Gravitational Waves: Inspiral, Merger, and Detection

An interactive compact-binary inspiral. The main view is the physical system: two black holes orbit on a Keplerian separation $a = (G M / \omega_{\mathrm{orb}}^2)^{1/3}$ that shrinks as gravitational waves carry away energy, while the leading quadrupole radiation spreads outward as a two-arm spiral that tightens and brightens as the frequency rises, then merges and rings down. The chirp mass $M_c = (m_1 m_2)^{3/5}/(m_1+m_2)^{1/5}$ sets the sweep $df/dt = (96/5) \pi^{8/3}(G M_c/c^3)^{5/3} f^{11/3}$, so $f \sim \tau^{-3/8}$ climbs to merger and the strain amplitude $h = (4/D)(G M_c/c^2)^{5/3}(\pi f/c)^{2/3}$ grows with it (about $10^{-21}$ for a 30+30 solar-mass binary at 400 Mpc, the GW150914 case). Diagnostic strips show the chirp strain $h(t)$, a matched filter that peaks sharply at coalescence and recovers the chirp mass, and a LIGO arm whose 4 km length changes by $h L / 2$, a sub-proton displacement.

Figure 1. Two black holes spiral together on a shrinking orbit and radiate a two-arm gravitational-wave ripple that tightens into the merger and rings down; the chirp strain, a matched filter that recovers the chirp mass, and a LIGO arm changing length by h L / 2 (a sub-proton displacement) are shown as diagnostics. Method: Keplerian inspiral with leading-quadrupole radiation, the chirp-mass frequency sweep, antenna response, and matched filtering; Canvas2D, deterministic.

m1 (Msun)30

m2 (Msun)30

distance (Mpc)400

WHAT TO TRY

Vary each control and watch the rail readouts respond.

Compare the diagnostic plot against the live scene.