Planets to be redefined again?

[bilby]

That's not an answer.

I am confident that it is.

 

[Bomb#20]

So, do you propose that the primary criterion, for deciding what qualifies as a planet, should be that the category must result in a small enough number of planets as to be able to be readily memorized by schoolchildren?

Perhaps we should also return to the ancient definition of element, because four elements are easy to remember, while 91 is far too many for anybody (except Tom Lehrer, obvs.), and that's before we even consider elements without extant primordial isotopes.

How do you get 91??

If you count stuff which is truly primordial you have only 84. And if you count stuff that's present from decay then you have 93.

How would you expect me to know that? I'm no Tom Lehrer, you know.

That's not an answer.

91 was an old answer to the elements occurring in nature and it's almost accurate. Technetium does not have the half life to remain, nor is it in the decay chain of anything with enough half life. By a strict look at decay chains it's valid, 91 elements on Earth.

Sounds like you know how he got 91.

However, there is a very low but non-zero rate of neutron capture by U-238 which then decays to Np-239, then Pu-239.

Actually the right answer is 94. Turns out Technetium-99 occurs naturally in uranium ore, in parts per quadrillion.

 

[Loren Pechtel]

So, do you propose that the primary criterion, for deciding what qualifies as a planet, should be that the category must result in a small enough number of planets as to be able to be readily memorized by schoolchildren?

Perhaps we should also return to the ancient definition of element, because four elements are easy to remember, while 91 is far too many for anybody (except Tom Lehrer, obvs.), and that's before we even consider elements without extant primordial isotopes.

How do you get 91??

If you count stuff which is truly primordial you have only 84. And if you count stuff that's present from decay then you have 93.

How would you expect me to know that? I'm no Tom Lehrer, you know.

That's not an answer.

91 was an old answer to the elements occurring in nature and it's almost accurate. Technetium does not have the half life to remain, nor is it in the decay chain of anything with enough half life. By a strict look at decay chains it's valid, 91 elements on Earth.

Sounds like you know how he got 91.

But it's always been wrong. Np and Pu have been known to be naturally occurring for a long time.

However, there is a very low but non-zero rate of neutron capture by U-238 which then decays to Np-239, then Pu-239.

Actually the right answer is 94. Turns out Technetium-99 occurs naturally in uranium ore, in parts per quadrillion.

Didn't know that bit. Guess it must be a fission fragment.

 

[lpetrich]

Wikipedia has  List of gravitationally rounded objects of the Solar System - the Sun and all the geophysically-defined planets -  Planetary-mass object

I'll list them by mean radius (ikm), mass (Earth masses), -, mean density (g/cm^3), and moment of inertia (mass*radius^2), when I can find any of these. I've sorted by radius.

• Sun 696,000 333,000 - 1.409 0.070
• Jupiter 69,911 317.8 - 1.326 0.276
• Saturn 58,232 95.2 - 0.687 0.22
• Uranus 25,362 14.5 - 1.270 0.23
• Neptune 24,622 17.1 - 1.638 0.23
• Earth 6,371 1.000 - 5.513 0.331
• Venus 6,052 0.815 - 5.243 0.337
• Mars 3,390 0.107 - 3.934 0.364
• (Jupiter) Ganymede 2,634 0.0248 - 1.936 0.312
• (Saturn) Titan 2,576 0.00225 - 1.880 0.341
• Mercury 2,440 0.055 - 5.427 0.346
• (Jupiter) Callisto 2,410 0.0180 - 1.830 0.355
• (Jupiter) Io 1,815 0.0150 - 3.528 0.378
• (Earth) Moon 1,737 0.0123 - 3.346 0.303
• (Jupiter) Europa 1,569 0.0804 - 3.010 0.346
• (Neptune) Triton 1,353 0.00358 - 2.061
• 134340 Pluto 1,188 0.00218 - 1.853
• 136199 Eris 1,163 0.0027 - 2.43
• (Uranus) Titania 789 0.00059 - 1.72
• (Saturn) Rhea 764 0.00039 - 1.23 0.399
• (Uranus) Oberon 761 0.00050 - 1.63
• (Saturn) Iapetus 736 0.00030 - 1.08
• 36472 Makemake 715 0.00052 - 2.1
• 225088 Gonggong 615 0.00029 - 1.74
• (Pluto) Charon 604 0.00025 - 1.65
• (Uranus) Umbriel 585 0.00020 - 1.40
• (Uranus) Ariel 579 0.00023 - 1.67
• (Saturn) Dione 562 0.00018 - 1.48 0.33
• 50000 Quaoar 545 0.00020 - 1.7
• (Saturn) Tethys 533 0.00010 - 0.98
• 90377 Sedna 500
• 1 Ceres 470 0.00016 - 2.16
• 90482 Orcus 458 0.00008 - 1.4
• 120347 Salacia 423 0.00008 - 1.5
• 136108 Haumea 390 0.00066 - 1.885
• (Saturn) Enceladus 252 0.000018 - 1.61 0.332
• (Uranus) Miranda 236 0.000011 - 1.20
• (Saturn) Mimas 198 0.000006 - 1.15

 

[lpetrich]

As one can see, minor planets and moons are mixed together, and moons overlap with the major planets.

