= Pulsar timing
{title2=$t_n^{\rm arr}=t_n^{\rm model}+r_n$}
The mature experiment uses channel-template comparison, <pulsar dedispersion>, GPS clock-offset transfer, <Solar system> <barycenter> corrections and connected pulse counts.<Binary Pulsars and Relativistic Gravity by Joseph Hooton Taylor Jr.>[1993 lecture, III, pp. 77–81, Figures 3–5, equations 1–2]{ref}
For a geometric illustration, let a perfectly uniform source emit pulse $n$ at $t_n=t_0+nP_s$, with spin <period> $P_s$, and let $z_1$ increase away from the observer. At leading order in orbital <velocity> divided by the <speed of light>, an extra path length $z_1$ adds $\Delta_R=z_1/c$. Consecutive arrivals then obey
$$
P_{\rm app}\simeq P_s\left(1+\frac{d\Delta_R}{dt}\right)=P_s\left(1+\frac{v_\parallel}{c}\right).
$$
A receding source has $v_\parallel>0$ and a longer apparent <period>. This derivation isolates the geometric <Doppler effect>; a precision relativistic clock model also needs <gravitational redshift> and <time dilation>.
\Image[/binary-pulsar-arrival-orbit-geometry.png]
{title=How orbital geometry becomes a pulse arrival-time signal}
{id=binary-pulsar-arrival-orbit-geometry}
{description=Original edge-on geometric illustration and functional timing workflow. Positive z points away from the observer, so a longer path gives positive delay. The chosen eccentricity is 0.6 and argument of periapsis is 40 degrees. The pulse trace is schematic; the boxes summarize functions rather than historical equipment or a mandatory processing order.}
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