X-Ray Pulsar Timing: Barycentric Delay Correction

Millisecond Pulsar

Spacecraft Trajectory

Orbital angle 40°

Distance from Sun 1.20 AU

Position-knowledge error 0 km

Live Readouts

Roemer delay

0 s

Shapiro delay

0 μs

Timing jitter σ

0 μs

Photons folded

Uncorrected (detector clock)

Barycentric-corrected

How it works

A millisecond pulsar's rotation is stable to a few parts in 10¹⁵ — an X-ray detector that folds enough incoming photons modulo the known period P reveals a sharp pulse. But that only works if every photon's arrival time is first converted from the spacecraft's own clock to time at the Solar System Barycenter (SSB), because the craft's changing distance from the SSB shifts the light-travel time by far more than P.

Roemer delay:   Δt_R = (r⃗_sc · n̂) / c
Shapiro delay:  Δt_S = -(2GM☉/c³) ln(1 - cosθ)
Folded phase:   φ = [(t_detector + Δt_R + Δt_S) / P] mod 1

Here r⃗_sc is the spacecraft's position vector, n̂ is the unit vector toward the pulsar, θ is the angle between the Sun and the pulsar as seen from the craft, and 2GM☉/c³ ≈ 9.85 μs is the solar Shapiro constant. Roemer delay alone can reach ~25 minutes at 3 AU — thousands of pulse periods — so an uncorrected fold is pure noise (left profile). Shapiro delay is tiny except when the line of sight grazes the Sun.

Orbital angle / Distance — move the craft; the true Roemer delay updates live and the geometry redraws.
Position-knowledge error — the onboard navigation solution used to compute the correction is never perfect. This slider adds a random residual (σ = error/c) to every barycentric correction, smearing the right-hand profile — exactly the effect that limits real X-ray pulsar navigation (XNAV) precision.
Pulsar choice — swaps in the real sky position and spin period of three navigation-relevant millisecond pulsars.

This is the barycentering step every XNAV and ground-based pulsar-timing pipeline performs before any position fix or clock comparison is possible — get the position wrong and the "lighthouse" blurs into background noise.

Sun Spacecraft X-ray photons

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