Stephen Ashworth

A Binary Mass-Orbit Nomenclature for Planetary Bodies

British Interplanetary Society, London

49 Princes Street, Oxford OX4 1DE, UKE-mail sa@astronist.demon.co.uk

Tel. 44 (0) 1865 250290

Abstract

When in 2006 the IAU General Assembly attempted to resolve the question of what may and what may not be considered a planet, the result was the creation of a new class of Solar System bodies called dwarf planets. But deficiencies in the definitions agreed on that occasion will force the existing nomenclature to be revised. The application of the qualifying adjectives giant, terrestrial and dwarf to planets is capable of being expanded into a comprehensive system of binary classification which describes separately an object’s mass over nine orders of magnitude and its type of orbit. Applying descriptive terms to specific mass classes matches physical reality surprisingly well. Under this system, bodies such as Pluto and Eris are still termed dwarf planets, but other qualifying terms are also made available for greater precision and clarity in different contexts.

Keywords

Planetary nomenclature, giant planet, terrestrial planet, dwarf planet.

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1. An unsatisfactory definition

On 24 August 2006, the 26th General Assembly of the International Astronomical Union (IAU 2006) attempted to settle the status of bodies orbiting the Sun as follows:

(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.

(2) A “dwarf 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 [2], (c) has not cleared the neighbourhood around its orbit, and (d) is not a satellite.

(3) All other objects [3], except satellites, orbiting the Sun shall be referred to collectively as “Small Solar System Bodies”.

Footnotes:[1] The eight planets are: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune.[2] An IAU process will be established to assign borderline objects into either dwarf planet and other categories.[3] These currently include most of the Solar System asteroids, most Trans-Neptunian Objects (TNOs), comets, and other small bodies.

Following this decision, Pluto and similar bodies are defined as dwarf planets. But at the same time the IAU states that Pluto is not a planet, but is instead a member of a different class of objects: “It was agreed that ‘planets’ and ‘dwarf planets’ are two distinct classes of objects”. This stipulation lacks the logic and clarity normally associated with scientific definitions.

The definitions suffer from other problems. Firstly, the condition of hydrostatic equilibrium for a planet in paragraph (1) is redundant, any object large enough to clear its orbital neighbourhood being automatically large enough to assume a closely spherical shape. The extent of that neighbourhood is poorly defined, particularly in the case of a planet in a significantly eccentric orbit or in the remote outer Solar System.

The specific reference to the Sun was out of date even in 2006, as by that time the majority of known planets by any definition (over 150: UC Berkeley 2005; Royal Museums Greenwich 2005) were orbiting stars other than our Sun, and assuming continued progress in astronomy the large majority of natural orbiting bodies of planetary mass to be discovered in future will continue to be exosolar ones.

Finally, it is anomalous that dwarf planets should receive special attention while terrestrial and giant planets do not, suggesting that the definitions currently in force are a makeshift solution to the immediate problem raised by the discovery in 2005 of Eris rather than the result of a considered overview of the planetary realm.

For these reasons it will be necessary to revisit the IAU planetary definitions. It will be seen that it is in fact possible to create a more satisfactory set of definitions, and the purpose of this article is to describe such a set.

2. Parochials versus universals

The first point to be made concerning planetary definitions is that some concepts are parochial to our own Solar System, while others are of general applicability throughout the astronomical universe.

The concepts of planet, giant and dwarf may clearly be used in the planetary system of any star, while a trans-Neptunian object is specific to the Solar System, since only the Solar System has a planet named Neptune to which this class can be related. A centaur is also a parochial, since the term is used for planet-crossers in the outer Solar System, not for planet-crossers in general – Apollo asteroids, for

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example, are not classified as centaurs, even though their orbits may cross one or more planetary orbits in the inner Solar System. Unless the term is extended to cover all such cases, a planet-crosser discovered in an exosolar system would not be a centaur. It may be desirable to adopt a term such as centauroid for the general case.

The concept of a planet brings with it two principal senses: the idea of a natural object orbiting the Sun or another star, and the idea of a body in a certain size range: not so large that it generates heat and light from nuclear fusion as does a star, but not so small that an astronaut standing there could leap from its surface into space in a single bound. A planet is a world, of which our planet Earth is the prototype.

These general ideas have led to problems as astronomy progressed. The largest satellite of a giant planet can easily match for size the smallest independently orbiting planet in the system; in our own Solar System, Ganymede and Titan are both larger than Mercury, though in terms of mass the planet is still greater than either of the moons. Titan, too, though a mere moon, possesses far more Earth-like surface conditions than does Mercury, with a substantial atmosphere and a methane-based hydrosphere where the planet has neither. The principal satellite of Saturn is thus more of an Earth-like world in terms of its surface conditions than the independent planet, which is more like the Moon. Should the nomenclature not try to reflect this in some way?