I've included moment of inertia because it is a measure of amount of central concentration. The moment of inertia of some object around some axis is the sum of (mass of that bit) * (distance from that axis)^2 over every bit of that object. For a spherical one, it is the same in all directions, while for an equatorial bulge produced by spin, the moment of inertia for the spin axis is larger than for the equatorial directions. For definiteness here, I've used the polar moment of inertia.

Constant density: moment of inertia = 2/5 = 0.4

If the material has an equation of state of (pressure) ~ (density)^2 ("n = 1 polytrope") then its size is independent of its mass, something close to true of Jovian-mass planets.

Pd2: moment of inertia = (2*(pi^2 - 6))/(3*pi^2) = 0.261

Something called the Darwin-Radau equation can be used to estimate an object's moment of inertia from its departure from sphericity, its mass, its size, and its rate of rotation. This departure can be in shape (flattening) or in gravity. That usually gives very good results if the object is not too concentrated in its center, and in this case, that equation gives 0.263.

The Darwin here is Charles George Darwin, a grandson of the famous biologist.

Sources of values of moments of inertia:

• Precession: Venus, Earth, Mars
• Libration: Mercury, Moon -- oscillations around synchronous rotation
• Interior modeling: Jupiter
• Darwin-Radau estimates: (Jupiter), Saturn, Uranus, Neptune, Io, Europa, Ganymede, Callisto, Enceladus, Dione, Rhea, Titan

All also with the help of departures from sphericity of these bodies' gravity.

 

[lpetrich]

I must note that the Sun's moment of inertia is from stellar-structure modeling. We have a much clearer picture of the interior of the Sun than the interior of our home planet.

Here is everything with a moment of inertia:

• Sun 696,000 333,000 - 1.409 0.070
• Jupiter 69,911 317.8 - 1.326 0.276
• Saturn 58,232 95.2 - 0.687 0.22
• Uranus 25,362 14.5 - 1.270 0.23
• Neptune 24,622 17.1 - 1.638 0.23
• Earth 6,371 1.000 - 5.513 0.331
• Venus 6,052 0.815 - 5.243 0.337
• Mars 3,390 0.107 - 3.934 0.364
• (Jupiter) Ganymede 2,634 0.0248 - 1.936 0.312
• (Saturn) Titan 2,576 0.00225 - 1.880 0.341
• Mercury 2,440 0.055 - 5.427 0.346
• (Jupiter) Callisto 2,410 0.0180 - 1.830 0.355
• (Jupiter) Io 1,815 0.0150 - 3.528 0.378
• (Earth) Moon 1,737 0.0123 - 3.346 0.303
• (Jupiter) Europa 1,569 0.0804 - 3.010 0.346
• (Saturn) Rhea 764 0.00039 - 1.23 0.399
• (Saturn) Dione 562 0.00018 - 1.48 0.33
• (Saturn) Enceladus 252 0.000018 - 1.61 0.332

There's a clear break between the Earth and Neptune - Saturn, Uranus, and Neptune are very centrally concentrated (MoI = 0.22 - 0.23), while Earth and everything smaller have MoI usually between 0.33 and 0.36, with some of them extending outward to 0.30 and 0.40. There isn't much statistical difference between terrestrial planets and moons.

Jupiter is somewhat less centrally concentrated than its fellow giant planets, however, and the Sun is even more centrally concentrated than any of the planetlike bodies.

There is a statistical difference between terrestrial planets and moons in mean density, however. The lack of differentc in moment of inertia is due to the density contrasts being similar for ice and rock, and for rock and iron.

Earth interior structure: notice the compression of its interior.

• Geos 306, Lecture 13, Mineralogy of the Earth and its Core
• geology - What is the pressure at the center of the Earth? - Earth Science Stack Exchange
• gravity - What is the pressure at the center of the Earth? (Or a neutron star) - Physics Stack Exchange

 

[lpetrich]

Another article:
Redefining Planets Across the Universe - SciTechDaily

I'd earlier linked to the arxiv version, and here is the published version:
Quantitative Criteria for Defining Planets - IOPscience


Looking at exoplanets, there are not many that are observed below the Earth's mass and radius, because of limits of detection. But there are a large number of them between the Earth and Neptune in mass and radius -- super-Earths and mini-Neptunes -- thus filling that gap.

There are also plenty that fill in the gaps between the giant planets, though the radius levels off at around Saturn to Jupiter mass, and starts to decline after a few Jupiter masses.

Also, every known exoplanet is dynamically dominant over its surroundings. Between being rounded and being dynamically dominant, "planet" is a good label for them.