Astronomy & Celestial Mechanics
the sky, computed
Concept

Viscous spreading — where it appears

The broadening of a disc or ring of orbiting material as collisions or turbulence carry angular momentum outward. The inner part falls in, the outer part moves out, and the rate measures the disc's effective viscosity.

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

A wave whose crests count out 35 grams per square centimetre of ring. Optical depth across a spiral density wave in Saturn's A ring, drawn outwards from the 5:3 inner Lindblad resonance with Mimas at 131,988 km. The wave is launched at the resonance on the left and damps away to the right. Its wavelength is not constant: it starts at about 17.6 km and has shortened to 3.58 km by the last crest drawn, because the wavenumber grows in proportion to the distance from resonance and the ring's own self-gravity is the only restoring force in the dispersion relation. That makes the pattern a chirp with exactly one unknown in it. Fitting the 24 crest positions actually drawn here — the square of each one's distance from resonance against its number, which is a straight line — returns a surface density of 35.0 grams per square centimetre against the 35 the profile was built from. The rings have been weighed this way rather than by anything touching them: the mass per unit area follows from counting bright bands in a light curve as a star sets behind the ring.

A ring weighed by the wave crossing it

Saturn's rings are a few tens of metres thick and spread over an area larger than the Earth, made of pieces nobody can resolve, and nothing has ever landed on them. Their mass per unit area is nevertheless known to a few per cent — from the rate at which the crests of a wave crowd together as it travels outwards.

gravitation · Planetary rings The mass it takes to keep the ellipses aligned. The surface density, in grams per square centimetre, that a 58 km wide ring at the ε ring's distance needs for its own gravity to cancel the differential precession, against the ratio q of the change in a·e across the ring to its width, in linear secular theory. A ring whose edges differ little in eccentricity needs a great deal of mass, because its self-gravity has little lever. The ε ring's q = 0.66 gives 208 g/cm², a ring mass of 39 × 10¹⁵ kg — a moonlet a few tens of kilometres across.

A narrow ring that holds its own ellipse together

Uranus's ε ring is an ellipse of ice a few dozen kilometres wide, narrow where it passes closest to the planet and wide where it is furthest. The planet's flattening turns the inner edge's ellipse faster than the outer edge's, and without something to stop it the two would come apart within a century. They have stayed aligned since the ring was found. What holds them is the ring's own gravity — and the amount needed to do it is a weighing of the ring.

gravitation · Planetary rings

Named alongside it

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

Optical depthPlanetary ringShepherd moonStellar occultationSurface densityDispersion relationLindblad resonanceResonance overlapRoche limitSelf-gravity wakeSpiral density wave

All concepts