Again, bodies have been discovered in interstellar space not bound to any planetary system, but which in terms of mass and composition appear to resemble planets as generally understood. It is now accepted that bodies of planetary mass are frequently ejected from a planetary system during its chaotic period of formation (statements of fact made here which are common knowledge easily found in non-specialist encyclopedias are not specifically referenced to the technical literature.). Should these be termed planets or not? A number of alternative terms have come into use.

The upshot of these considerations is that when we speak of a planet we have in mind two characteristics: what kind of orbit it occupies, and what kind of body it is in itself. While orbital dynamicists tend to focus their attention on one of these characteristics, planetary geophysicists tend to focus on the other, and this is reportedly the underlying cause of the disagreements which created controversy at the IAU General Assembly in 2006 (Boyle 2010, ch.9).

These two characteristics are to a large extent independent of one another, leading logically to a binary nomenclature: we shall need one term to describe a body’s orbit, and a second, independent term to describe its nature. The terms giant planet, terrestrial planet and dwarf planet represent a binary system in embryo, but this system needs to be developed further.

3. Categories of orbit

The modern controversy about the applicability of planetary status to various astronomical objects emerged from the discovery of Solar System bodies smaller than the classical planets, starting with Ceres in 1801, which were associated with large populations of smaller bodies in similar orbits (“similar” being defined by semi-major axis or equivalently orbital period, while eccentricity and inclination may be different). It was felt that in such cases the planetary accretion process had stalled before reaching its logical conclusion – that of condensing into a single dynamically dominant body commensurate in size and gravitational influence with the existing planets, ranging in mass from Mercury to Jupiter. As a result, the current IAU definition adopted in 2006 requires a planet to have “cleared the neighbourhood around its orbit”, in other words to have cleared its orbital zone of other bodies, either by incorporating them into itself, or by capturing them into orbit around or resonant with itself, or by scattering them out of that zone altogether.

A glance at the Solar System demonstrates this principle. If we take our own planet, then the largest object next to Earth in the orbital zone strongly influenced by Earth’s gravity is of course the Moon, whose mass is 0.012 of Earth. The remaining near-Earth asteroids which orbit in this region have a trivial mass, even in comparison with the Moon. Earth itself thus accounts for more than 98.7% of the mass in its orbital zone, and it has captured into orbit around itself almost all the remainder of that mass, reasonably qualifying it for planetary status.

Earth has a small gravitational influence on Venus and Mars, and they reciprocally on Earth, but those influences are not great enough to cause major disruption to the orbits of any of these planets over

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the lifetime of the Solar System. Venus, Earth and Mars therefore define three distinct orbital zones, each of which is occupied by a planet.

The largest occupant of the Asteroid Belt, Ceres, on the other hand, accounts for only about one-third of the mass found today in the orbital zone that would be defined if a body of planetary mass was located in its position, and Ceres has no significant gravitational influence over the other two-thirds. Thus in the case of Earth, the primordial belt of planetesimals has undergone runaway accretion in which almost all of them were either incorporated into one body, captured by that body or scattered out of the zone. But in the case of the Asteroid Belt that runaway accretion has not taken place: the planetesimals have not coalesced into one single body as gravitationally dominant in their own region as Earth in its, but remain as a large population of smaller bodies. This is why it was thought reasonable to describe Earth as a planet, but not Ceres.

A word already exists to describe an orbiting planet-like object which is for some reason less than a planet, and it might at first appear surprising that the word planetoid was not officially adopted in 2006 for smaller worlds such as Pluto and Ceres.

Had it been adopted, the classification scheme would then have suggested itself in which the eight major planets known prior to 1930 were described as planets, and all smaller bodies in independent heliocentric (or sidereocentric) orbits as planetoids. Under this scheme, Mercury would be the smallest planet, and Eris the largest planetoid.

However, the mass of Mercury is twenty times that of Eris: in our own Solar System at least, there is a gap of more than a full order of magnitude between the sizes of the smallest planet and the largest planetoid. If a term descriptive of the mass is added, the use of two separate nouns becomes redundant.

The IAU’s actual decision to use the term dwarf planet for Eris reflects this reality. In the resolution quoted in section 1 above, the term was explicitly tied to the fact that Eris had “not cleared the neighbourhood around its orbit” (being a member of the Kuiper Belt population). It would thus be a planetoid under the suggested definition above, but speaking of a dwarf planetoid would not add any further information: dwarf planet is sufficient to cover both its small size and its lack of gravitational dominance.

The practical results – while perhaps not the intended purpose – of the IAU definitions agreed in 2006 and currently in use are that a planet is any substantial non-stellar body in heliocentric orbit, and that the dwarf members of this class have the two, causally linked characteristics of small size relative to the others, and membership of a population of similarly small bodies in their orbital vicinity which under different circumstances could have accreted to form a single body but have in fact not done so.

But there is a snag. The criterion for a dynamically dominant planet depends on two factors: in addition to its mass, its distance from the Sun is also important. The more distant a planetary body is, the greater its mass needs to be for it to dominate its surroundings to the same extent and over the same period of time, as both the circumference of its orbit and its orbital period increase. Thus a Mars-sized body, and even an Earth-sized one, might not be able to fulfill a criterion of dynamical dominance if located sufficiently far from the Sun.

