Astronomy & Celestial Mechanics
the sky, computed
Concept

Solar radius — where it appears

The radius of the Sun's visible surface, 695,700 kilometres by convention, defined where the gas becomes opaque. Measured at the limb it depends on the wavelength and on how the edge is defined, and eclipse timings and helioseismology give values that differ by a few hundred kilometres.

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

A limb 6.2 kilometres from its highest point to its lowest. The Moon's edge, drawn as the height of the local horizon above a mean circle, against position angle around the limb. The profile has an root-mean-square amplitude of 1.2 kilometres and reaches 3.1 at its extremes, which at the Moon's distance is 3.35 arcseconds — against a solar radius of 960. The valleys marked are the places where sunlight survives longest at second contact and reappears first at third, which is what produces Baily's beads. Every eclipse timing is a measurement of when a particular point of this profile crossed the solar limb, so extracting a solar diameter from a contact time requires the profile at the libration of that day, to a precision of a few hundred metres.

A solar radius measured past a mountain range

The most accurate way to measure the Sun's diameter is to time an eclipse. What is timed is the moment sunlight vanishes behind the Moon's edge — and the Moon's edge is a horizon with mountains on it, so the measurement is a difference between the Sun's limb and a lunar landscape that has to be supplied from somewhere else.

sky · Phases and eclipses The edge of the Sun, computed. The brightness of the Sun at 500 nanometres across its limb, as a fraction of the brightness at the centre of the disc, against height above the level where the photosphere's radial optical depth is one, from the radiative transfer along each line of sight through a grey model atmosphere. Inside the disc the brightness falls gently with limb darkening; at the edge it falls to nothing over about two hundred kilometres. The steepest point of the fall — the inflection point, which is what a solar radius conventionally means — is 335 km above the radial τ = 1 level, because a ray grazing the limb passes through 270 times more atmosphere than a vertical one and becomes opaque that much higher up, at about 336 km. The brightness falls to one per cent 555 km above the τ = 1 level and to a thousandth at 694.

The Sun is three hundred kilometres larger seen edge-on

The radius of the Sun measured from images and eclipses and the radius measured from its oscillations disagree by about three hundred kilometres, and neither is wrong. A line of sight grazing the limb passes through hundreds of times more atmosphere than a vertical one and becomes opaque higher up — so the edge a telescope sees sits above the surface the waves feel, and every other definition of the edge, from the detector's threshold to the colour of the light, moves it again.

sky · Phases and eclipses

Named alongside it

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

Bailys beadsContact timingDatumEclipse contactEclipse geometryHelioseismologyInflection pointLaser altimetryLibrationLimb darkeningLunar limb profileOpacity

All concepts