= Binary-pulsar orbital decay
{title2=$\dot P_b<0$}
Decreasing <orbital period>, distinct from spin slowdown. <Joseph Hooton Taylor Jr.> inferred <masses> using <binary-pulsar periastron advance> and <binary-pulsar Einstein delay>, then tested the independent period derivative against the <general relativity> <quadrupole formula>. Correcting differential Galactic <acceleration> gave indirect <gravitational radiation> evidence. This was not a terrestrial strain measurement.<Binary Pulsars and Relativistic Gravity by Joseph Hooton Taylor Jr.>[1993 lecture, V–VI, pp. 84–87, equations 5–9, Figures 10–11]{ref}
In particular, the raw measured derivative schematically contains
$$
\left(\frac{\dot P_b}{P_b}\right)_{\rm obs}=\left(\frac{\dot P_b}{P_b}\right)_{\rm intrinsic}+\frac{a_\parallel^{\rm relative}}{c}+\hbox{other kinematic contributions}.
$$
Here $a_\parallel^{\rm relative}$ is positive when the source's recession accelerates. Its contribution follows by differentiating the leading <Doppler effect>. A decreasing observed <orbital period> alone therefore does not identify a unique energy-loss mechanism.
For fixed <masses>, <binary orbital energy> is $-Gm_1m_2/(2a)$ and <Kepler's third law> gives $P_b\propto a^{3/2}$. Positive outgoing <gravitational radiation> predicted by the <quadrupole formula> makes the orbital <energy> more negative, reducing $a$ and $P_b$. This sign argument explains shrinking orbits, but a quantitative test also needs the predicted magnitude and <orbital eccentricity> dependence.
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