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Polski🌊 Gravitational Waves — Binary Inspiral & LIGO Detection
Simulate a binary black hole merger and the gravitational waves it produces. See the chirp waveform h(t), the inspiral trajectory, and how LIGO's interferometer detects the spacetime strain.
Physics & Equations
Gravitational wave frequency during inspiral: f(τ) ∝ (GM_chirp/c³)^(−5/8) · τ^(−3/8), where τ is time to merger. Chirp mass M_c = (m₁m₂)^(3/5)/(m₁+m₂)^(1/5). Strain h(t) ∝ (πf)^(2/3)·cos(2πft). Merger frequency at ISCO: f_ISCO = c³/(6^(3/2)·π·GM_total).
LIGO Detection
LIGO measures the strain h = ΔL/L — the fractional change in arm length caused by passing gravitational waves. For GW150914, h_peak ≈ 10⁻²¹, meaning the 4 km arms changed by ~10⁻¹⁸ m — smaller than a proton. LIGO must distinguish this from seismic noise, thermal fluctuations, and quantum shot noise.
The Chirp Signal
As two black holes spiral inward, they lose energy to gravitational radiation, so they orbit faster and closer. This produces the characteristic "chirp": increasing frequency and amplitude culminating in the merger. The chirp mass can be extracted from the frequency evolution with extremely high precision — LIGO's most sensitive measurement.
About this simulation
This simulator renders the final phase of a binary black-hole inspiral as a real-time WebGL fragment shader. Two point masses m₁ and m₂ orbit a common centre at a separation that shrinks over time (from 0.85 to 0.04 shader units as progress goes 0→1), so orbital angular frequency ω grows roughly as separation−3/2 — a stylised stand-in for the real energy loss to gravitational radiation. The emitted wave's frequency is 2ω, and its quadrupole radiation pattern (a cos 2θ angular dependence) visibly warps a background spacetime grid, colouring stretch blue and squeeze red. Chirp mass Mc = (m₁m₂)3/5/(m₁+m₂)1/5 and the merger frequency fISCO = c³/(63/2πGMtotal) are computed from the real physical constants G, c, and M☉ and displayed live alongside the animation.
What it shows
Two glowing points (the black holes) spiral inward on a warped grid representing spacetime. As they close in, concentric ripples of the gravitational-wave strain expand outward, sweeping up in frequency and amplitude — the "chirp" — until a bright merger flash marks the innermost stable circular orbit (ISCO) and a brief ringdown.
How to use it
Drag the m₁ and m₂ sliders (in solar masses) to change the binary, or click a preset — GW150914, GW170817, Light BH, or Massive — to jump straight to a known configuration. Use Pause/Restart and the speed slider to control playback, and watch the stats panel for live chirp mass, orbital/GW frequency, separation, and inspiral phase.
Did you know?
LIGO's first detection, GW150914 (2015), came from two black holes of about 36 and 29 solar masses merging 1.3 billion light-years away, producing a peak strain of roughly 10⁻²¹ — a distortion thousands of times smaller than a proton across a 4 km detector arm. GW170817, a neutron-star merger, was also seen in light, launching multi-messenger astronomy.
Frequently Asked Questions
What is chirp mass and why is it the key measurable quantity?
Chirp mass Mc = (m₁m₂)3/5/(m₁+m₂)1/5 is the single combination of the two component masses that controls how fast the gravitational-wave frequency sweeps upward during inspiral. Because the frequency evolution can be timed extremely precisely, LIGO can measure Mc to far higher accuracy than it can measure m₁ and m₂ individually — it is the first and most robust number extracted from any detection, and this simulator recomputes it live from your slider values.
Why does the wave's frequency and amplitude both increase as merger approaches (the "chirp")?
As the two masses radiate energy away as gravitational waves, their orbit has no choice but to shrink, and Kepler-like dynamics then force the orbital (and so gravitational-wave) frequency to rise as the separation shrinks. Because tighter, faster orbits also radiate more strongly, the wave amplitude climbs at the same time as its frequency — the combined frequency-and-amplitude sweep is what gives the signal its rising "chirp" sound and appearance, exactly as coded in this simulation's omega ∝ separation−3/2 relation.
What is ISCO and why does the merger happen there?
The innermost stable circular orbit (ISCO) is the smallest orbit around a compact object at which a stable circular path can still exist; closer than that, general relativity leaves no stable orbit at all, and the two bodies plunge together. This simulation ramps a merger flash once the inspiral progress approaches 1 (the ISCO separation) and computes the corresponding real-world frequency as fISCO = c³/(63/2πGMtotal), which for stellar-mass black holes falls in LIGO's most sensitive band, a few hundred Hz.
How does the shader turn the physics into the blue/red rippling grid?
Each pixel's distance and angle from the binary's centre feed a retarded-time phase (accounting for the wave travelling outward) multiplied by a quadrupole angular factor cos 2θ, which is the correct m=2 angular pattern for gravitational radiation from an orbiting mass pair. That combined value is the local strain, used to radially displace ("warp") a background grid and to colour it — blue where the shader's math calls for stretching, red where it calls for squeezing — giving a direct visual analogue of the "+" polarization pattern real interferometers are built to detect.
What's the difference between the GW150914, GW170817, Light BH, and Massive presets?
GW150914 (36+29 solar masses) reproduces LIGO's first-ever detection in 2015; GW170817 (about 1.4+1.4 solar masses) represents a binary neutron-star merger — lighter objects that spiral for far longer and were also seen across the electromagnetic spectrum as a kilonova. Light BH (5+5) and Massive (50+50) let you compare how total mass changes the chirp mass, the merge time (heavier binaries merge faster in this model), and the ISCO frequency, which scales inversely with total mass.
Simulate a binary black hole inspiral: watch the chirp waveform grow in frequency and amplitude as the pair spirals inward, and see how LIGO interferometer detects the passing wave.
3D · Three.js / WebGL renderer · 60 FPS target · runs fully client-side, no install