Astronomy & Celestial Mechanics
the sky, computed
Concept

Kinematic distance — where it appears

A distance obtained by measuring a cloud's radial velocity and assuming it moves on a circular galactic orbit. Inside the solar circle every velocity corresponds to two distances, and streaming motions bias the result systematically rather than randomly.

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

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

the Milky Way measured from inside it — the tangent-point construction. Left: the disc in plan, with the Sun at 8.2 kpc from the centre and four lines of sight at galactic longitudes 20°, 40°, 60°, 80°. Each one grazes a circle of radius R₀ sin l, and at that tangent point the whole circular velocity lies along the line of sight, so the largest velocity in the spectrum belongs to a radius the geometry fixes and no distance has to be measured. Right: the four radii and speeds that yields, on the model curve they are read against. The construction reaches only radii inside the Sun's, which is why the outer curve — the half of it that carries the argument — needs distances after all.

A galaxy measured from inside it

The Milky Way is the one galaxy nobody can photograph, and the only one whose rotation can be measured without knowing a single distance. A line of sight at a chosen longitude grazes a circle of known radius, and the fastest gas along it is orbiting there.

galaxies · Galactic structure One velocity, two distances — 4.7 and 9.5 kiloparsecs. The radial velocity of gas along a line of sight at galactic longitude 30 degrees, against distance from the Sun, for a flat rotation curve. The velocity rises to a maximum at the tangent point — where the line of sight is tangent to a circle of radius R₀ sin l — and falls again beyond it, so every velocity below the maximum corresponds to two distances. A cloud observed at 84 kilometres a second is at either 4.7 or 9.5 kiloparsecs, and nothing about its velocity says which. The two possibilities differ by a factor in distance and by its square in luminosity and mass, so the ambiguity is not a refinement — it decides whether a star-forming region is an ordinary one nearby or a monster on the far side of the Galaxy.

One velocity and two distances

Inside the Sun's orbit a line of sight crosses each galactocentric radius twice, and the two crossings have identical radial velocities. So a cloud's velocity gives two candidate distances, near and far, differing by a factor — and nothing about the velocity says which, though the choice decides whether the object is ordinary or extraordinary.

galaxies · Galactic structure Arms drawn into a disc that has none. Left: 1400 gas clouds spread uniformly over a disc between 3 and 13 kpc from the Galactic centre (cross), seen from above with the Sun (ring) 8.2 kpc out; the two thin curves mark where a two-armed spiral density wave of pitch 12° has its arms. The clouds have no arms in their positions, only in their motions: each streams by 10 km/s in a pattern locked to the arms. Right: the same clouds placed at their kinematic distances, read from their velocities with a circular rotation curve and on the correct side of every tangent point. The streaming has moved them by up to a few kiloparsecs, along lines of sight, and into bands. Lines of sight within 12° of the Galactic centre and 18° of the anticentre, where the velocities carry no distance, are left out. Counted in square kiloparsecs between 4 and 12 kpc, the densest fifth of the map holds 30 per cent of the clouds in reality and 45 per cent in the kinematic map.

A spiral drawn by velocities alone

A map of the Milky Way's gas is built by turning each cloud's velocity into a distance with a circular rotation curve. Gas in a spiral arm does not move on circles: it streams by ten or fifteen kilometres a second in a pattern locked to the arms, so the distance errors are locked to the arms too. Read that way, a disc with no arms in it at all comes out of the calculation with arms.

galaxies · Galactic structure

Named alongside it

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

Galactic planeTangent pointMolecular cloudRotation curveStreaming motionTerminal velocityThe 21-centimetre lineDegeneracyDensity waveDifferential rotationDistance ambiguityGalactic longitude

All concepts