Astronomy & Celestial Mechanics
the sky, computed
Concept

Astrometric prediction — where it appears

The computation of where an occultation's shadow will fall, from the star's position and the body's. An error in either becomes a cross-track miss of that angle times the distance, so a milliarcsecond is 29 kilometres at Kuiper belt range.

Named by 3 essays across one field — each of them below, with the objects they name alongside it.

7 clocks, and a body 233 kilometres across. A stellar occultation reduced. Each horizontal segment is one observer's chord: the star vanished, the star came back, and the interval multiplied by the shadow's 21.4 km/s across the ground is the length drawn. The longest, at an offset of -28 km, is 252.3 kilometres. The dashed ellipse is the limb fitted to the chords by least squares in the half-length squared, and its equivalent-area diameter is 233.9 km against the silhouette's true 232.9 — the residual is the shape the fitted ellipse cannot hold, not an error in any timing. The two open marks are observers inside the predicted path who saw nothing, and they are measurements: they bound the limb inside their own offsets, which is what fixes the extent when the positive chords all fall on one side. At 0.12 s per contact the length precision is 2.6 km, 1.10 per cent of the body — a size measured with a clock rather than with an angle, on an object no telescope resolves.

A shape measured by the edge of a shadow

When a small body passes in front of a star the observable is two times. Multiply the interval by the body's speed across the sky and it becomes a chord across a silhouette no telescope can resolve — and enough chords give a profile to a kilometre or two, for an object a few hundred across.

sky · Occultations 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 The astrometry an occultation campaign has to have. How far the shadow lands from where it was predicted, against the angular error in the positions it was predicted from, for a Centaur at 15 AU, a Kuiper belt object at 40 AU, Uranus at 19 AU. The conversion is one line — an angle times a distance — and one milliarcsecond at one astronomical unit is 0.7255 kilometres. The horizontal bands are each body's own shadow width, which is its diameter, and the crossing is the accuracy at which a campaign stops being a lottery: a Centaur needs 23.0 mas, a Kuiper belt object needs 4.1 mas, Uranus needs 3701.0 mas. Before the all-sky astrometric surveys the typical error was tens of milliarcseconds, which is thousands of kilometres at these distances, so events by small bodies were found by accident and not by appointment. The same event then measures the body's position to a few milliarcseconds or better, which improves the ephemeris that predicts the next one.

Each event pays for the prediction of the next

An occultation is predicted from two positions and lands where the arithmetic says. Recording it then measures the occulting body's position to a few milliarcseconds — better than a year of imaging — so the observation that the prediction made possible improves the ephemeris the next prediction comes from.

sky · Occultations

Named alongside it

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

The Fresnel scaleRing systemShadow pathStellar occultationAlbedoCatalogueThe central flashDiffractionEphemerisThe half-light radiusImmersion and emersionLight curve

All concepts