Concept

Top shaped asteroid — where it appears

An asteroid shaped like a spinning top, with an equatorial ridge and flattened poles, common among small fast rotators. The shape is thought to form as loose material slides towards the equator when spin weakens gravity there.

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

Where a spinning sphere of rubble is steepest. The slope of the surface of a spinning sphere of loose material against latitude — the angle between the local vertical and the combined pull of gravity and rotation — for spins of 30%, 60%, 80%, 90%, 97% of the critical rate, measured in its square, at which the equator would lift off: for a density of 1.19 g cm⁻³ the critical period is 3.03 hours and these are periods of 5.5, 3.9, 3.4, 3.2, 3.1 hours. The slope is zero at the pole and at the equator, where the pull and the vertical are aligned by symmetry, and steepest in between: at 30% it peaks at 10° at latitude 40°, at 97% at 70° at 10°. The band marks the angle of repose of loose rock, 30° to 40°. From 80% of the critical rate the steepest band is past it: the surface begins to slide well before the equator has lost its weight.

A surface that slides before the body sheds

A rubble pile spun towards its limit does not wait for its equator to lose its weight. Long before that, its mid-latitudes grow steeper than loose rock can stand, and the surface flows — downhill, which on a spinning body means towards the equator. The ridge that so many small asteroids wear is built in that interval, at spins a sixth slower than the one that would fling material off, and whether it is built at all depends on a cohesion of less than a pascal.

orbits · Rubble piles

Where tumblers should be found. Rotation period against diameter, with lines where the damping time equals 10 million years, 100 million years, 1 billion years, 4.5 billion years, and the 2.2-hour limit below which rubble cannot spin. A body above a line has not had time to settle since it was last disturbed that long ago. Above the 4.5-billion-year line nothing has had time; the measured tumblers ʻOumuamua, Apophis, Toutatis, Mathilde are marked.

A tumble that measures how stiff rubble is

Most asteroids spin cleanly about one axis. A few tumble, turning about one axis while that axis wanders round another, and they keep tumbling because the internal friction that would settle them works slowly. How slowly depends on the asteroid's size, its spin and how stiff and lossy its interior is — so where the tumblers stop, on a chart of period against size, is a measurement of the inside of bodies nobody has ever drilled into.

orbits · Rubble piles

Named alongside it

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

Cohesion Effective potential Rubble pile Spin barrier YORP effect Angle of repose Surface slope

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