Why are planets spherical?

Seth Jarvis

Anthony Garcia wrote in to ask, “Why are planets perfect spheres, or at least appear to be perfect?”

Nature loves spheres. It can’t get enough of them.

Soap bubbles are spherical because that shape most efficiently balances the outward pressure of the air within the bubble against the surface tension of the soap film.

When water splashes and for a brief instant a droplet of water is neither rising nor falling and is momentarily weightless, what shape does the droplet’s surface tension force the water to take?  A sphere.

bubble-droplet_450

Nature loves spheres. In the case of bubbles and droplets of liquid, surface tension creates a sphere to minimize surface area.

Stars are perfect examples of natural spheres.  The mass of a star is mind-bogglingly large and creates an equally mind-bogglingly large amount of gravity. What shape does Mother Nature give to so much mass to minimize its enormous volume?  A sphere.

Stars are huge, dynamic, energy-making monsters shaped by their enormous gravity into spheres.

Stars like our Sun are huge, dynamic, energy-producing concentrations of Hydrogen and Helium, compacted by their enormous gravity into spheres.

The reason planets appear spherical is because gravity compresses the planet into a shape that most evenly distributes the gravitational force among the planet’s mass.

Whether it is shaping water droplets, stars, soap bubbles or planets, nature seeks to minimize the surface area needed to contain a given volume, and the shape that keeps volume at the absolute minimum a sphere.

Any object in weightless space larger than a couple of hundred miles in diameter has enough mass for its gravity to overcome large-scale irregularities and force it into a spherical shape.  This gravitational compression also generates significant amounts of heat at the center of the planet. This heat melts, or at least softens, any solid materials within the planet, facilitating the planet’s collapse into a spherical shape.

Objects in space smaller than about 100 miles in diameter, such as most asteroids, comet nuclei and small moons, lack the mass to create a gravitational field strong enough to compress themselves into spheres.  These little worlds often take on what I call the “sick potato” look.

gaspra_91_galileo_450

The 12.5 mile-long, 7.5 mile wide asteroid Gaspra, imaged in October 1991 from a distance of 1,600 miles by the Galileo spacecraft en route to Jupiter.

A really large asteroid, such as Ceres (diameter = 600 miles), has enough mass for its gravity to compress it into a sphere.

ceres_450

The 600 mile-wide asteroid Ceres as seen by the Hubble Space Telescope.

However, “perfect” spheres are hard to find in space.

Pretty much everything is space rotates, and rotating a non-rigid sphere causes it to “bulge” at its equator from the centrifugal forces acting on it.

This spinning distorts large planets into a slightly squashed shape known as an “oblate spheroid.” This means that a planet’s diameter measured through its poles is smaller than the diameter measured through its equator.

Whereas the difference between the polar diameter and the equatorial diameter of Earth is a barely noticeable 0.3%, the oblateness of Saturn, a large, gaseous and rapidly spinning planet,  is greater than 10%.  You can easily see Saturn’s polar flattening through a telescope.

oblate-saturn

Saturn's polar diameter is 33,700 miles, but its equatorial diameter is 37,360 miles.

There may not be such a thing as a “perfect” sphere in nature, but there is no doubt that spheres, nature’s favorite shape, are perfectly lovely.

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52 thoughts on “Why are planets spherical?

  1. Hi, your prior link to “Let’s Play Earthball” in reply to Cy on March 7, 2011 at 11:59:AM is pulling a 404. I’d heard that the Earth is particularly smooth for a sphere – in fact, smoother than an equivalent sized egg. And, Olympus Mons is a larger mountain than anything on Earth, but is that due to a lower gravity on Mars?

