ~10hr day. For this reason, I’m not sure that being a “pot-belly” is that big a deal for planetary status; the biggest of our “real” planets is the most oblate of all.

      2. The issue isn’t an object being round but it being in hydrostatic equilibrium, meaning squeezed into a round or nearly round shape by its own gravity. An oblate spheroid still meets this condition. Jupiter is obviously shaped by its own gravity, as is Haumea.

      3. Exactly my point, laurele: even the largest planet in our system is obviously deformed thanks to its spin rate. Why then should sphericity be a deciding factor amongst the smallest?

        As you always say: hydrostatic equilibrium is the key.

      4. Hi Laurele… I wanted to say thank you for explaining about hydrostatic equilibrium. I appreciate that – I’m much clearer now.

    1. Not nearly as many as on the head of a pin, but it still depends on which wing they favor in flight. ^_~

  8. I think, space enthusiastics spent more time trying to defining “planet” than necessary…!
    To me, the classification may consider whether it revolutes around a star or another object . In this classification, the size of the body may be disregarded… (Sorry for Ganymede…!) Sphereoidness (in percent) may be an additional “small” limit for classification. If we accept Eris, Sedna,… as a planet, except Mike Brown, who looses or gains ? ( I know, increasing the number increases space enthusiastics…!)
    Anyway, as I proposed many times, definin boundary of a solar system may be more important than defining planets…! (Sorry for NASA-Voyager mission scientists…!)
    Finally, the “asteroid” needs more acceptable definition… The definition available today seems “too large”…!

  9. OK! I’ve got it, To make it simple if there is life on a Planet its a Planet if not its a piece of Rock and/or Gas floating around the Cosmos :)….

  10. I agree. The focus should be on searching and studying them instead of figuring out some doubtful bureaucratic definition. And really, do we really need a precise definition so badly. It’s like with a continent. Much closer to our lives on this planet. We don’t have a definition for it, but living just fine.

    “Continent is more a convention than strict definition.” (c) Universe today.

    Similarly with planets. For almost a 100 years there was 9 planets in the Solar system. It just is. Was. I still don’t see a reason to change that. It’s like they have nothing else to do at IAU. Other than mess up with definitions and be dissatisfied with anyone else but them to name extraterrestrial objects.

  11. SO, I know it’s been a week, but I’ve been thinking: maybe we can use this set of mathematical descriptions to actually end the controversy, as well as give ourselves a standard yardstick by which to measure “planet-hood.”

    The paper is mostly about putting a firmer mathematical figure upon the definition imposed by the IAU upon the planetary bodies in our own solar system. As such, it does well enough. There are many who disagree fundamentally with the IAU’s definition, however, and the new math described does little to remove those objections: at the end of the day, planet-hood still depends just as much upon a body’s distance from its host star as it does the mass of the body in question.

    That said, the paper DOES show a way to a possible compromise, in my opinion.

    Let us decide (arbitrarily & a priori) that “Mercury shall be a planet, Thus Spake the [IAU/divine authority of one’s choice].” ^_~ Then let us further allow that an object which cannot clear its neighborhood may have work to do earn full planetary status, thus keeping the IAU supporters happy. We then use the mathematics shown in the Margot paper to define a lower limit, or a “standard planet” if you will, as follows.

    The authors propose that if a planet’s value of PI (mass divided by the mass needed to clear its orbit) is >1, then it fits the IAU’s description. Accepting that for the moment, Pluto would need to be about half again as large as Mercury to be a planet in that orbit. However: we’ve already decided that “Mercury is a Planet Forever, according to the Decree of [previously cited authority], Amen.” So all we actually need to do to get a lower boundary on “planets” vs. everything smaller is to calculate Mercury’s value of PI using the semi-major axis of something like say, Sedna, instead of its own.(*) (We could even put it in a 1,000 AU orbit and then do the math, but in the words of Mary Poppins, that’s going a little bit too far, don’t you think…?)