At present the qualifier dwarf is being used to indicate low values of a quantity which is essentially that body’s mass divided by some function of its distance from the star it orbits. This is an unfortunate choice of term, since the upper size limit on dwarf planets as currently defined becomes larger as one proceeds through the outer Solar System and beyond, as Pluto is indeed fourteen times more massive than Ceres, and on average fourteen times further from the Sun. A dwarf in the outer Kuiper Belt might be the same size as a major planet in the inner Solar System.

This is not a problem at present, since such a large gap still remains between the masses of Eris and Mercury. But if in future a trans-Neptunian object of mass comparable with Mercury or greater is discovered, then the question of how a dwarf planet can, despite its name, be more massive than a regular planet in another part of the Solar System will become unavoidable, and the whole debate on definitions will be reopened.

Since orbital dominance and mass are thus partly independent variables, the most satisfactory solution would be one in which they are described by independent qualifying terms.

Since it is currently generally accepted that a body such as Pluto is legitimately described as a planet, with the controversy focused not on the noun but on the adjective used to qualify that noun, and on whether the adjective may or may not be removed, it is assumed here that the word planet may

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reasonably and uncontroversially be used as a basic umbrella term to describe all substantial non-stellar bodies in heliocentric (or sidereocentric) orbit.

From this starting-point, the state of motion of any astronomical body smaller than a star falls into one of three possible orbital states. These are discrete and non-overlapping, thus the corresponding terms are unambiguous:

• A planet is a body which orbits the Sun or another star.

• A nomad is a body which does not orbit any star.

• A satellite is a body which orbits a planet or a nomad.

In each case, a certain range of masses is applicable in order to exclude physically distinct types of body such as stars at the top of the scale and meteoroids at the bottom. Appropriate mass ranges shall be discussed further in section 4 below. Here we shall have more to say about the orbits.

If a body is orbiting the Sun, about six different types of orbital motion are possible. To begin with, the most fundamental distinction from the dynamical point of view is between planets which are and those which are not gravitationally dominant, and it is suggested here that the existing well-established terms major and minor are employed for this purpose, coinciding more or less with their current usage:

• A major planet is dynamically dominant in its orbital neighbourhood, and contains most of the mass within that zone (as do the eight major planets known following the discovery of Neptune).

• A minor planet is not dynamically dominant in its orbital neighbourhood, and represents less than half the total mass within that zone (as do all known members of the Asteroid and Kuiper Belts).

Within the class of minor planets, the following four or five cases may be distinguished, using the following suggested terms:

• A group planet (or beltoid planet): a member of a group or population or belt of similar bodies, following an approximately circular orbit (for example, Ceres).

• A scattered planet: a member of a group which has been scattered into a strongly elliptical orbit, but not so far that it encounters a major planet (Eris; Sedna).

• A centauroid planet: a scattered body whose elliptical orbit touches or crosses that of a major planet (centaurs; Apollo asteroids; comets). Such orbits are not stable over astronomical timescales.

• A resonant planet: a scattered body whose elliptical, major-planet-approaching or crossing orbit is in a resonance with that major planet (Pluto in a stable 2:3 resonance with Neptune; also quasi-satellites in a less stable 1:1 resonance).

• A trojan planet: a member of a group or population centered at either of the two stable Lagrange points controlled by a major planet, and thus a special case of a 1:1 resonant planet (the largest Jupiter trojan, Hektor, is too small to be counted as a dwarf planet).

The intention of the IAU resolution was clearly that any body large enough to be considered a dwarf planet might be found in any of these minor planet orbital states, and this intention is adhered to here. However, the word dwarf is not used because in normal usage it denotes size alone, not size in combination with distance from a star. In astronomy in particular, dwarf is used to indicate the opposite of giant. But minor is both broader in meaning, and already well-established in use more or less for this very purpose.

Looking beyond our own Solar System, bodies are beginning to be found which resemble planets but are not bound in orbit around any star. A number of suggestions have been made as to what to call

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them, including interstellar planetary mass object, planemo, planetar, and sub-brown dwarf (the definition of a planetar, however, overlaps with the category of brown dwarfs). The common-sense terms interstellar planet, free-floating planet, rogue planet, orphan planet and nomad planet have also achieved currency.

The qualifiers of the last three of these (rogue, orphan, nomad) work as either a noun or an adjective, and the latter is chosen here, since it does not necessarily imply origin within a solar system. While a rocky nomad must presumably have formed in orbit round a star and subsequently been ejected, it is not yet clear whether this must also always be the case for a gas giant, or whether gas giants can form in interstellar space through gravitational collapse in the same way as a star. Meanwhile the word nomad, from the Greek nomas, is a nice variant on the word planet, from the Greek planetes, with an appropriately similar meaning.

