“Stars are simple — given a star’s mass and age, you know its basic structure and history.”
— David Spergel, Princeton University chair of astrophysical sciences 
"Planets are complex, varied, and notoriously hard to define ... just ask Pluto."
— Martin Conrad, Amateur Worldbuilding Enthusiast
So, I'm not going to spend a lot of effort on creating a planet (or world) classification, à la Star Trek™, but taking a cue from the HEC Periodic Table of Exoplanets , the following table lists planet classes by mass ranges, with “official” classifications (as well as my own less prosaic class names).
As the old riddle asks: "Which is heavier: a pound of gold or a pound of feathers?"
The riddle, of course, hangs on the density of the materials mentioned. "A pound is a pound the world around" to modify the old saying. But a feather sculpted out of gold is far heavier than an identically shaped feather taken from a goose. It is the density of the two materials that makes the pound of feathers (uncompressed) take up far more volume than the pound of gold, and for a planet, the amount (mass) of the material composing it and the density of that material will result in a body of a given radius, enclosing a given volume.
For instance, a “mini‑Neptune”  is a planet with a mass up to 10 times that of Earth, a low‑density core and mantle of volatiles, and a thick atmosphere of hydrogen‑helium, but with a radius that can be as small as 1.6 Earth radii. In size, it may appear to be an Earth-like planet, but in character it is anything but. Its composition and atmosphere are more like an ice-giant, such as Uranus or Neptune (hence the name).
Another case-in-point: Mercury has 38% of Earth’s gravity—awkward, but not impossible for humans to get around in: after all, the Apollo astronauts managed well enough on the Moon in less than half of that. Mercury's gravity is due to having a density of 98% that of Earth, but that density is, in turn, due to most of its mass being composed of solid iron, with very little lithosphere and no hydrosphere. So, though Mercury has only 5.5% of Earth’s mass, because of the density of that mass, it has all condensed under gravity into just under 40% of Earth’s radius.
Remember as well, when we speak of a planet's gravity, we're talking here about surface gravity; so even though Mercury's mass is less than a twentieth of Earth's, its composition and resultant smaller radius means that its surface is closer to the center of a much denser body. And, the inverse-square law tells us that cutting the distance in half quadruples the effect—in this case, of gravity.
Similarly, a planet with a mass similar to Earth, but with more silicates in its mantle and less iron in its core could still have a similar density and gravity, but be larger in radius than Earth and still possess a habitable ecosystem.
Reading the labels on the graph, we see that only the masses and radii associated with points along the green line are those which indicate truly Earth‑analog worlds in terms of composition.
I have chosen to designate those worlds which lie specifically along the green line in the graph as geotic planets, to indicate their special Earth-analog possibilities (though not necessarily Earth-twin conditions). These planets are usually described by astronomers and cosmologists as "terrestrial" planets, but I have chosen to avoid that term because of its potential to imply that a planet is more Earth-like than it actually is.
If we zoom in to the smallest geotic mass ranges, we can see that those planets which fall into those ranges need not necessarily have Earth-like radii.
If we track across from the 1.5 Earth radius line to the green line and then down to the mass axis, we arrive at a mass of ~4.65 Earth radii.
Finally, if we specify a mass of 3.375 Earth-masses, and track up to the green line of geotic planets, we find a radius in the range of about 1.657 Earth-radii:
The Density Dilemma
Recall that calculating the radius from a known mass and density uses the relation:
However, making the same magnitude change in the mass (taking it from 2.5 to 2.0), and leaving the density at 1.1:
Composition of Planets
Note 1. The terms "gas", and "rock", are largely self-explanatory (see the next note about "metal"), but "volatile" is perhaps less obvious. In this sense, it means a substance which has a low boiling point and easily changes from a solid or liquid to a vapor.
Note 2. The term "metal", here, is the chemical definition, not the astronomical one. Remember, to astronomers, any element that is not hydrogen or helium is a "metal", even if it's a liquid or a gas. Although, the word "helium" is based on the name of the original Greek sun-god, Helios, and (having the Latin suffix "-ium") means Sun-metal. Stars were originally assumed to be made of metal, so when helium's lines were found in the Sun's spectrum—and no element then-known on Earth produced such lines—the element was misnamed. By the time anyone realized the error, the name had stuck.
However, from what is known of planetary accretion disks , it is safe to surmise that the materials most present are gasses like hydrogen and helium, volatiles such as water, carbon dioxide, ammonia, methane, etc., silicate dust and rocks, and iron. Heavier elements may be present, if the supernova explosion that created the cloud from which the disk formed was the death of a truly massive star.
Above, we declared a planet with a mass of 3.375 Earth-masses and 1.675 Earth-radii, which results in a surface gravity of 1.2011 Earth-gravities. We now use those same figures for mass and radius and calculate the planet’s density (relative to Earth):
Multiplying by 0.718 gives 3.96 g/cm³, which is slightly more than the mean density of rock in the table above, and almost identical to the density of Mars, which is 3.9335 g/cm³.
Taken together, the values for mass, radius, gravity, and density tell us that this planet is a Prodigal, nearly 3.5 times more massive than Earth and nearly 1.7 times Earth's size, with a surface gravity just over 120% of Earth's. It is composed of more material, in general, but the density of that material results in a larger volume, or planetary radius. This implies that a larger proportion of the planet's composition is probably in silicate rocks or volatiles, rather than metals.
Gaseous and Rocky planets
What about the range between the upper end of the gaseous density range (1.5 g/cm³) and the lower end of the rocky density range (3.9 g/cm³)—corresponding loosely to the realm of the volatiles? The table below shows a potential division of densities within the volatiles range:
So, combining the above tables, we can build a very general density-based planetary definition:
This serves to highlight—yet again—that mass, radius, surface gravity, density, etc., cannot alone be used to determine the type of planet under consideration; a cross-comparison of all of these characteristics (as well as others), must be taken into account.