    So using an object with Mercury’s mass in Sedna’s orbit, and a Hill Radius of 2 times the square root of 3 (per the paper) gives us a PI(sp) = ~3.9 x 10^-3, where ?PI(sp) is the planet-clearing capability of Mercury in Sedna’s orbit, a.k.a., our “standard planet.” This produces a mathematically discrete, IAU-inspired lower limit for any prospective planetary body’s orbital clearance capabilities. Everything with a lower PI value can be safely shunted into any desired sub-planet category desired, and everything with a higher value is hereafter to be known forever as a planet. Selah.

    The catch is, this new lower limit elevates Pluto, Ceres and Eris (and possibly others) all back to full planetary status. Also, it’s waaay more complicated than it needs to be, but remember: we’re trying to make both sides of the argument happy. This method allows us to keep Pluto as a planet, while allowing the IAU to keep its ridiculous orbitally-biased definition. Everybody wins.

    (*) The idea here is to attempt to place an outermost boundary on the orbits of truly “planetary” objects; if we’re going to limit our definition of the term “planet” based on orbital characteristics and not just size, then this seems like a reasonable step to take. As it turns out, if you set PI(sp) to Pluto’s orbit instead of Sedna’s you get PI(sp)= 2.53 x 10^-2, which still allows Pluto & Ceres back in the club, but leaves Eris and the other dwarf planets out in the cold, aha. Hey look: 10 planets, just like the IAU wanted!

    1. I also think that, on balance, Margot’s model has merit… certainly when set alongside the IAU’s arbitrary definition. However what, then, is PSO J318.5-22 ? At six times the size of Jupiter it’s definitely not a brown dwarf, but a planetary object of more presence there could hardly be. And given that it is wandering around in interstellar space, what object better encapsulates the Greek etymology of ‘planet’ ?

      1. “And given that it is wandering around in interstellar space, what object better encapsulates the Greek etymology of ‘planet’ ?”

        An excellent point, my friend.

    2. I recognize that your heart is in the right place, but, much as I love Pluto – this is not an argument about Pluto – it’s an argument about bad-science versus science-science.

      “Everybody” does not win when autocrats are allowed to decree “science” – whether it’s the IAU or the Spanish Inquisition. There is no validity to the IAU’s position on this issue, so why would I (or anyone) support some sort of compromise.

      Suppose someone said “but remember: we’re trying to make both supporters of Galileo and Pope Paul happy”. No, we’re not. In this case, there can be no compromise, because one side is right, and one side (The IAU and its ilk) is wrong – and wrong in a dangerous and anti-science way.

      1. I hear you, Bergmanson. This is why I found it laughably hilarious that placing “None Shall Call it Otherwise” planet Mercury in Pluto’s orbit resulted in math which showed the only two once-regular planets in our system becoming full-blown planets again, while tossing all the rest out.

        In other words, the whole thing was half intended to be a bit of reductio ad absurdum, using the IAUs nonsensical definition to provide what everyone wanted in the first place: they want simple grade-school text books that won’t need rewriting with dozens of new planets every few years; we want My Very Excellent Mother Consistently Jams Silverware Under the Nectarine Plate.

        I think there’s common ground here. ^_~

      2. It was pretty clear that you found the IAU’s position absurd – I certainly agree. Not sure I agree about the second part – I want the textbooks rewritten if new discoveries or new information is available – I never liked those “mnemonic devices” anyway – they are more about memorization than learning.

  12. @tsuchan You’re welcome! Glad I could help!

    @Bergmanson We could go back to the Stern-Levison study from 2000 which distinguished “uber planets,” those which gravitationally dominate their orbits, from “unter planets,” those that do not gravitationally dominate their orbits. Neither author said the latter should not be classed as planets. What is wrong with saying some planets gravitationally dominate their orbits, and some do not, but both fall under the umbrella of planets? I don’t mind the term “dwarf planet” for the latter as long as dwarf planets are acknowledged as a subclass of planets. This essentially amounts to enacting Resolution 5b from the 2006 IAU GA, which was voted down 333-91 (with four percent of the group participating).

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