When we speak of a nomad, we are normally thinking of an interstellar nomad, but it would in principle be possible for an intergalactic nomad also to exist, thus one which is moving faster than the escape velocity of the nearest galaxy.

Finally, a satellite may be orbiting any planet or nomad. A satellite of a planet is therefore also orbiting a star, but is necessarily orbiting its planet closer and more frequently, and it is this more immediate connection with the planet which determines its status. By definition a satellite must be less massive than its primary.

There has been some discussion as to whether Pluto and Charon should be classified as a double dwarf planet, or binary dwarf planet, rather than a dwarf planet and a satellite, but it is hard to understand the purpose of introducing such a term. It would moreover be an illogical use of words. Since it is generally agreed that by definition a planet orbits the Sun directly, and not indirectly by virtue of its orbiting something else that is orbiting the Sun, a double planet would be a contradiction in terms: both of two bodies orbiting one another cannot be primarily orbiting the Sun. An analogy with the concept of a double star does not help because the term star contains no information about an object’s state of motion, whereas the term planet does.

The intention of the proposal is nevertheless clear enough: Pluto is not orbiting the Sun directly, but is orbiting the barycentre of the Pluto-Charon system, and is therefore a satellite of Charon, just as Charon is of Pluto: they are mutual satellites of each other, and there is no primary object in the system. The correct term would therefore be to describe Pluto and Charon as a double satellite: neither is dominant, both orbit the the barycentre of the system, which in turn orbits the Sun. But such a claim would be obviously incorrect: at 11.6% of Pluto’s mass, Charon is almost an order of magnitude less massive, and Pluto is clearly the primary.

Meanwhile the same logic would apply equally to every planet that has satellites, regardless of whether the barycentre was located within the body of the primary or outside it, since the precise location of that theoretical point above or below a planetary surface is not of physical significance either dynamically or geophysically. All planets with satellites wobble to a greater or lesser extent under the gravitational influence of the satellites. The advantages of singling out Pluto and Charon as a distinctly different class of object may therefore be doubted. However, a ruling on this question does not affect the mass-orbit classification scheme under discussion here.

4. Categories of mass

Having set out the orbital possibilities, we now turn to the nature of a body itself, which comprises most fundamentally its mass, its dimensions, its density, its composition and its internal structuring. Its surface conditions depend secondarily upon the amount of radiation received from a nearby star (or stars). For a given mass or range of masses, therefore, a wide variety of different densities, compositions and surface conditions are possible – as demonstrated in our own Solar System by the contrasts between say Mercury, Titan, Ganymede and Io (whose masses differ by less than a factor of two). Nevertheless, if one has to take a single number as being most fundamental, it would have to be the total mass of the body.

Unlike the classification of orbital states, in which each definition was distinct from all the others, the masses of bodies vary smoothly and continuously from stars through brown dwarfs to planets and all the way down through asteroids and meteoroids to grains of dust. Furthermore, the surface conditions on a particular world are only loosely associated with its mass because of the huge variety of different

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compositions and different environmental conditions (level of insolation, tidal forces) possible at any given mass.

The splitting of a range of masses into distinct categories is therefore arbitrary in its placement of dividing lines. But once this is recognised, the classification scheme may still be useful in providing a broad overview – it is still meaningful to describe one world as a giant and another as a dwarf, even though specific properties such as the presence or absence of an atmosphere, magnetosphere, solid surface, geothermal activity and so on may not be accurately predicted by that classification.

A linguistic problem arises here in that there are different expectations for the sizes of objects in different types of orbits; thus in normal speech one would expect a giant moon to be orders of magnitude smaller than a giant planet. Yet even in the Solar System moons and planets overlap in size, and in solar systems in general are almost certain to overlap in mass; furthermore large moons and small planets may be comparable in terms of their surface conditions, Titan and Earth being a case in point.

Again, a particular body may move from one type of orbit to another without changing its size or its basic physical characteristics, being captured into orbit around a planet, for example, as Triton is believed to have been, or ejected into interstellar space. This is why for scientific purposes the prejudice that bodies in different types of orbits will have intrinsically different sizes needs to be overcome and a single set of mass-related terms applied to all bodies, regardless of their orbital state, as is appropriate for a binary description.

The nature of those terms has already been widely discussed. John Davies wrote as long ago as 2001 (p.208): “What the whole debate may be telling us is that there are at least three types of planets; rocky terrestrial planets like the Earth and Mars, giant planets like Jupiter and Neptune and a recently recognised class of ice dwarfs which encompasses Pluto, Charon, some of the large icy satellites and the large trans-Neptunian objects”.

Again, following conversations with a number of astronomers, journalist and author Alan Boyle (2010, pp.197-198) wrote: “Even before Pluto was discovered, the solar system was divided into two classes of planets: the rocky worlds like Earth, and the gas giants beyond. Pluto has pointed the way to the solar system’s third great class of planets, no less important than the other two.” And he reported the words of planetary scientist and Principal Investigator of NASA’s New Horizons mission to Pluto, Alan Stern: “the new view is four terrestrial planets, four gas giants, and hundreds of Plutos”.

