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Here's the IAU definition of a planet (source):

A celestial body that (a) is in orbit around the Sun, (b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape, and (c) has cleared the neighbourhood around its orbit. (p. 1)

Part b) is the sticking point. What qualifies whether something is assuming hydrostatic equilibrium? M. Burša gives the criterion in his 1984 "Secular Love Numbers and Hydrostatic Equilibrium of Planets":

K_s <= 4 criterion for hydrostatic equlibrium.

(screenshot source). On the next page, Burša tabulates the k_s Love numbers for the major bodies:

Table II of K_s Love numbers

Importantly, note the values of k_s = 237 and 293 for Mercury and Venus respectively. Burša concludes:

The secular Love numbers k_s computed (Table II) demonstrate that the actual state of Venus, Mercury and of the Moon is far from hydrostatic equilibrium.

The oblateness of these bodies is incompatible with their rotation rates under pure hydrostatic equilibrium.

Please correct me if I have this wrong. It appears that the IAU definition of a planet excludes Mercury and Venus due to the hydrostatic equilibrium requirement, and that this has been clear since 1984.

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    $\begingroup$ If you are saying that Venus and Mercury aren't planets because they aren't perfectly round, then you can make the same argument for Earth and even Mars for that matter. Jupiter is nearly perfect but only because there is no surface to have an imperfection on. $\endgroup$
    – Deko Revinio
    Commented Feb 10, 2023 at 16:55
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    $\begingroup$ No, it's not because they aren't perfectly round. It's because they are far from hydrostatic equilibrium as shown by them being more oblate than can be explained by their rotational period and hydrostatic equilibrium. Earth and Mars meet the criterion for hydrostatic equilibrium: K_s = 0.938 and 1.27 respectively, which are less than 4. But The K_s for Mercury and Venus do not meet this criterion, far from it. $\endgroup$
    – Schroeder
    Commented Feb 10, 2023 at 17:32
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    $\begingroup$ The entire IAU definition is arbitrary. Part c), for example, has nothing to do with the properties of the object, and exists solely to minimize the number of planets on our solar system. For example, if you picked up Mercury and dropped it in the Kuiper Belt, it suddenly stops being a planet simply by virtue of location; likewise, any "planet 9" we find will fail this definition regardless of mass (as it will lie in the mind-body filled outer dollar system). $\endgroup$
    – Izzy
    Commented Feb 11, 2023 at 17:33
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    $\begingroup$ @Izzy If planet 9 exists (which we do not yet know is true) and if it responsible for the perturbations seen in KBOs, etc, it almost certainly will qualify as a planet. Moreover, the designation is anything but arbitrary. Planetary dynamicists say that the solar system is very close to being dynamically full. There is only room for about eight planet-like objects in the inner solar system, and that happens to be the number of planetary objects in the inner solar system. $\endgroup$
    – David Hammen
    Commented Feb 11, 2023 at 18:26
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    $\begingroup$ @Izzy And yep, you're an American. (Your profile says so.) It is predominantly Americans who oppose the very well deserved demotion of Pluto. This is partly due to the poor education system in the US, partly due to exaggerated national pride. Pluto was the only object formerly designated as a planet discovered by an American. Pluto is not a planet. (And I too am an American.) $\endgroup$
    – David Hammen
    Commented Feb 11, 2023 at 18:31

6 Answers 6

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You are citing a paper that has been cited only six times in the peer reviewed scientific literature since it was published in 1984, which was almost 40 years ago. One of those six citations was a self-citation. Papers that are as resoundingly under-cited as that are not definitive.

With that, the "hydrostatic equilibrium" aspect of what makes a planet a "planet" simply is not well-defined. The cited paper definitely is not definitive. The bottom line from the cited paper should not be that Mercury and Venus are far from hydrostatic equilibrium. The bottom line one should deduce from that paper is that the metric used in that paper is not a good metric for hydrostatic equilibrium, and hence the low citation rate.

