Astronomy & Celestial Mechanics
the sky, computed
Concept

Comet nucleus — where it appears

The solid body of a comet: a few kilometres of ice, dust and rock, dark and porous, inside the coma it produces. Its mass and spin respond to the push of its own outgassing, which is how its density can be estimated.

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

Also named here as outgassing — the same set of essays touches all of them, so they are one junction rather than several.

An impulse delivered inside 0.5 AU, and a comet 2050 hours early. Above: Marsden's outgassing law, the factor g(r) that scales a comet's non-gravitational acceleration, against distance from the Sun over one orbit of a comet with perihelion at 0.336 AU and aphelion at 4.09. It is close to an inverse square inside the water snow line and then falls off a cliff, because water ice that is not being heated does not sublimate. Half the whole revolution's impulse is delivered inside 0.55 AU — a few weeks out of a 3.3-year orbit — so the force is effectively a kick at perihelion rather than a perturbation spread around the path. Below: what a kick of that kind does to the timekeeping. A transverse component changes the semi-major axis and so the period, by 2.5 hours per revolution here, and a constant change in the period accumulates as the square of the number of revolutions rather than in proportion to it. After 40 returns the comet arrives 2050 hours — more than 85.4 days — before an orbit fitted without the term predicts, and doubling the number of returns multiplies the discrepancy by 3.90. That is why the effect was found in the eighteen-twenties from nothing but arrival times, and a century and a half before anyone photographed a jet.

A comet that arrives a day early

Encke's comet returned two and a half hours ahead of prediction, every revolution, for decades before anybody could say what was pushing it. The force is a rocket — a few tonnes a second of vapour leaving the sunward side of a rotating nucleus, delivered almost entirely in the few weeks around perihelion, and it accumulates in the arrival time as the square of the number of returns.

orbits · Non-gravitational forces Spun apart, or run out of ice: two clocks against size. Numbers of orbits against nucleus radius, both axes logarithmic, for a comet on 41P's orbit losing mass at 41P's rate per unit area. Solid: the orbits until the nucleus has lost all its mass to sublimation, growing in proportion to the radius. Dashed: the orbits until outgassing torques, changing sense at random from one orbit to the next, spin it past the rate at which a strengthless body of density 500 kg/m³ comes apart (a period of 4.7 hours) — growing as the fourth power of the radius, because each orbit's change of spin goes as the inverse square and a random walk needs the square of the number of steps. With a torque efficiency of 0.01, about what other comets' measured spin changes suggest, the two clocks cross at a radius of 1.2 km; with 41P's own 0.044, at 3.3 km. Smaller nuclei are spun apart before they run out of ice; larger ones run out first. The crossing moves as the two-thirds power of the efficiency.

The jet that pushes a comet also turns it

The gas a comet sheds near the Sun pushes its orbit, and because the vents are not arranged symmetrically about its spin axis, it also twists the nucleus. In 2017 one small comet's day more than doubled in two months. The twist per orbit grows as the inverse square of the nucleus's radius while its supply of ice grows only as the radius, so below about a kilometre a comet is spun apart before it runs out of ice — and the shortage of small comet nuclei may be the result.

orbits · Non-gravitational forces

Named alongside it

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

OutgassingGauss planetary equationsJupiter-family cometMarsden parametersMoment of inertiaNon-gravitational accelerationNon-gravitational forcesNucleus rotationOrbit determinationPerihelion passageRandom walkResidual

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