    1) I’d like more information on a material’s elasticity (or, a group of materials composing a protoplanet’s (average?) combined elasticity?). Is there another name for this term ( http://en.wikipedia.org/wiki/Elasticity_%28physics%29 )? Or, where can I get some numbers on different materials’ rate of elasticity as used in this type of generalized thought-experiment? Perhaps based on density? Ices, vs. less-dense spheres (the moon) vs. heavy/dense spheres? (I mean, I can see modulus and elastic limit and a bunch of other things to calculate stuff under earth terms, for small items – but not for melting a million-billion tons of randomized ‘rocky’ mass or ices, or of the varying solar-system planets’ densities) I’m betting you’re trying to keep this math-lite, but I’d actually like to see a link to some general-type formulas so I could play around with them.

    2) Amber and others have asked about super-small gas-planets. You’ve said: (roughly) ‘If there’s enough hydrogen and helium for a significant gravitational pull on itself, it will form a sphere.’ I’m assuming that you’re talking about enough mass to overcome a gases ability to bounce away from one another (However, that’s influenced by the temp of the gas, correct?). Basically, we’re discussing the formation of gas-clots, ranging in size from stars (gas-clots big enough to auto-start a fusion reaction), gas-giants (protostars who didn’t have quite enough mass to form a star (Jupiter?)), and smaller gas-giants. Katie’s answer included ‘with not much more than a few times the mass of Earth’. Why would it need to be more massy than Earth, if it were cold enough; and/or protected enough from the solar wind stripping off the hydrogen/water; or formed far from any star, ie: independent rogue planet? Earth is many times more massy than the smallest spherical bodies caused by internal gravitation. Why do gas-giants need to mass so much more? (I understand that because of density they’re going to be much larger in diameter than any comparable rocky planet.) Tim’s answer implied that all gas-planets must have a core. Which may be true in this solar system, but in original first generation systems there was no matter other then H, He (and a little, what Li? Be?) – stars *can* form out of just those elements… so why couldn’t a too-small star (ie: protoplanet) form? And in those cases (basically composed of just H & He), what’s the minimum mass (and what would the size & density work out to be: also, got a formula for that so I could create my own planets of varying sizes?)?

    3) Sean’s answer: “That amount of rock has just barely enough mass to pull itself together into a sphere, but not enough mass for the gravity-induced pressure at the center of sphere the heat the interior to its melting point to create a differentiated interior like Earth has (core, mantel, lithosphere, etc.)” What are the approximate numbers for those limits; ie: sphere-forming and average melting point of rocky planets (and ice planets) to form differentiated interiors?

    And is Sean’s minimums-sized sphere unlike many of the asteroids we have which are collections of boulders; ie: it’s actually ‘connected’: melted and/or (fairly) mechanically locked together (perhaps the terminology is ‘deformed into one another’?) Yes, it’s probably not very stable, and if I hit it with a large rock going very fast, it’d probably fracture, but you should get the drift of what I mean by saying ‘being one object’…

    Also, “When you figure out a rocket engine that can move that kind of mass around” – since Sean’s sphere is free-floating in space, and not in orbit – any rocket engine will move it. Each action has equal and opposite reaction, so a lot of thrust will produce a really tiny movement of the 9 million-billion tons, but it *does* move. Me? I’d set up a large railgun with nuclear reactor power-sources run off of my specially imported uranium (since we can’t guarantee that those boxes are packed with the correct ores).

  2. From Clark Planetarium Education Department staff member Robert B.:

    The formation of planets and planetary systems is not completely understood. Models of planet formation are complex and depend on many factors. You have correctly deduced that one factor is the temperature of the gas. Below are some references to assist in your research that have more detailed information, including various mathematical formula:

    (The author of the first three references is Philip Armitage of the University of Colorado).
    Planetary formation and migration (a brief overview of the subject) http://www.scholarpedia.org/article/Planetary_formation_and_migration
    Lecture notes on the formation and early evolution of planetary systems
    http://arxiv.org/abs/astro-ph/0701485
    Astrophysics of Planet Formation, Cambridge University Press, 2010

    Protostars and Planets V, Edited by B. Reipurth, D. Jewitt, and K. Keil, University of Arizona Press, Tucson, 2006.
    See two sections in Chapter 7, titled “Formation Of Giant Planets” and “Gaseous Planets, Protostars And Young Brown Dwarfs: Birth And Fate”.

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