It is hard to find any paper that is definitively accepted as defining a good parameter regarding hydrostatic equilibrium. Mercury and Venus are very slow rotators and are close to the Sun, and hence subject to tidal forces. These get in the way of establishing a good metric. The Earth is still recovering from the glaciation that ended about 12000 years ago. Moreover, there are signs that parts of former tectonic plates have dived almost to the core mantle boundary. The Earth is not in hydrostatic equilibrium. The Moon and Mars also are not in hydrostatic equilibrium. There are fast rotators such as Haumea that are triaxial in shape. This makes little sense from a naive hydrostatic equilibrium point of view. As an aside, Mike Brown, the discoverer of Haumea, was one of the key killers of Pluto as a planet. Mike Brown proudly uses @plutokiller as his Twitter username. "Hydrostatic equilibrium" is not a good metric unless one uses "approximately in hydrostatic equilibrium" as a rather fuzzy qualifier.

Regarding the other two attributes:

  • Orbiting the Sun is well-defined, okay, but wow. That means there are eight planets in the entire universe. All of the exoplanets that have been discovered to date are not "planets." However, this part of the definition completely bypasses several potential problems:

    • The brown dwarf / super-Jupiter problem. There's no clear dividing line between a brown dwarf and a super-Jupiter.
    • The newly forming star system problem. Things that might eventually become planets are not quite yet planets in those newly forming star systems.
    • The rogue planet problem. Whether planet-sized objects ejected from a star system still count as planets is debated, and that perhaps includes the hypothetical fifth giant planet that some posit was ejected from our solar system early in its formation.

  • The "clearing the neighboring" concept also is well-defined; there are multiple metrics that agree that the gap between the eight planets and the myriad non-planets is a huge multiple order of magnitude gap. We don't know whether this applies outside the solar system. It probably doesn't apply for newly formed star systems, but it probably does apply for star systems more than a few hundred million years old. Almost all of the exoplanets orbiting stars other than the Sun would most likely qualify as planets were it not for the "planets orbit the Sun" clause.

One of the chief proponents of the "clearing the neighborhood" qualification, Mike Brown (mentioned above) used as evidence for the proposed demotion of Pluto's status a previously written paper by one of the key opponents of the "clearing the neighborhood" qualification, Alan Stern, who is the chief scientist for the New Horizons spacecraft that flew by Pluto and is continuing to this day. Two other papers were also used, all showing a huge gap between Mars and Pluto.

That paper by Stern found a parameter with a vast six order magnitude gap between Mars and Pluto. In that paper, Stern proposed that the eight objects in the solar system that have "cleared their neighborhood" using his own parameter be called überplanets while the lesser objects that still appear to be round-ish be called unterplanets. The IAU decided to call them planets and dwarf planets, with the exception that moons did not qualify as either a planet or dwarf planet. Dwarf planets must be objects that orbit the Sun as opposed to orbiting a planet or dwarf planet. Stern's proposal would have designated some of the larger moons as unterplanets.

