Astronomy & Celestial Mechanics
the sky, computed
Concept

Strength regime — where it appears

The size range in which a body is held together by the strength of its material rather than by its own gravity. Its energy to shatter falls with size, so strength-dominated bodies are weakest near the largest size in the range, a few hundred metres.

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

A wall at 2.33 hours that bends into a slope below 598 metres. The fastest rotation period a body of bulk density 2 g/cm³ can hold against its own spin, against its diameter, on logarithmic axes, for cohesive strengths of 0, 10, 100, 1000 pascals. With no cohesion the limit is the density-only barrier √(3π/Gρ) = 2.33 hours at every size. A cohesion C adds a stress that does not depend on size to a gravitational stress that goes as the square of the radius, so small bodies are held mostly by cohesion and can spin faster in proportion to their smallness: below the corner the limiting period goes as the diameter. The corner is where the two stresses are equal, at a diameter of 189 m for 10 Pa, 598 m for 100 Pa, 1.9 km for 1000 Pa. The scaling is the strength-regime form with a single coefficient of order one; detailed limits depend on the angle of friction and the shape. What the figure makes plain is why the observed spin barrier is sharp for kilometre-sized asteroids and fades below a few hundred metres, and why a handful of fast rotators a few hundred metres across can be rubble piles with a few tens of pascals of cohesion — a strength far below that of any rock — rather than monoliths.

A spin barrier with a corner in it

A rubble pile cannot spin faster than a period set by its density alone — 2.3 hours for most asteroids — at any size. Give it a cohesion of a few tens of pascals, weaker than any rock, and the barrier bends into a slope below a corner at a few hundred metres. The thermal torque that drives bodies to the barrier doubles their spin in a time that grows as the square of their size, so the bodies it pushes hardest are the ones that can go past.

orbits · Rubble piles The weakest bodies are a few hundred metres across. The energy per unit mass needed to shatter a body and disperse half of it, against the body's diameter, for basalt and water ice, from fits to impact simulations calibrated on laboratory fragmentation. Small bodies are held together by material strength, which falls with size because a larger body contains larger flaws; large bodies are held together by their own gravity, which rises with size because the fragments have to be thrown apart as well as broken. The two regimes meet in a minimum at 235 m for basalt and 204 m for water ice, where a body needs the least energy per kilogram to destroy of any size — 127 J/kg and 57 J/kg, the kinetic energy per kilogram of motion at only 16 and 11 metres a second. A collisional population is therefore not self-similar: it has a preferred size, and its size distribution records it.

The size at which a body is easiest to break

A pebble is held together by the strength of its rock and a moon by its own gravity, and somewhere between them is a size that has too little of either. Bodies a few hundred metres across are the weakest in the solar system — sixteen metres a second of impact energy per kilogram is enough to scatter one — and a population grinding itself down records that weakness as a knee in its size distribution.

orbits · Collisional cascade

Named alongside it

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

Rubble pileAsteroid beltAsteroid spinBulk densityCohesionCollisional cascadeCritical spin periodDebris discDisruption thresholdDohnanyi slopeGravity regimeNear-earth asteroid

All concepts