Gravitational Wave Chirp
Leading-order chirp teaching model: waveform, frequency evolution and shrinking binary orbit up to an ISCO cutoff.
About this tool
Choose masses, luminosity distance and starting frequency, then Calculate. Waveform, frequency and 3D use the same inspiral. Model time selects a state; playback traverses the full model interval in 12 screen seconds. No audio is generated. Physical elapsed time is shown separately in the table. Reset restores the heavy-binary example and waveform view, stops playback and clears results without calculating again.
Circular non-spinning point masses at leading quadrupole order (0PN): M_c=(m₁m₂)³ᐟ⁵/(m₁+m₂)¹ᐟ⁵, f(τ)∝M_c⁻⁵ᐟ⁸τ⁻³ᐟ⁸. Phase is integrated analytically, not accumulated across frames. h₊ is face-on plus polarization with a chosen initial phase; the table gives its positive amplitude, not |h₊(t)|. GW frequency is twice the orbital frequency. Kepler separation uses a fixed spatial scale, with symbolic body sizes. Display sampling can make fast orbits appear to rotate differently.
Masses and times are in the observer frame; luminosity distance does not determine redshift here. Real source masses require the appropriate redshift conversion. f_ISCO=c³/(6³ᐟ²πG(m₁+m₂)) is a conventional Schwarzschild test-particle cutoff, not an exact comparable-mass binary ISCO or merger frequency. 0PN becomes quantitatively unreliable near cutoff. No spin, eccentricity, matter effects, detector response, merger or ringdown; presets are not measured events.
Frequency spans the full model duration. The waveform shows at most the final four seconds, shortened at high cutoff frequency to retain adequate sampling. Times refer to the cutoff, not a simulated merger. Without WebGL, calculations, waveform and time controls remain available.