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    $\begingroup$ My understanding is that the hydrostatic equilibrium attribute was a bone tossed to the planetary geologists who only wanted the first two attributes, while planetary dynamicists only wanted the first and last attribute, but with the first attribute expanded to orbiting a star rather than the Sun. That was a no-harm, no foul bone to toss as anything large enough to have cleared its orbital neighborhood would easily be large enough to pull itself into a more or less rounded shape. (The potato radius is only about 200 to 300 km.) $\endgroup$
    – David Hammen
    Commented Feb 10, 2023 at 22:27
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    $\begingroup$ Papers that are as resoundingly under-cited as that are typically garbage. – That’s a gross overgeneralisation. Most under-cited papers have simply not turned out to be considered very relevant by the scientific community and that’s about it. What you can say from the citation count is that the paper in question is not an established reference for these values. $\endgroup$
    – Wrzlprmft
    Commented Feb 11, 2023 at 6:55
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    $\begingroup$ @Wrzlprmft I've toned down that aspect. The one thing that can be definitively said with regard to that very low citation count is that the metric used in that paper definitely is not a definitive metric. $\endgroup$
    – David Hammen
    Commented Feb 11, 2023 at 12:49
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    $\begingroup$ @wizzwizz4 There is no such other paper. One big problem is that papers such as the one cited by the OP assume a planet with an interior with uniform density and behaves as a perfect fluid. (That paper is far from alone in this regard.) Okay, so they've found a way to prove that terrestrial planets don't have a uniform density and don't act as a perfect fluid. There is no good metric regarding hydrostatic equilibrium (or lack thereof) for an object that has undergone differentiation into a core (possibly with multiple parts), a mantle (possibly with multiple parts), a crust, and maybe oceans. $\endgroup$
    – David Hammen
    Commented Feb 11, 2023 at 17:50
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    $\begingroup$ @Schroeder There are very, very few papers that use the secular Love number as a metric for hydrostatic equilibrium, and all have very low citation numbers. Those papers are pretty much ignored, I suspect because the secular Love number is widely viewed as being a poor metric. Then again, I haven't found any metric that is widely accepted. I have however found plenty of papers with much higher citation numbers that simply assume that Venus (for example) is in hydrostatic equilibrium and move on from there. $\endgroup$
    – David Hammen
    Commented Feb 12, 2023 at 12:57
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I directed this question to Mike Brown, and he answered on Twitter. Mike Brown is about as authoritative as possible.
enter image description here

The real answer here is to not get too hung up on definitions, which I admit is hard when the IAU tries to make them sound official and clear, but, really, we all understand the intent of the hydrostatic equilibrium point, and the intent is clearly to include Merucry & the moon

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    $\begingroup$ Isn't it more than a little ironic (and possibly hypocritical) for the guy who basically killed Pluto's status as a planet - which it had "enjoyed" for 76 years - based on getting hung up on definitions (as opposed to conventions)? $\endgroup$
    – Deepak
    Commented Feb 11, 2023 at 15:54
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    $\begingroup$ @Deepak The demotion of Pluto's status was very similar to the demotion of Ceres and the three other first discovered asteroids from planethood status in the mid 19th century. The first four asteroids were discovered in the early 1800s and were quickly called planets. No more were discovered for 40 or 50 years. But then the floodgates opened. Were all of those things "planets", or perhaps not a single one of them? The choice made at the time was none of them were planets. The floodgates opening on Kuiper Belt Object (KBO) discoveries partly motivated the demotion of Pluto. $\endgroup$
    – David Hammen
    Commented Feb 11, 2023 at 17:37
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    $\begingroup$ The response says "we all understand the intent of the hydrostatic equilibrium point", but presumably if that was the case, the question wouldn't arise in the first place? It feels at best like half an answer - the other half being an explanation of what that intent actually is. $\endgroup$
    – IMSoP
    Commented Feb 11, 2023 at 18:08
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    $\begingroup$ @William Herschel of Ostropol Here we have a direct and public answer from a high-level expert at the very top of the field of planetary science who was at the center of the process and controversy of the IAU’s redefinition of a planet. Yes, it’s one man’s opinion, but due to his extreme seniority, his opinion matters a lot. It also gives excellent insight into the intentions behind the IAU’s definition and what its authors had in mind, that is not clear from the text alone. That lets us correctly interpret it. $\endgroup$
    – Schroeder
    Commented Feb 12, 2023 at 11:38
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    $\begingroup$ @Schroeder That should have been included in the answer! The reader shouldn’t have to wonder why they should care about the opinion of some Twitter rando who happens to have taken a vaguely relevant username. $\endgroup$
    – William Herschel of Ostropol
    Commented Feb 12, 2023 at 18:56
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One subtle aspect of all this is that a "planet" need not be currently in hydrostatic equilibrium". From https://solarsystem.nasa.gov/planets/in-depth/:

The IAU therefore resolves that planets and other bodies, except satellites, in our Solar System be defined into three distinct categories in the following way:

A planet is a celestial body that (a) is in orbit around the Sun, (b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape [Emphasis added], and (c) has cleared the neighbourhood around its orbit.