The problem is to find a non-arbitrary starting-point. Since there is, at least in principle, a fairly clear physical boundary between the largest gas giant planet and the smallest brown dwarf, the method chosen here is to take the largest possible planet and work downwards. A figure of 13 Jupiter masses is usually taken to represent the boundary between giant planets and brown dwarfs.

Unfortunately this boundary is in practice a fuzzy one because the criterion for a brown dwarf, that the fusion of deuterium takes place during the earlier part of its life, does not lead to a clear minimum mass, but also depends on the composition of the body. This fuzziness cannot be easily resolved: brown dwarfs in general do not usually generate heat by nuclear fusion since the period of time while they do so is a relatively short fraction of their overall lifetimes, and therefore their status as brown dwarfs is theoretical rather than observational. But their masses can be found observationally, and the mass of a body is often its first quantitative body property to be measured.

The practical solution is therefore to choose an arbitrary giant planet / brown dwarf dividing line in terms of mass somewhere near the middle of the range of fuzziness, and to accept that some of the largest giant planets thus defined may also have exhibited brown dwarf behaviour early in their history, while some of the smallest brown dwarfs may have failed to do so.

In round numbers, the notional boundary between planets and brown dwarfs (slightly adjusted to 12.6 Jupiter masses) is equivalent to 4000 Earth masses, or 2.4 x 1028 kg. From this starting-point, mass classes can be constructed such that each class contains bodies within a single order of magnitude size range, thus from 4000 to 400 Earth masses, from 400 to 40, and so on.

(Alternatively one might have used a figure of 1.9 x 1028 kg = 1000 √10 = 3162 Earth masses, thus placing Earth exactly in the centre of a mass band on a logarithmic scale. But this would put the giant planet / brown dwarf dividing line at around 10 Jupiter masses, which is too small, unless one decides to redefine the term brown dwarf to include all non-stellar bodies of 10 Jupiter masses and above. Here it is decided to steer closer to physical reality, and allow Earth to sit in the lower half of its logarithmic mass band.)

In order to create a set of descriptive terms, the three words giant, terran and dwarf are employed in their common-sense meanings to define broad classes, with the prefixes super-, mid- and sub- added in

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an obvious way to create a set of more specific terms within each class. Terran is employed as a shorter and thus more convenient variation of the common description terrestrial for rocky worlds.

Everything below the mass of a subdwarf is covered with the term infradwarf.This reasoning produces the following nomenclature (Table 1).

Mass (kg) Mass (Earth masses) Term Class2.4 x 1028 – 2.4 x 1027 4000 – 400 supergiant giants2.4 x 1027 – 2.4 x 1026 400 – 40 midgiant giants2.4 x 1026 – 2.4 x 1025 40 – 4 subgiant giants2.4 x 1025 – 2.4 x 1024 4 – 0.4 superterran terrans2.4 x 1024 – 2.4 x 1023 0.4 – 0.04 midterran terrans2.4 x 1023 – 2.4 x 1022 0.04 – 0.004 subterran terrans2.4 x 1022 – 2.4 x 1021 0.004 – 0.0004 superdwarf dwarfs2.4 x 1021 – 2.4 x 1020 0.0004 – 0.00004 middwarf dwarfs2.4 x 1020 – 2.4 x 1019 0.00004 – 0.000004 subdwarf dwarfs2.4 x 1019 and below 0.000004 and below infradwarf –

Table 1. Proposed nomenclature by mass classes

The billionfold difference in mass between the smallest possible planet defined on this system, and the largest, may thus be divided into three broad categories covering a factor of a thousand each, or into nine narrow ones covering a factor of ten each, according to whatever is more suitable for a particular discussion.

This simple scheme maps surprisingly well onto the known Solar System bodies, as follows. (Only named bodies are included, thus excluding some recently discovered Kuiper Belt objects which at the time of writing have not yet been named. Masses are drawn from standard encyclopedias since precision is irrelevant, and the bodies named are given in order of decreasing mass.)

• Supergiants: none are known in the Solar System, but many have been found orbiting stars other than the Sun.

• Midgiants: Jupiter and Saturn. The midgiant/supergiant boundary is at 1.26 Jupiter masses, thus anything significantly larger than Jupiter (by more than a factor of 1.26) becomes a supergiant.

• Subgiants: Neptune and Uranus.

• Superterrans: Earth and Venus.

• Midterrans: Mars and Mercury.

• Subterrans: Ganymede, Titan, Callisto, Io, Moon, Europa.

• Superdwarfs: Triton, Eris, Pluto, Makemake, Titania, Oberon, Haumea, Sedna.

• Middwarfs: Rhea, Iapetus, Charon, Ariel, Umbriel, Dione, Tethys, Quaoar, Ceres, Orcus, Vesta.

