Astronomy & Celestial Mechanics
the sky, computed
Concept

Catalogue — where it appears

A compiled list of positions and brightnesses against which every new measurement is referred. Its systematic errors do not average down with repetition, so improving the frame retroactively improves every observation ever made against it.

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

One over a noisy parallax, at three precisions. The distribution of the distance obtained by inverting a parallax, for a star truly at 100 parsecs measured with fractional errors of 5, 10, 20 per cent. At five per cent the distribution is nearly symmetric and inverting is harmless. At twenty per cent it is strongly skewed: the mean sits at 105 parsecs rather than 100, and the tail runs to distances several times the truth, because a parallax scattered a little towards zero is a distance scattered a long way outward. The asymmetry is a Jacobian and nothing else — the parallax measurement is unbiased and symmetric throughout. Above about twenty per cent the mean of the distribution stops existing at all, because the density falls only as the inverse square of the distance and the integral of d times that diverges.

The distance is not one over the parallax

A parallax is measured with symmetric errors and a distance is one over it. Inverting a noisy positive quantity is not a change of units — it is a change of distribution, and the one that comes out is skewed, biased outward, and above about twenty per cent error has no mean at all.

starlight · Parallax 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.

Systematic errorAstrometric predictionDistance estimationEphemerisJacobianLutz kelker biasMilliarcsecondOccultation astrometryOrbit determinationParallaxParallax zero pointPosterior

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