In other words, the shape of a "planet" must correspond to some hydrostatic equilibrium, but possibly not the one corresponding to current conditions. Wieczorek et al. [1] have proposed that Mercury once rotated rapidly in a retrograde direction and became slowed down by tidal interactions with the Sun. If Mercury became too rigid to maintain equilibrium with such changing rotation, it would be frozen into a past equilibrium shape which would match the subtly worded IAU definition.

In the end,this is all a bit fuzzy because a precise equilibrium is not required.

Reference

Mark A. Wieczorek and Alexandre C. M. Correia, Mathieu Le Feuvre, Jacques Laskar, Nicolas Rambaux (2011). "Mercury's spin-orbit resonance explained by~initial retrograde and subsequent synchronous~rotation", Nature Geoscience 5(1), 18-21. https://doi.org/10.1038%2Fngeo1350

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    $\begingroup$ +1 for making sense of their oblateness. $\endgroup$
    – J.G.
    Commented Feb 12, 2023 at 22:58
  • $\begingroup$ That is an interesting point. So despite the use of the present tense, they don't explicitly say that it's the hydrostatic equilibrium from current conditions. I would normally read that into the use of the present tense. In either case, I'm going to go with Mike Brown's point that there is an intentional axiom behind the definition's crafting that Mercury through Neptune are planets. $\endgroup$
    – Schroeder
    Commented Feb 22, 2023 at 8:43
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No planet is in perfect hydrostatic equilibrium as no planet can be considered an ideal fluid but always has some finite rigidity. So their rotational flattening is always different from that of an ideal fluid (for the Earth for instance it is 1/298 rather than 1/233). And the IAU definition does not require a strict hydrostatic equilibrium in the sense of an ideal fluid, but merely that "it has sufficient mass for its self-gravity to overcome rigid body forces".

Anyway, the IAU does not relate at all to the definition of hydrostatic equilibrium used in the paper quoted by the OP, nor does the paper reversely suggest to use this as a criterion for a planet. The OP is just making here a non-existing connection in his question. The IAU does in fact not give a concrete theoretical physical definition of 'hydrostatic equilibrium' in this context at all. This epression is clearly just used in their definition of a planet to give a broad physical interpretation of the object to be 'nearly round'. The point is that a perfect ideal fluid just subject to its own gravity will be perfectly round i.e. a sphere (or an ellipsoid flattened due to rotation). But the IAU does not consider this to be a criterion to be a planet as they realize that objects have evolved from their initial state shortly after the formation of the solar system by cooling down and becoming partially rigid. It would be absurd to disqualify an object as a planet just because of this evolution. The crucial point is that they are still being held together by gravity. This is in contrast to irregularly formed rocks floating in the solar system, which have been created much later (e.g. by collisions of larger, already partially rigid objects) and that are held together by rigid body forces i.e. electrostatic forces.

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    $\begingroup$ Note that even stars are not ideal fluids that are in a strict hydrostatic equilibrium. Every star that undergoes fusion has a convective zone somewhere inside it, and that means the star is not quite in hydrostatic equilibrium. Quasi hydrostatic equilibrium is a guiding principle rather than a hard and fast rule. $\endgroup$
    – David Hammen
    Commented Feb 12, 2023 at 18:41
  • $\begingroup$ See the condition for hydrostatic equilibrium in equation 27 in the original question. Also, there is a definable sense in which bodies can be close or far from hydrostatic equilibrium; Mercury and Venus are far from hydrostatic equilibrium. $\endgroup$
    – Schroeder
    Commented Feb 22, 2023 at 8:08
  • $\begingroup$ @Schroeder The IAU does not relate at all to the definition of 'hydrostatic equilibrium' used in the paper you quoted, nor does this paper suggest to use this as a criterion for the definition of a planet. The connection you are trying to make is just not there. See also my edited answer above. $\endgroup$
    – Thomas
    Commented Feb 24, 2023 at 19:25
  • $\begingroup$ @Thomas The connection most certainly is: the IAU definition of a planet requires hydrostatic equilibrium with no quantitively definition of that included. We then go to the scientific literature and look for quantitively definition and find some. Perhaps other definitions could be made, but unless they are significantly conceptually different (as is Alan Stern's) they should be in agreement. $\endgroup$
    – Schroeder
    Commented Mar 5, 2023 at 10:59
  • $\begingroup$ @Thomas The fact that this paper predates efforts to precisely define a planet by decades, so it's not relevant that it doesn't suggest it's criteria for that purpose. He just defines it in general for any body. $\endgroup$
    – Schroeder
    Commented Mar 5, 2023 at 11:00
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It's about the Size of the deviation in absolute terms. Look at the values it gives for what Mercuries and Venusers flattening shoudl be, 1.013 and .061 parts mer million respectively, even if you multiple those numbers by k_s you get 18 and 240 parts per million respectively. Those are absolutely tiny values.