• Subdwarfs: Pallas, Enceladus, Miranda, Proteus, Hygiea, Mimas, Nereid, Interamnia, Davida, Juno, Eunomia.

How closely does the bottom of the range match physical reality? Just as the top of the planetary mass range is loosely defined by the fuzzy physical distinction between supergiant planets and brown dwarfs, so the bottom of the range is also loosely defined, according to the 2006 IAU resolution, by the physical criterion that a planet (whether dwarf or not) should be massive enough to adopt “a hydrostatic equilibrium (nearly round) shape”.

This is, however, a function not only of mass but of composition, icy bodies relaxing to roundness more readily than rocky ones. The IAU specified in an earlier (16 August) draft of the

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resolution that a hydrostatic equilibrium shape was generally expected of all bodies having a mass of at least 5 x 1020 kg and a diameter of at least 800 km (appropriate to a body of density 1865 kg/m3), and further noted that Pallas, Vesta and Hygiea (or Hygeia) might also be considered planets if they were found to have sufficiently rounded shapes, despite their falling well below that critical mass.

The relevant physical criterion therefore defines a range of masses rather than a sharp physical cutoff point at a single value. It is proposed to apply the same philosophy here as was earlier applied to the top of the range: to define the nomenclature according to a precise value of mass; to associate one physical property with bodies significantly over that value and another with those significantly below it; and to accept that bodies close to the dividing line may exhibit the one property or the other regardless of whether they are above or below it.

This procedure is justified by the fact that the geophysical properties of interest to planetary scientists, such as internal differentiation and volcanic activity, are not ones that simply switch on at some critical mass for a given composition, but rather are present to a greater or lesser degree over a range of masses, depending also upon other factors such as tidal heating.

The critical mass stated by the IAU is only a factor of two above the dividing line given here between middwarf and subdwarf categories, with Pallas and Hygiea, singled out as candidate dwarf planets, falling into the lower category. It is therefore noted here that the bottom end of a proposed classification of planets into nine mass brackets, each an order of magnitude in size, matches the pre-existing minimum physical criterion of planethood surprisingly well:

• Bodies from middwarfs upwards will possess a hydrostatic equilibrium shape, though a few irregularities will be found close to the bottom of the middwarf bracket as is demonstrated by the case of Vesta.

• Subdwarfs may or may not be rounded, representing the fuzzy area where the mass figure alone is not predictive of shape; however, most of those remaining to be discovered will be in the Kuiper Belt and therefore of softer, icy composition.

• Infradwarfs are not expected to be found in hydrostatic equilibrium shape.

The boundary between middwarfs and subdwarfs corresponds to a diameter of 771 km, assuming a density of 1000 kg/m3, or 612 km, assuming a density of 2000 kg/m3.

The boundary between subdwarfs and infradwarfs corresponds to a diameter of 358 km, assuming a density of 1000 kg/m3, or 284 km, assuming a density of 2000 kg/m3. It is thought that defining mass classes below this size would not be of practical value.

It thus becomes unnecessary to submit each borderline body separately to a special committee for consideration on its merits for inclusion into one category or another. The mass of a body is one of its most fundamental properties which is measured, or at least estimated, during the normal course of astronomical discovery. That body then falls automatically into one or another mass class without any more exact observations of its precise shape, or a judgement along the lines of “how round is ‘round’?”, needing to be made.

The long-established term asteroid has been used for members of the Main Asteroid Belt between Mars and Jupiter, and for small inner Solar System bodies which may have originated in and been scattered out of that belt, as well as for exosolar analogues of that belt. However, it tends to conjure up the image of an irregular body, and it seems unlikely that Ceres will very often continue to be referred to as the largest asteroid once it has been examined close-up by the Dawn spacecraft in 2015 and revealed as a miniature planet in its own right.

The suggestion would be to retain asteroid as a synonym (or a better alternative) to infradwarf, thus covering all bodies in heliocentric (or sidereocentric) orbit smaller than subdwarf size. An asteroid would then be by definition any body in such an orbit of mass between 2.4 x 1019 kg and perhaps 1000 kg, the lower limit depending on where one wanted to draw the line between the smallest asteroids and the largest meteoroids.

The word planetoid is similar in meaning to asteroid, and may also be regarded as a synonym for a body in the same mass range.

In its 2006 resolution, the IAU covered this category of bodies with the somewhat unwieldy term Small Solar System Bodies (all four words capitalised). Again it would probably be more convenient to

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use the general term asteroid or planetoid for these. But a ruling on this question does not affect the mass-orbit classification scheme under discussion here.

Regarding the terran/giant boundary, a point recently made in a news release from San Francisco State University (2014) by Stephen Kane is of interest:

“What we’ve learned, just over the past few years, is that there is a definite transition which occurs around about 1.5 Earth radii”, he [Kane] continued. “What happens there is that for radii between 1.5 and 2 Earth radii, the planet becomes massive enough that it starts to accumulate a very thick hydrogen and helium atmosphere, so it starts to resemble the gas giants of our solar system rather than anything else that we see as terrestrial.”