In the case of Uranus, noting that its radius is only 4 times that of Earth (compared to Jupiter’s 11.21 Earth radii and Saturn’s 9.45 Earth radii) and that Uranus’ mass is only 14.54 Earth masses (again compared to Jupiter at 317.8 Earth masses and Saturn at 95.16 Earth masses) reveals that despite its density value, it must be an ice giant, rather than a gas giant.
Much closer to home, Venus also has the proper composition and falls into the proper ranges for mass (0.815 of Earth's), radius (0.9499 of Earth's), and density (0.951 of Earth's) to have an Earth-like gravity (0.904 of Earth's). However, it is now well-established that Venus is not a human-habitable world: it orbits at 0.723 AU, inside even the optimistic inner limit for the Sun’s habitable zone. Its surface temperature is hot enough to melt lead, and its extremely slow and retrograde rotation has doubtless contributed to its hostile surface conditions, as well as other factors such as lack of plate tectonics, etc.
"Gaean" Means Earth-twin
The lower two types of Geotics (Tellureans and Herculeans) in the above table, then, are planets possessing mass and radius ranges which, when associated with suitable compositions and other parameters, produce somewhat Earth-analog planets.
I use the specific term “Gaean” to designate worlds which:
- Are a subset of the Geotics (Tellureans and Herculeans), which is to say that they fall somewhere on the green line in the graphs above; and,
- Have mass and density combinations which result in radii and gravities which are truly Earth-like in terms of human habitability, if not precisely Earth-twins.
Note that this means that Venus is not termed a Gaean, because it is not an Earth-twin. The term Gaean refers only to those Geotics (Tellureans and Herculeans) which have Earth masses, radii, densities, gravities, and ecospheres which make them human habitable.
Extensive number-crunching in Python™ and Excel™ (with oft-repeated consultations of the graph above), has shown that the mass ranges listed in the table below produces gravities and densities in the Earth-analog range, when combined with the radius figures also listed.
In Habitable Planets For Man, Stephen H. Dole states that, "... the mass of habitable planets may vary over the range 0.4 to 2.35 Earth masses; the radius may vary from 0.78 to 1.25 Earth radii; while surface gravity may range from 0.68 to 1.5 g."
He also indicates on page 60 that tolerable/habitable rotation rates might be specified to be limited to the range of "... 96 hours (4 Earth days) per revolution at the lower end of the scale and 2 to 3 hours per revolution at the upper end...," but since rotation rates are completely independent of any other characteristic of the planet, that's not crucial to our current discussion.
The minimum mass value is set to that producing 0.68g on a planet with a radius of 0.780 Earth-radii. The maximum mass value comes directly from Dole's numbers.
The minimum radius comes directly from calculating the radius a planet must have if it possesses 0.40 Earth-masses and has a gravity 1.5 times that of Earth:
The maximum radius comes directly from Dole's work (though the radius can go up as high as 1.255 and still produce Gaean gravities.)
Note that 1.25 is slightly larger than the value given in this graphic from NASA reproduced below:
For instance, a mass of 1.65 and a radius of 0.40 results in a gravity of 10.3125 times that of Earth!
Using the mass range [0.40, 2.35] and a radius range of [0.78, 1.25], and stepping through the calculation at 0.05 units on both criteria resulted in 20532 mass/radius combinations, of which 15828 (77.1%) were either <0.68g or >1.5g.
Using the same mass range and a radius range of [0.58, 1.20], and this time stepping through at 0.01 units on both criteria resulted in a total of 67252 mass-radius combinations, of which 19097 (28.4%) produced surface gravities either 0.68 < g < 1.50.
So, don't assume that giving your planet just any mass in the range of [0.40, 2.35] Earth masses and just any radius in the range [0.78, 1.25] Earth-radii means it is an Earth-twin (Gaean) by default.
The numbers above are a rough guideline, only. Always do the math!
There are a few things to note, here:
- The masses of Uranus and Neptune are similar, and both lie in a range between 10 and 20 Earth masses.
- There is a sizable (78.012 Earth-masses) gap between the masses of Neptune and Saturn.
- There is an even larger gap (222.641 Earth-masses) between the masses of Saturn and Jupiter.
- As mentioned above, gas giants can possess masses of up to 13 Jupiter masses, or about 4131 Earth masses.
Above about 13.0 Jupiter masses, bodies become brown dwarfs, capable of deuterium fusion in their cores (and will perhaps even fuse hydrogen for a brief period of their lives), and thus should be treated as stars rather than as planets.
Thus, it is sensible to treat Saturn as representing about the midpoint of the lower-end of the gas giant range, with ice giants filling in the almost 80 Earth-mass gap between Neptune's mass and that of Saturn.
This modifies the Mass Classification Table from above to:
Note that although all those with a mass <10.0 Earth-masses are "terrestrial" planets, Midgeans and Pygmeans are Lithics and Prodigeans and Taloseans are Leviathans, leaving only the Geotics as Gaean-possible planets.
Rearranging the table to a more organized structure and adding an alphanumeric category gives us:
Note that, by the above classifications, several Solar System moons would be planets in their own right, were they to be directly in orbit around the Sun. I discuss this in my blog Planets and Worlds, Part 3: Moons.
4. modified from http://www.mdpi.com/2078-1547/5/2/296/htm
5. Stephen H. Dole. Habitable Planets for Man. (New York: American Elsevier Pub., 1970), 58.