Shapiro Time Delay (Fourth Test of GR)
Also known as: Gravitational time delay · Radar echo delay
Light slows down (in coordinate time) as it passes deep in a gravity well — not because its local speed changes, but because spacetime is curved. A radar pulse grazing the Sun on its way to Venus and back returns up to ~240 microseconds late. Irwin Shapiro proposed this as the 'fourth classical test' of general relativity.
A radar pulse travels from Earth past the Sun to a target and back; a curved-space clock shows the round-trip echo arriving late, with the delay growing as the impact parameter slider brings the path closer to the limb.
Equivalent forms
Curved spacetime stretches the very path of light, so even a round-trip radar echo carries the fingerprint of gravity.
Shapiro predicted in 1964 that radar signals passing near the Sun would be delayed by curved spacetime. MIT's Haystack and Arecibo radars bounced pulses off Mercury and Venus (1966-1971), measuring the ~200 microsecond delay. The Cassini spacecraft (2002) refined the prediction to 1 part in 100,000 — among GR's most precise confirmations.
- Solar-system radar/ranging tests of GR; the strongest single-parameter PPN constraint comes from Cassini.
- Pulsar-timing: the Shapiro delay of pulses grazing a binary companion measures neutron-star masses precisely.
- Must be modeled in deep-space navigation and very-long-baseline interferometry.
- 'Light physically slows below c.' — Locally light always travels at c; the delay is in global coordinate time from curved geometry.
- 'It's the same as light bending.' — Related but distinct: deflection is spatial, the Shapiro delay is temporal.
- 'The delay grows linearly near the Sun.' — It grows only logarithmically with impact parameter.
- In the Schwarzschild metric the coordinate speed of light dr/dt is reduced near mass M.
- Integrate the null condition along the nearly straight path with closest approach b.
- The extra (Shapiro) travel time over the flat-space value is .
- The logarithm grows slowly, so the effect is largest for rays grazing the limb (small b).
- For a round trip past the , microseconds.
Limiting cases
What if…
The logarithm grows and the delay peaks at the limb — the best place to measure the effect.
No curvature, no extra delay: light takes the flat-space travel time.
Round-trip past the Sun
- per unit ln.
- Multiply by the logarithm for Earth-Venus geometry, round trip doubles it).
- .