Astronomy & Celestial Mechanics
the sky, computed
Concept

Narrow ring — where it appears

A planetary ring far sharper than viscous spreading alone would allow. Its edges are held by the resonant torque of a nearby satellite, and the balance between that torque and the ring's own viscosity is the only measurement of ring viscosity available.

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

Two dips a side, 36.5 seconds apart, symmetric about a body 256 km across. One observer's light curve across a small body with two narrow rings, at a chord 44 km from the centre. The body itself removes the star for 11.2 seconds; the four brief dips, two either side of it, are ring crossings, at 391 km and 405 km from the centre and 7 km and 3 km wide radially. The evidence that they are rings and not two more objects is the symmetry: each pair sits at equal times before and after mid-event, to within 0.07 s here, and two independent bodies have no reason to do that. Each dip is drawn wider than the ring is thick because the chord crosses obliquely — the path length through the material goes as 1/cos, which is also why a ring is deeper near the ansae. Nothing in this light curve was looked for: Chariklo's rings turned up in 2013 in a run recorded to measure a diameter, and every ring system found since has been found the same way.

A star that blinked before it should have

In March 1977 three teams watching a star pass behind Uranus recorded it dimming five times before the planet arrived — and then, symmetrically, five times again on the way out. The symmetry is the whole argument — nothing but a set of rings concentric with the planet produces a mirror image about closest approach.

sky · Occultations An edge where two torques balance, 21 kilometres from the shepherd. Two torques on the edge of a ring, against distance from a shepherding moon, both axes logarithmic and both scaled by the same combination of surface density, radius and orbital rate so that only their shapes are being compared. The flat line is the viscous torque, which comes from collisions between ring particles and does not care how far away anything is; it is drawn for a kinematic viscosity of 12 square centimetres a second, within the range ring seismology gives. The falling line is the moon's, summed over the first-order resonances that crowd together as the gap narrows, which makes it an inverse cube. A flat curve and an inverse cube cross once, and the crossing is where an edge can sit: closer in the moon wins and pushes the material back, further out viscosity wins and the ring spreads. For Daphnis and the Keeler gap the balance lands 20.8 kilometres out against a measured half-width of 21, which is agreement to well inside the uncertainty on the viscosity — and it is the only handle anybody has on that viscosity, since the quantity being inferred is the collision rate among particles a metre across, a billion kilometres away.

An edge is a balance, not a boundary

A ring of particles spreads, because collisions move angular momentum outward. Something has to push back, and the something is a small moon whose torque falls as the inverse cube of the gap. A flat curve and an inverse cube cross once, and the crossing is the sharp edge — which is why an edge exists at all rather than a gradient.

gravitation · Planetary rings

Named alongside it

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

Ring systemAngular momentumAstrometric predictionDiffractionThe Fresnel scaleImmersion and emersionLight curveMean motion resonanceOptical depthPlanetary ringRadial profileResonance

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