A shared barycenter
Each body follows an orbit whose radius is inversely proportional to its mass. The heavier object stays closer to the center.
Leading-order inspiral
Astrophysics / dynamic spacetime
Listen to the universe ring.
Two compact objects orbit a shared center of mass. Their changing quadrupole moment carries energy outward as gravitational waves—stretching one direction while squeezing the other by less than the width of a proton across a detector.
PHYSICS-DRIVEN ORBIT
LIVE STRAIN & CHIRP
TEACHING APPROXIMATION
03 / Detector strain
The chirp writes itself in time.
Frequency and amplitude rise together as orbital energy leaves the system.
EARLIER INSPIRAL
TOWARD MERGER
04 / Read the orbit
Mass in motion changes the geometry.
A binary has no changing mass dipole in its center-of-mass frame. The first radiative term is quadrupolar: a directional change in how mass is distributed.
Twice the orbital rhythm
For a near-circular binary, the dominant gravitational-wave frequency is twice the orbital frequency: fGW = 2forb.
Energy flows outward
Radiation removes orbital energy and angular momentum. The separation shrinks, so the orbit—and the wave—accelerate.
A rising chirp
The characteristic combination 𝓜, the chirp mass, governs how quickly the measured frequency sweeps upward.
CHIRP MASS𝓜 = (m₁m₂)3/5 / (m₁+m₂)1/5
SEPARATION, CIRCULAR ORBITr = [G(m₁+m₂)/(πf)2]1/3
FREQUENCY EVOLUTIONdf/dt = 96π8/3/5 · (G𝓜/c³)5/3f11/3
05 / Read the signal
Space stretches. The instrument compares light.
Laser interferometers compare two perpendicular arms. A passing wave changes their relative optical path lengths, producing a dimensionless strain h = ΔL/L.
LASERPHOTODETECTOR
Plus polarization
Alternately stretches horizontal space while squeezing vertical space, then reverses.
Cross polarization
The same transverse pattern is rotated 45°. General relativity predicts both tensor modes.
Strain, not a force
At h ≈ 10−21, a 4 km arm changes by only about 4 × 10−18 m.
06 / Know the boundary
Inspiral equations stop before spacetime becomes most violent.
The controls use leading-order, quasi-circular post-Newtonian relations. They are excellent for intuition during inspiral, but numerical relativity is needed through merger and black-hole perturbation theory describes ringdown.
Newtonian circular separation, leading quadrupole amplitude and luminosity, leading chirp evolution, inclination-dependent plus/cross modes.
Spin precession, eccentricity, higher harmonics, detector antenna response, cosmological redshifting of source-frame masses, merger, and ringdown.
The moving 3D surface encodes phase and relative amplitude. It is not a literal picture of curved spacetime or a claim that waves travel through a material sheet.
07 / Primary sources
Trace the signal back to the instruments.
OBSERVATIONAL DATAGWOSC · GW150914 event recordOpen source ↗
DATA METHODGWOSC · Signal processing tutorialOpen source ↗
NUMERICAL RELATIVITYLIGO · GW250114 merger simulationOpen source ↗
THEORYBlanchet et al. · Binary inspiral at 2PN orderOpen paper ↗
THEORYPoisson · Gravitational radiation from inspiraling compact binariesOpen paper ↗
Reference preset: GW150914 masses and distance use the GWOSC event record. The interactive waveform is generated from the displayed approximation; it is not downloaded detector strain and should not be used for parameter estimation.
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