Gravitational Wave Sky Localization: Detector Triangulation

Source Direction

Right ascension 200°

Declination 18°

Timing precision σ 0.20 ms

Detector Time Delays

Hanford ↔ Livingston0.0 ms

Hanford ↔ Virgo0.0 ms

Livingston ↔ Virgo0.0 ms

Est. sky patch— deg²

How it works

A gravitational wave is a plane wavefront by the time it reaches Earth, so it sweeps across the detector network at the speed of light. If detector j sits at position r_j relative to Earth's center and the wave arrives from unit direction n̂, the arrival-time offset between two detectors is:

Δt_ij = (r_j − r_i) · n̂ / c

Real numbers: the Hanford–Livingston baseline is ≈3,000 km, so Δt_HL ranges from −10 ms to +10 ms depending on where on the sky the source is. Measuring Δt for one detector pair only tells you the angle between n̂ and that baseline — the source could be anywhere on a ring (a cone of directions) around the baseline axis. This simulator draws that ring for each of the three LIGO/Virgo baselines, using the actual site coordinates.

One pair → a ring of equally-likely directions.
Two pairs (e.g. H–L and H–V) → the rings cross at (generically) two points on the sky.
Three detectors → the third ring resolves which of the two crossings is real, and timing uncertainty σ (from finite sampling and signal-to-noise) fattens each ring into a band, so the final localization is a patch, not a point — exactly how LIGO/Virgo alerts an "error ellipse" to telescopes for multi-messenger follow-up (as with the neutron-star merger GW170817, whose kilonova was found this way).

Right ascension / declination pick the true source direction. Timing precision σ widens or narrows the three bands — a tighter σ (better SNR) shrinks the crossing patch and the "Est. sky patch" readout. Randomize source jumps to a new direction so you can watch the three bands re-converge around it.

LIGO Hanford LIGO Livingston Virgo GW source

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