The rounded shape of planets and moons is something that has been recognized since the earliest days of astronomy. However, the reasons why large celestial bodies tend to be spherical has not always been properly understood. With space exploration over the past half-century, we have now visited and studied numerous objects within our solar system directly, from asteroids just a few hundred meters across to the gas giant planets measuring over 140,000 kilometers in diameter.
Across this vast range of sizes and compositions, a pattern has emerged: when a celestial body grows massive enough, its own gravity pulls it into a rounded shape approximating a sphere.
This transition seems to occur around 200-400 km in radius for most composition types. The physics underpinning this phenomenon concerns the competition between mechanical strength forces at short ranges, like chemical bonds between atoms, and the long-range force of gravity. At astronomical scales above a certain size, gravity prevails to pull material towards a compact central point equally from all directions. This Science Shot reviews the physics of sphericity and hydrostatic equilibrium in detail as it applies to planets, moons, asteroids, and other solar system bodies to elucidate why a spherical shape is so ubiquitous past a critical size threshold.
The Physics of Sphericity
On small scales, various short-range forces dominate, which determine the structure and shape of objects. The electromagnetic force governs how atoms bond together into molecules and lattice structures. Chemical bonds can have quite directional preferences in crystals and other solids, resulting in elaborate geometries and symmetries being adopted. The strong nuclear force binds nuclei together, which themselves then interact electromagnetically to share electrons.
These complex interaction networks between particles result in a mechanical strength that prevents small accumulations of material, ranging from microscopic dust grains up to rubble pile asteroids a few kilometers in scale, from being molded into spheres. Their overall shapes are largely determined by random chance based on how particles collided and stuck together during their formation. These objects have insufficient mass for gravity to become the primary factor controlling their structure.
However, gravity has two key properties that allow it to eventually overtake these short-range forces when enough material is brought together. Firstly, gravity is always attractive, pulling any two masses together. Secondly, gravitational attraction obeys an inverse square law, meaning the force decreases proportional to the inverse square of the distance between objects. This means gravity pulls material preferentially towards the center of mass.
The gravitational force grows stronger in proportion to accumulating more mass, while the various mechanical strength forces play roles that generally do not directly scale up with increasing size past the scale of individual atoms/molecules.
The pressure induced by an object's gravity acting to compact itself ultimately overpowers any ability for mechanical strength to retain more irregular shapes when objects exceed the hundreds of kilometers in radius scale for primary rocky/metallic compositions, or the hundred or so kilometer scale for weaker icy objects rich in volatiles. Gravity pulls from all directions equally towards the center of mass, exerting an isotropic pressure that favors adopting a highly symmetric spherical shape for stability. This transition towards dominance of gravity depending on size helps explain key differences observed between tiny asteroids, dwarf planets like Ceres, terrestrial planets, and gas/ice giants.
Roundness Versus Hydrostatic Equilibrium
It is important to distinguish between the related but distinct concepts of "roundness" and "hydrostatic equilibrium" when assessing sphericity. Roundness is a necessary but insufficient criterion for an object to be definitively considered to be pulled into shape equilibrium by its own gravity.
Roundness merely implies an approximating spherical form, but says nothing about the internal physical state of the body. Numerous examples like Saturn's moon Mimas and many small asteroids exhibit roundness but not hydrostatic equilibrium. Meanwhile, Saturn's largest moon Titan and most dwarf planets meet the full criteria for hydrostatic equilibrium - namely having a shape dictated primarily by balanced self-gravitation for a spinning body rather than inherent material strength.
Determining whether questionable borderline cases (e.g. Vesta, Enceladus) are in true equilibrium remains an active area of investigation via space mission data. The development of hydrostatic equilibrium also generally requires more mass than simple roundness, with estimates ranging from needing at least 250-400 km radius for icy dwarf planets up to ~600 km or more for rocky bodies devoid of lower density ices. Rubble pile asteroids held together relatively weakly by their collective gravity can be round without achieving sphericity or equilibrium.
Composition and Size Effects
The precise spherical size threshold depends considerably on composition and average density, since mechanical strength will vary. Pure ices are easier to deform plastically under gravity, enabling roundness and potential hydrostatic equilibrium at smaller scales, whereas dense iron-rich asteroids require more mass to pull them into highly symmetric shapes. Lower density correlates strongly with lower critical radii to enable sphericity.
As stated previously, pure ice objects may transition around or below 200 km radius from irregular contact binaries or more ragged appearances into rounded dwarf planets. Saturn's low density mid-sized moons of Mimas and Enceladus demonstrate this, along with the similar Neptunian moon Proteus all being round despite their sub-400 km diameters. This size threshold creeps higher for rock-ice mixtures constituting many Kuiper Belt dwellers, up towards ~400 km, a benchmark just met by the dwarf planet Ceres at 467 km radius along with the rounded Saturnian satellites Rhea and Iapetus.
Of planets and larger well-differentiated moons, worlds denser than water ice are commonly near 800 - 1000 km or more in radius. Gravity remains strong enough across all larger objects to ensure near perfect sphericity and hydrostatic state. This includes Earth's moon at 1700 km radius. Pure silicate/iron objects likely require upwards of ~500 km before rounding fully occurs. Asteroids like Vesta (diameter ~500 km) represent borderline cases whose shapes provide constraints for formation models accounting for past fragmentation events.
Rapid rotation further works against perfectly uniform sphericity via centrifugal effects, but cannot prevent overall roundness. Oblate shapes result, like Saturn's 10.7 hour rotation causing a >10% equator-pole radius difference. Slow rotators (the Sun and Moon) approach ideal uniform spheres to very high precision. Determining the precise interplay between gravity, mechanical strength, bulk composition, rotational state, diameter and subsequent roundness/sphericity remains an active area of study based on spacecraft imaging across the solar system.
Conclusions
All planets and larger moons overwhelmingly demonstrate highly spherical shapes thanks to sufficient mass to be in hydrostatic equilibrium. This begins reliably occurring across all compositional classes once radii exceed ~800-1000 km. The gas giants represent extreme examples over 140,000 km in diameter, where gravity dominates to pull the fluid materials into perfectly smooth spheroidal forms. Rocky worlds smaller than 500 km radius conversely tend to be irregular in shape, or at best generically rounded but not truly in gravitational equilibrium. They instead retain shapes controlled more by initial formation and random collisions between smaller particles.
Roundness generally emerges across intermediate sizes between 100-800 km radii but depends strongly on rock versus ice fractions. While rotation and collisions can subsequently distort otherwise gravitationally balanced spherical shapes, attaining basic roundness emerges as an almost universal gravitational outcome for larger complex multi-material solar system bodies, as confirmed by recent spacecraft surveys over half a century of spaceflight.