How Big is a Planet?

Stars are fundamentally different to planets and one surprising way in which they differ is just how big they can get. Heavy stars get hotter and they puff-up from very fast fusion rates – stars heavier than the Sun fuse hydrogen chiefly via the much faster carbon-nitrogen-oxygen cycle, which is a minor cycle in the present Sun. What faster fusion rates means is that the big, fat stars are BIG – some are much larger than the Sun. Some are so large and violently bright that they’re losing mass into space, forming gigantic nebula. One spectacular example is Eta Carina and its rather pretty nebula.

But what about planets? “Cold” matter – anything less than a 10,000 K – supports itself against the remorseless pressure of gravity by electrostatic forces, rather than the fusion heat of a star’s interior (which is over 3,000,000 K at a minimum.) As the pressure increases – and thus the planet’s mass – the electrons and nucleii of the planet’s core part company, becoming pressure ionised. Past this point the planet is supported by the mutual Pauli exclusion of electrons, which has some strange properties, one of which is increasing mass causes the planet’s size to shrink. When this happens the core is said to be composed of degenerate matter. Shrinking a planet releases energy and this causes the interior to become increasingly hot, puffing the planet up slightly. As a result planets heavier than Jupiter are roughly all the same size – roughly Jupiter size (about 10% of the Sun’s diameter.)

But that’s planets composed of so-called “cosmic abundancies” of matter – about 3/4 hydrogen, 1/4 helium and a bit of everything else. Planets can lose all their gaseous hydrogen/helium as they form and thus be composed of things like water, carbon, sulphur, “silicates” (chiefly metal oxides) and iron. Other elements are too rare to make bulk components of a planet, though they can be selectively concentrated in the outer crust (like uranium/thorium and potassium seem to be on Earth.) A new paper has come out discussing just how big a planet made of such things can get, with some interesting results…

Mass-Radius Relationships for Solid Exoplanets

…one of the co-authors is Marc Kuchner, who has previously enticed us with descriptions of carbon-rich planets, and planets made of ice. A few years ago one of the first exoplanets in a circular habitable zone orbit was discovered…

HD 28185

…and it masses about 5.7 Jupiter masses. Most exoplanet watchers assumed it might have habitable moons – if moon mass scales linearly with planet mass it should have about 4-5 moons as big as Mars – but one brave soul thought the planet itself might be a “super-Earth” made of Earth-like stuff. At that mass, if silicate/iron mixes didn’t get denser with pressure, the planet would be as big as Jupiter (about 12 Earth diameters) with about 12 gees gravity. But, as the new paper describes in detail, such materials get a LOT denser with pressure, and the MAXIMUM size a super-Earth can get to is 3 Earth radii. Thus HD 28185b would have a surface gravity of 200 gees – a most unsuitable home for life-as-we-know-it.

Hypothetically, though, what would such a planet be like? Firstly it would have 1800 times the radioactive material heating up only 9 times the surface area – thus a radioactive heat flow of 16 watts (cf. Earth’s mere 0.08 W.) Such a heat-flow would mean the planet would remain at 130 K even without a star – though that’s an average temperature, and in reality much of the surface would be lava. With so much tectonic activity and so much mantle heat flow gases and volatiles wouldn’t remain trapped in its mantle for long – it would probably be wrapped in a thick layer of superheated steam and carbon dioxide, the surface aglow at over 900 K before its heat could escape into space. Even in interstellar space the planet would glow a dull red and remain at hellish temperatures for billions of years.

2 Replies to “How Big is a Planet?”

  1. Am I reading this right, that the maximum size for a super-Earth is 3 Earth radii? Interesting! I need to download this paper.

  2. Hi Paul

    You are indeed reading that correctly – a Super-Earth is at most 3 Earth radii wide. In fact there can be no natural planet at equilibrium bigger than about 1.1 Jupiters wide. So anything BIGGER is either a star, heated by massive tides and other processes, or ARTIFICIAL. The last option is especially likely if the object is bigger than what would be reasonable for its mass – say an object as heavy as Neptune but as big as Jupiter. Or a single Jupiter massed object that’s twice Jupiter’s size – it’s probably a SupraJovian Habitat like Paul Birch has envisaged.

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