A gravitational wave sweeps across the Earth as a plane wavefront at the speed of light, so it reaches each detector at a slightly different time. If detector j sits at position rj and the wave arrives from unit direction n̂, the arrival-time offset between two detectors is:
Δt_ij = (r_j − r_i) · n̂ / c
This map is a flat equirectangular projection of the whole sky (right ascension across, declination up/down) — the same kind of "probability sky map" LIGO/Virgo actually sends to telescopes. For each point on the sky this simulator recomputes Δt for all three real baselines and paints it in that pair's colour whenever it falls within σ of the value the true source direction would produce. One baseline alone lights up a whole band (a ring of equally-likely directions, cut open by the map projection); two baselines cross in two spots; the third band picks the real one and — widened by timing uncertainty σ — the three-way overlap becomes a compact bright patch, exactly the region a telescope would search after a real alert (as with the neutron-star merger GW170817).
- Right ascension / declination place the true source; drag the map or scroll to zoom in on the resulting patch.
- Timing precision σ — tighter σ (better SNR) narrows every band and shrinks the overlap patch and its "Est. sky patch" reading.
- Est. sky patch is measured directly off the map: every grid cell where all three bands overlap is summed with its true solid angle (a cos(declination) correction, since a degree of longitude covers less sky near the poles). A cheaper estimate that only multiplies two bands' angular widths — ignoring the angle at which the rings actually cross — was checked against this direct count and found to under-count the true patch by roughly 2–5× whenever the crossing angle is shallow, which is common for this baseline geometry; this simulator always uses the direct grid count instead.
- Randomize source jumps to a new direction so you can watch all three bands re-converge.