Astronomy & Celestial Mechanics
the sky, computed
Concept

Dual-frequency — where it appears

Tracking or ranging on two radio frequencies at once, so that the delay from charged particles, which depends on frequency, can be measured and removed. It is how plasma along the path is calibrated out of navigation data.

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

Four media, and only two of them care about the frequency. The four propagation delays between a tracking station and a spacecraft, in metres of round-trip range, against the angle between the target and the Sun. The troposphere contributes a few metres and depends only on the elevation; the ionosphere is smaller at X band and scales as the inverse square of the frequency; the solar plasma rises steeply towards conjunction and scales the same way; and the Sun's gravitational delay rises as a logarithm and has no frequency dependence at all. That last distinction is the whole of the calibration strategy: transmitting and receiving at two widely separated frequencies measures the two plasma terms and removes them, leaving the troposphere to a weather model and the relativistic term to theory. Near conjunction the plasma exceeds everything else by an order of magnitude, which is why a spacecraft passing behind the Sun is both untrackable and the best available laboratory for measuring the relativistic term.

Four media between the antenna and the spacecraft

A deep-space range measurement is a round-trip time, and the signal spends that time passing through a troposphere, an ionosphere, the solar wind and a curved region of spacetime. All four delay it, none of them is the orbit, and the whole of the navigation depends on removing them.

spaceflight · Radiometric navigation Bits bought with carrier, until the carrier cannot hold. For the Voyager-like link at 165 AU, the thermal Doppler noise of the carrier loop over a 60 s count, in millimetres a second, against the data rate the remaining power carries, as the modulation index rises. The noise stays under the 0.03 mm/s the solar plasma and the troposphere already impose all the way to the index of 81.8 degrees, where the carrier falls to the 15 dB-Hz a loop needs to stay locked and the noise is 0.012 mm/s. Past that line the Doppler is not noisier; it is gone. The limit on the data's share is the loop's lock, not the precision.

One signal that carries the bits and the Doppler

A spacecraft is navigated by the same radio signal that brings its data home, and the transmitter's watts have to be divided between the two jobs by a single number, the modulation index. Near the Earth the division hardly matters. Out past the planets, where the inverse square has taken almost everything, the carrier needs a fixed minimum to stay locked, and every watt above it is data — so the most distant spacecraft is flown at the edge of losing the signal it is navigated by.

spaceflight · Radiometric navigation

Named alongside it

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

Solar plasmaCoherent transponderDeep-space networkDispersionIonosphereLight timeMedia calibrationNavigationRange residualThe Shapiro delaySolar conjunctionSystematic error

All concepts