Astronomy & Celestial Mechanics
the sky, computed
Concept

Very long-baseline interferometry — where it appears

The technique of combining radio telescopes thousands of kilometres apart by recording signals against atomic clocks. It delivers angular positions to tens of microarcseconds, and it is what ties the Earth's orientation to a frame defined by quasars.

Named by 4 essays across 3 fields — each of them below, with the objects they name alongside it.

A nanosecond across the Earth is 35.69 nanoradians on the sky. The angular accuracy of a differenced-delay measurement against the length of the baseline it is measured on, both axes logarithmic, for three levels of delay precision. The relation is σ_θ = cσ_τ/B and nothing else, so every curve is a straight line of slope −1.00: the only two ways to measure an angle better are a better clock or a wider Earth, and only one of those is available. The three marked baselines are the ones that exist — the deep-space complexes in California, Spain and Australia, 8,400, 10,600, 11,700 kilometres apart. On the longest of them a delay good to 0.05 nanoseconds is 1.28 nanoradians, which at 0.52 astronomical units is 100 metres across the line of sight; a more typical 0.15-nanosecond measurement on the shortest baseline is 5.35 nanoradians. What makes any of this survivable is that the same pair of antennas observes a quasar a few degrees away immediately afterwards. The quasar is at infinity, its position is known better than the measurement, and subtracting its delay from the spacecraft's removes the clock offsets, the water vapour over each dish and the station coordinates in one step — so the number that comes out is not a delay at all but an angular separation from a fixed point in the sky.

An angle measured against a quasar

A tracking station measures how fast a spacecraft is receding, which is one number where three are wanted. The two missing angles come from the Earth's rotation, slowly, and near a planetary encounter there is no time for slowly — so the position is instead measured directly, as a difference of arrival times between two antennas, referred to a quasar a few degrees away.

spaceflight · Radiometric navigation A wobble that should have stopped seventy years ago. Left, the path of the Earth's rotation pole across its own crust over 13 years, as the sum of two circular motions: the 433-day Chandler wobble at 150 milliarcseconds and the annual wobble at 90. The spiral is a beat, and its period measured off the drawn path is 6.39 years against the 6.39 the two frequencies require. Right, the same path's radius against time. Two numbers in this figure are the argument. The first is the Chandler period itself: a rigid Earth of dynamical ellipticity 0.0032737 would wobble freely at 305 days, and the observed 433 is 42 per cent longer because the Earth deforms under its own wobble and the oceans move with it — the period is a measurement of the planet's elasticity, made by watching a free motion rather than by forcing anything. The second is the damping: at a quality factor of about 100 the wobble should decay in 38 years, and it has been running for as long as anyone has watched. Something is exciting it continuously, and the excitation is fluctuating pressure at the bottom of the ocean and in the atmosphere. What the figure cannot show is the excitation itself, which is not periodic and is only visible statistically.

A wobble that should have stopped

The Earth's rotation pole wanders across its own crust in a circle a few metres wide. A rigid Earth would do it in 305 days; it takes 433, and the difference is a measurement of the planet's elasticity. At the observed damping it should have died out within a human lifetime, and it has not.

sky · Precession A frame whose precision stops improving because its sources move. The uncertainty in the orientation of a celestial reference frame, in microarcseconds, against the number of extragalactic sources it is built from. The falling line is what averaging alone would give: each source's position is measured to about 200 microarcseconds and combining N of them improves the frame as one over the square root of N. The upper curve adds the part that does not average down in the same way — the wander of a quasar's radio centroid as new components are ejected along its jet, which is a real motion of the thing being used as a fixed point. Three catalogue generations are marked. The frame gained an order of magnitude in a quarter of a century, and it gained it by observing more sources rather than by observing any of them better, which is the signature of a limit that is in the objects rather than in the instrument.

A frame made of things that are not points

Every position in astronomy is measured against a set of objects declared to be fixed. The objects chosen are quasars, because they are the most distant things there are — and each of them is a jet whose radio brightness centre wanders by tens of microarcseconds as new material is ejected from the core.

sky · Celestial sphere The power a source loses to its own photons, against how bright it is. The ratio of the power a synchrotron source loses by inverse-Compton scattering of its own photons to the power it radiates as synchrotron emission, against its brightness temperature, both on logarithmic axes. To first order the ratio goes as the fifth power of the brightness temperature over 10¹² K — so at 10¹¹ K it is 10⁻⁵, negligible, and at 10¹² K it is one. The scattered photons are scattered again, and each order multiplies by the same factor, so the second-order curve rises as the tenth power: at twice the limit the total loss is 1056 times the synchrotron power, and the electrons radiate away their energy in hours as X-rays and gamma rays. A steady source cannot sit above the line where the ratio is one. That is the inverse-Compton catastrophe, and it makes 10¹² K a ceiling on the brightness temperature of any incoherent synchrotron source at rest.

A temperature that is a speed

No steady synchrotron source can be brighter than about a trillion kelvin, because above that its electrons lose their energy scattering their own photons faster than they can radiate it. So when a radio source is measured brighter — as the cores of quasars routinely are — the excess is not a hotter source. It is a source coming towards the observer, and the brightness temperature becomes a measurement of how fast.

starlight · Synchrotron radiation

Named alongside it

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

QuasarAngular accuracyAngular momentumBaselineBeat frequencyBrightness temperatureChandler wobbleClock offsetDeep-space networkDelta-DORDifferential measurementDynamical ellipticity

All concepts