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  • $\begingroup$ That's a fair point, yet raises the question of what should be the quantitative criteria for deciding whether or not a planet is in hydrostatic equilibrium? Here I've found one and by that criteria, Mercury and Venus are not in H.E.. Is there a quantitively criteria, or is the definition mush? $\endgroup$
    – Schroeder
    Commented Feb 22, 2023 at 8:46
  • $\begingroup$ @DavidHammen also advocate approx. equlib., and pointed out the Alan Stern paper, which def's hydrostatic equlib.: "its shape becomes determined primarily by gravity rather than mechanical strength or other forces (e.g. surface tension, rotation rate) in less than a Hubble time, so that a body would on this time scale or shorter reach a state of hydrostatic equilibrium in its interior." $\endgroup$
    – Schroeder
    Commented Feb 22, 2023 at 10:07
  • $\begingroup$ According to nssdc.gsfc.nasa.gov/planetary/factsheet/mercuryfact.html the difference between the Equatorial and Polar Radii is 2.2 km, thats less then the htight of Mercury's highest mountain, and a Quarter of the height of mount everest. $\endgroup$
    – blademan9999
    Commented Mar 1, 2023 at 12:54
  • $\begingroup$ Ok, it's roundish. So what? Mercury is observed to be "far from hydrostatic equilibrium", so a significant point of the shape of the whole planet--not just mountains--is mechanical rather than hydrostatic equilibrium. The point is: what threshold of deviation from hydrostatic equilibrium are we to compare against? $\endgroup$
    – Schroeder
    Commented Mar 5, 2023 at 10:49
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Organizing comments into an answer: One resolution is that the definition in the question is incomplete. The actual text of the original Resolution B6 definition of a planet from the XXV IAU General Assembly in Prague adds a footnote:

(1) A planet[1] is a celestial body that (a) is in orbit around the Sun, (b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape, and (c) has cleared the neighbourhood around its orbit.

[1] The eight planets are: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune.

So Mercury and Venus are explicitly and axiomatically included in the definition of a planet.

This still leaves open the implicit question of whether exoplanets otherwise identical to Mercury and Venus would be considered planets. The phrase "hydrostatic equilibrium (nearly round)" is vague and not quantitive, but the footnote 1 could be interpreted to mean that quantitive realizations of this requirement must include bodies as far from hydrostatic equilibrium as Mercury and Venus are. Alternatively, "the eight" may be taken to mean that the 8 planets in our solar system are the only bodies that can ever be called planets, and everything else is an exoplanet. The parenthetical "(nearly round)" may be interpreted as a loosening of a strict hydrostatic equilibrium requirement, which would agree with inclusive interpretation of the footnote. However it may also be interpreted as an explanation of term hydrostatic equilibrium for the benefit of the laymen and not as a binding part of the definition.

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  • $\begingroup$ Mercury and Venus are not axiomatically included. They are included as, like the other planets mentioned in the footnote, they fulfill the condition (1) for an object to be considered a planet. $\endgroup$
    – Thomas
    Commented Mar 8, 2023 at 8:27

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