Astronomy & Celestial Mechanics
the sky, computed
Concept

Differentiation — where it appears

The separation of a planet's interior into layers of different density, heavy iron sinking to form a core beneath a rocky mantle. It lowers the moment of inertia below that of a uniform sphere, which is how it is detected.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Measured moment-of-inertia factors, from the Sun's 0.07 to the Moon's 0.3931. Eleven bodies whose interiors have never been sampled, arranged by the one interior quantity that has been measured for all of them. C/MR² is 2/5 for a uniform sphere and falls as mass is concentrated toward the centre, and the values here span from 0.07 to 0.3931. That spread is the content. The Moon at 0.3931 is barely differentiated — whatever iron core it has is a few per cent of its radius, which is why the Moon is the one large body in the inner solar system without a magnetic field of its own. Mercury at 0.346 is nearly as low as the Earth despite being an eighth of its mass, and for a body that small the only way to get there is an iron core filling most of the radius. The Sun at 0.07 is off the scale of anything a two-layer model describes; a star is not a planet with a bigger core but a body whose density falls by five orders of magnitude between centre and surface. The faint curves behind are the two-layer relation at a few density contrasts, drawn to show what kind of interior each value is consistent with — and the horizontal placement of each body on them is an illustration rather than a result, since one factor never fixes one core. Every number here was obtained by watching the body turn: a precession rate, a libration amplitude, a gravity field sampled on a flyby, or in the Sun's case the frequencies of its own oscillations.

Whether the heavy material sank

A moment of inertia is 0.4 of MR² for a uniform sphere and less for everything that has differentiated, and it is measured by watching a body wobble. Mercury's 0.346 says most of the planet is iron core; the Moon's 0.393 says almost none of it is.

gravitation · Moment of inertia A precession rate read as a moment of inertia. The rate at which the Sun's torque turns Venus's spin axis, in arcseconds a year, against the planet's moment of inertia factor C/MR², for its measured J₂ and spin. A more centrally concentrated planet is easier to turn. The rate measured from radar speckle, 44.58 ± 3.3″ a year (shaded), corresponds to C/MR² = 0.337, from 0.314 to 0.364 — a precession period of 29100 years.

A planet too slow to flatten, weighed by its wobble

Most planets reveal how their mass is arranged through the bulge their spin raises. Venus turns once in 243 days, too slowly to raise any bulge worth measuring, and the flattening it does have was put there by its mantle rather than its spin. Its interior was unweighed until radar echoes bounced off its surface for fifteen years measured how fast the Sun turns its spin axis — once in 29,000 years — and the rate gave a moment of inertia, and the moment of inertia a core.

gravitation · Moment of inertia

Named alongside it

The objects these essays reach for when they reach for this one.

Axial precessionHydrostatic equilibriumMoment of inertia factorOblatenessRadau darwin relationZonal harmonicCore formationGeoidGravity scienceLibration

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