Shapiro Time Delay (4th GR Test)

This interactive simulator explores Shapiro Time Delay (4th GR Test) in Gravity & Orbits. A radio signal grazing the Sun picks up an excess one-way travel time Δt ≈ (2GM/c³) ln[(r_E + r_E cos α)(r_R + r_R cos β)/b²] on top of the Newtonian light-time. Cassini, Mariner and Viking presets, with the round-trip delay readout in microseconds and an animated bent-photon path against a straight Newtonian baseline. The Cassini 2003 conjunction constrains |γ_PPN − 1| < 2 × 10⁻⁵ — the strongest weak-field GR test to date. Use the controls to change the scenario; watch the visualization and any graphs or readouts to connect the model with lectures, labs, and homework.

Who it's for: For learners comfortable with heavier math or second-level detail. Typical context: Gravity & Orbits.

Key terms

shapiro
time
delay
4th
test
shapiro time delay
gravity
orbits

Geometry

Preset

Lens mass M (M⊙)1 M⊙

Emitter distance r_E (AU)1 AU

Receiver distance r_R (AU)9.539 AU

Impact parameter b (R_⊙)1.6 R_⊙

Photon position0.5

Shapiro time delay is one of the four classical tests of general relativity: a radio signal that grazes a massive body picks up an extra travel time Δt ≈ (2GM/c³) ln[(r_E + r_E cos α)(r_R + r_R cos β)/b²], on top of the Newtonian light-time. For Cassini's 2003 superior conjunction (b ≈ 1.6 R_⊙) the round-trip excess is hundreds of microseconds and constrains the post-Newtonian γ-parameter to |γ − 1| < 2 × 10⁻⁵, the strongest weak-field GR constraint to date. Slide presets to compare Mariner, Viking, Cassini and a binary-pulsar geometry.

Measured values

Δt one-way132.429 μs

Δt round-trip264.858 μs

b1.113e+6 km

Naive path5259.01 s

How it works

Shapiro time delay simulator (4th classical GR test). A photon grazing the Sun acquires an excess one-way travel time Δt ≈ (2GM/c³) ln[(r_E + r_E cos α)(r_R + r_R cos β)/b²]. Built-in Cassini, Mariner and Viking presets; round-trip delay readout in microseconds, plus an animated bent photon path versus straight Newtonian baseline.