For a planet of Earth’s density, a radius of 1.6 Earth radii corresponds to a mass of 4.0 Earth masses, again aligning the notional boundary between terran and giant planets proposed in Table 1 reasonably closely with an observable physical boundary between different types of planet. But again, the physical boundary is a fuzzy one extending over a range of masses, and it needs to be accepted that some superterran planets will have surface conditions more closely resembling those on subgiants, and vice versa.

The mass classes are a convenience for rapid and uncontroversial categorisation of newly discovered worlds, and cannot be precisely predictive of the wide variety of surface conditions that will be encountered on closer examination.

5. Composition-mass-orbit categories of particular objects

Putting the mass and orbit terms together, and prefixing them if required with a term such as ice/icy, gas and rock/rocky in order to identify the predominant constituent, as is already normal practice, one arrives at the following descriptions of particular objects.

Pluto is most generally a dwarf planet, in agreement with the currently accepted terminology. It orbits the Sun independently, but like other dwarfs in our Solar System it has not undergone runaway accretion or acheived gravitational dominance, and is therefore from a dynamical point of view a minor planet.

Its fullest description would be as an icy superdwarf resonant minor planet, though one would not often want to be so inclusive, specifying at the same time its broad composition, its mass to within an order of magnitude, its specific orbital state, its gravitational significance and its general orbital state.

For dynamical purposes, one would refer to it as a minor planet or a resonant planet. For geophysical purposes, it would be a superdwarf planet, similar to other superdwarf planets such as Eris and Makemake, and also to superdwarf satellites such as Triton and Titania. The terminology also makes clear that it is significantly larger than mere middwarf planets such as Quaoar and Ceres, and middwarf satellites such as Rhea and Charon.

Earth and Venus are terran planets, or more specifically rocky superterran major planets. While it may seem odd to describe our Earth as superterran rather than midterran, the terminology is justified by the fact that most of Earth’s surface is not literally terrestrial at all, but oceanic, and Earth’s actual land surface area is similar to that of a midterran body such as Mars. Venus, too, is in a sense an oceanic planet, covered with a global ocean of carbon dioxide, not as a liquid but in the supercritical state. But it is no doubt true that exosolar superterrans will be discovered which lack volatiles and have surfaces of bare rock (if its existence is confirmed, this would be true of Alpha Centauri Bb); this is part of the natural variation of surface conditions which, as noted above, any classification by mass must accept.

Earth is located not too far below the middle of the superterran mass bracket located at 1.265 Earth masses, allowing a definition of exosolar Earth-analogues from 4.0 to 0.4 Earth masses to coincide with the superterran range, perhaps including also the midterran range if it is wished to include Mars-like and Mercury-like worlds. Those exosolar superterrans may, however, be independent major planets, or they may be satellites of giant planets, or they may be minor planets, perhaps resonant with a giant, an architecture which does not occur with planets of greater than superdwarf mass in our own Solar System.

Mars and Mercury are also terran planets, and more specifically they are rocky midterran major planets. Again, there are prospects of finding midterran planets or satellites in exosolar systems. Such midterran worlds, together with the superterrans, would invite investigation from the point of view of

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searching for indigenous Earth-analogue life, if located within a suitable range of distances from their local star.

Ganymede, Titan, Earth’s Moon and so on are subterran satellites. Currently all the subterrans known in our Solar System are satellites of major planets, comprising in fact their six largest satellites, but it is plausible that subterran planets may be found around other stars, and that they might or might not be gravitationally dominant in their respective orbital zones.

When one considers the terran worlds Titan, Mars and Earth in particular, it is clear that broadly terrestrial surface conditions are found on a wide range of bodies but that Earth is towards the top of that mass range, at least so far as the evidence of our own Solar System goes, again justifying superterran as a suitable descriptive bracket for our own planet.

Sedna has been referred to variously as a detached object, a distant detached object, an extended scattered disk object and an inner Oort cloud object. It is unusual in that its aphelion is over twelve times more distant from the Sun than its perihelion, yet unlike known cometary orbits it does not cross or approach the orbit of any known planet. It may have been perturbed into its current highly elongated orbit by a transient nomad visitor from interstellar space, or by another object similar to itself in mass, or by a yet undiscovered planet of the terran or giant classes. In either case it is, like Pluto, a superdwarf planet, but, unlike Pluto, a scattered planet.

The term comet is currently often applied not only to comets in the observational sense of a coma and tails of gas and dust, but to any asteroidal object with sufficient volatile content that, were it to pass close to the Sun, it would suffer outgassing and create the observable phenomenon of a comet. The present author finds this illogical since almost all of these bodies, residing in the presumed Oort cloud, do not in fact approach the Sun during their lifetimes, and do not in fact generate any observable halo or tail. Meanwhile, given such a definition, even large icy outer Solar System bodies such as Pluto would also have to be called comets, since they too would produce a cometary coma and tail if perturbed into a sun-approaching orbit.

