How an occultation becomes physics

Casting the shadow forecast

Everything starts with astrometry. The target star's position comes from the Gaia catalogue at the milliarcsecond level, and the body's orbit is refined with a dedicated ephemeris (NIMA) built from years of observations. Crossing the two on the sky gives the moment of closest approach (C/A) and the shadow's ground track — a band roughly as wide as the body itself, sweeping Earth at about 20 km/s.

A prediction lives or dies by its geometry: the geocentric ephemeris is stepped minute by minute against every catalogue star inside a search radius set by the apparent size of the Earth and of the body (~0.3 arcsec at 30 AU). Each candidate yields the closest-approach distance, the position angle of the track (measured from celestial north), the shadow velocity and the along-track timing.

Days before the event, the collaboration alerts observers along the predicted track and its uncertainty — fixed observatories and portable stations alike.

// every observed chord feeds the ephemeris back at ~mas level, sharpening the next prediction

Catching the blink

Each station records the target star with fast, GPS-time-stamped photometry. A station inside the shadow sees the star vanish; the instants of disappearance and reappearance define one chord across the body. Stations that record no dip matter just as much — negative chords bound where the limb cannot be.

Speed and timing are everything. Frame-transfer or EM-CCD cameras — and GPS time-inserted video — keep the dead time between exposures negligible, so no fraction of the event is lost; each light curve is built by differential aperture photometry against nearby reference stars.

The shape of the dip itself carries physics: square edges mean an airless body, gradual shoulders betray an atmosphere, and brief secondary dips flag rings or satellites.

// resolution is set by exposure time, the star's angular size and Fresnel diffraction (scale √(λD/2) ≈ 1 km) — sharper than any direct image of these bodies

From chords to a world

Each positive light curve measures one chord — a straight cut across the body at a single latitude, its length set by the sky-plane velocity and the timed duration. Projected together and corrected for each site's parallax, the chords trace the body's limb at the instant of the event.

An ellipse — the most general profile — is fitted to the chord extremities by minimising χ² over five parameters: the centre, the apparent major axis, the apparent oblateness and the orientation. Its equivalent radius (the radius of a disk of equal area) follows directly; combined with the body's absolute magnitude, it yields the geometric albedo.

// single-chord events still count: half the chord is a hard lower limit on the radius

Shape, spin and equilibrium

A single event freezes the apparent limb — an ellipse on the sky. But apparent oblateness ε′ = (a′−b′)/a′ blends the true flattening with the viewing angle: ε′ ≈ ε · sin²ζ, where ζ is the tilt between the spin axis and the line of sight. One occultation alone cannot separate the two.

Bodies larger than about 1000 km are expected to relax into figures of hydrostatic equilibrium — an oblate Maclaurin spheroid (a = b > c) when spinning slowly, or a triaxial Jacobi ellipsoid when spinning fast. Folding in a rotational light curve (period and amplitude) breaks the degeneracy and recovers the true 3-D shape and pole.

// an equilibrium figure ties shape to spin — and, with a mass, to the interior

From size to density

Size is only a silhouette; density is composition. When a body carries a satellite, the moon's orbit yields the system mass through Kepler's third law. Divide that mass by the volume of the spheroid measured at occultation and the bulk density emerges — the first, decisive clue to what a world is made of and how it is packed.

Near 1 g/cm³ points to an icy body; 2–4 g/cm³ betrays rock; a density below that of surface ice hints at internal porosity or a differentiated interior.

// Quaoar: ρ ≈ 1.7–2.5 g/cm³ from its moon Weywot — rock-rich and ancient

Atmospheres by refraction

An airless limb switches the star off in a single step. A gas envelope acts differently: it refracts the passing rays, bending them out of the observer's line so the star dims smoothly over seconds before it disappears, then brightens back the same way. Those gradual wings are the signature of an atmosphere.

Ray-tracing synthetic light curves for a model atmosphere — its gas, temperature and pressure — and matching them to the observed shoulders measures the surface pressure; when no wings are seen, it sets an upper limit. The technique reaches a few nanobar, far below any direct detection.

// Quaoar: < 21 nbar (1σ) for a global methane atmosphere; Pluto and Triton alone hold gravity-bound atmospheres among these worlds