It would seem more logical to restrict the term comet to the visual phenomenon observed when an icy asteroid or potentially an icy minor planet actually does approach the Sun sufficiently closely for outgassing to occur. This would then match the use of the term meteor, which is again a word for the visual effect resulting when a solid body – a meteoroid – encounters unusual conditions on falling into a planet’s atmosphere. However, a ruling on this question does not affect the mass-orbit classification scheme under discussion here.

Would any body in the three giant groups have to be either a major planet or a nomad? A subgiant satellite of a supergiant planet would have a mass between 0.01 and 0.001 of that of the planet, whereas in our own planetary system Charon, the largest known satellite relative to its primary, has 0.116 the mass of Pluto and the Moon 0.012 that of Earth. But these two examples suggest a rule in which the disparity in size between a primary and a secondary needs to get larger as the system is scaled up. While stars form readily in pairs closely matched in mass, the formation mechanism for stars is different from that for planets, suggesting that closely matched mutual satellites (or binary planets) analogous to double stars are unlikely to be found in practice.

Could a giant planet possibly also be a minor planet? It is reported that two planets of at least midgiant size (m sin i = 0.187 and 0.658 Jupiter masses) orbiting the nearby solar-type star HD 45364 (distance 107 light-years, spectral type G8V) have been found in orbits which almost touch but are stabilised by a 2:3 resonance, meaning that either the smaller one must be considered a midgiant resonant minor planet or the concept of dynamical domination of an orbital zone by a major planet must be modified to take account of such possibilities. The authors write in their introduction (Correia et al. 2009):

Among the known multi-planet systems, a significant fraction are in mean motion resonances, the majority of which are in low-order resonances. The 2:1 resonance is the most common (HD 73526, HD 82943, HD 128311, GJ 876), but other configurations are observed as well, such as the 3:1 resonance in HD 75732 or the 5:1 resonance in HD 202206.

Similarly, the eccentric orbits of the two supergiant planets of Upsilon Andromedae (c and d, with eccentricities between 0.25 and 0.3 – greater than the 0.248 of Pluto’s orbit) indicate that scattered major planets are possible. Meanwhile Neil Comins (2010, pp.180-181) has suggested that two planets,

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each having a mass similar to that of Earth, could stably occupy each other’s L4 and L5 Lagrange points: these would be superterran minor planets.

It is hoped that the nomenclature developed here will be sufficiently flexible to extend to these and other permutations of planetary size and orbit which are not found in our own Solar System.

6. Conclusion

It is concluded that the nomenclature concerning planets and other Solar System bodies, as well as their interstellar counterparts, can be improved and made more precise by adopting a conceptually simple and self-consistent binary terminology, one part of which specifies a body’s mass bracket, and the other specifies its orbital state.

Although using specific values of mass cuts roughly through the inevitable fuzziness at the top and bottom of the range, this usage has the advantage of applying a term to a body as soon as the mass has been determined, and does not leave that body in terminological limbo until more exacting observations of its composition and figure have been made.

This binary system is already implicit in current use of the terms giant planet, terrestrial planet and dwarf planet, but oddly contradicted by the IAU’s 2006 ruling that dwarf planets are not planets.

A revision of the current definitions will be forced if at some future time a trans-Neptunian object comparable in mass with Mercury is discovered.

The naming system proposed here supplies appropriate terms for a variety of bodies over nine orders of magnitude in mass and occupying a variety of different types of orbit.

References

Alan Boyle, The Case for Pluto: How a Little Planet Made a Big Difference (John Wiley, Hoboken NJ, 2010).

N. F. Comins, What If the Earth Had Two Moons? And Nine Other Thought-Provoking Speculations on the Solar System (St Martin’s Press, New York, 2010).

A. C. M. Correia et al. (2009), “The HARPS search for southern extra-solar planets XVI. HD 45364, a pair of planets in a 3:2 mean motion resonance”, Astronomy and Astrophysics, retrieved online as preprint: arXiv:0902.0597 (accessed 9 Feb. 2014), doi 10.1051/0004-6361:200810774.

John Davies, Beyond Pluto: Exploring the outer limits of the solar system (Cambridge University Press, Cambridge, 2001).

IAU news release 0603, “IAU 2006 General Assembly: Result of the IAU Resolution votes”, http://www.iau.org/public_press/news/detail/iau0603/ (accessed 2 Feb. 2014).

Royal Museums Greenwich, Nov. 2005, http://www.rmg.co.uk/explore/astronomy-and-time/astronomy-facts/faqs/how-many-extrasolar-planets-have-been-discovered-what-are-their-names (accessed 2 Feb. 2014).

San Francisco State University news release, 17 April 2014, http://news.sfsu.edu/kepler-astronomers-discover-new-rocky-planet-may-have-liquid-water (accessed 20 April 2014).

UC Berkeley News news release, 13 June 2005, http://www.berkeley.edu/news/media/releases/2005/06/13_planet.shtml (accessed 2 Feb. 2014).

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